Investigating the Hispanic/Latino male dropout phenomenon

Investigating the Hispanic/Latino male dropout phenomenon

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Investigating the Hispanic/Latino male dropout phenomenon using logistic regression and survival analysis
Vizcain, Dorian Charles
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[Tampa, Fla]
University of South Florida
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Grade retention
School leavers
Dissertations, Academic -- Measurement and Evaluation -- Doctoral -- USF
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ABSTRACT: This dissertation explored the factors associated with dropping out of middle school and high school among Hispanic/Latino male students. Predictor variables investigated were: age, home language, retention history, SES, program of studies, suspensions, and GPA. Data were from a large urban school district in the state of Florida. A sample of 865 Hispanic/Latino male Latino students in the 8th grade in 1995-96 was followed longitudinally every year to the year 2000-01. Survival analysis and logistic regression were used to examine the data. The research questions were: 1) What is the relation between age, home language, retention history, SES, program of studies, suspensions, and GPA and dropping out of middle and secondary school by Hispanic/Latino males? 2) At what grade levels do the predictor variables begin to affect the male Hispanic/ Latino students' propensity for early school leaving? When are they at greatest risk? Of the predictor variables included in this research, age, retention history, program of studies, suspension, and GPA, were found to be statistically significant in the students' decision to drop out of school. This research also found that approximately 31% of this Hispanic/Latino male sample dropped out prior to completing their high school education during the 5-year span. Investigating the most hazardous time for dropping out of school, results suggested that for these students it is well into their secondary education, very close to when they would actually graduate, during their junior to senior years. It may be the time close to their eighteenth birthday that lets them legally choose to leave school that triggers this hazardous time period.
Dissertation (Ph.D.)--University of South Florida, 2005.
Includes bibliographical references.
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by Dorian Charles Vizcain.

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Investigating the Hispanic/Latino male dropout phenomenon :
b using logistic regression and survival analysis
h [electronic resource] /
by Dorian Charles Vizcain.
[Tampa, Fla] :
University of South Florida,
3 520
ABSTRACT: This dissertation explored the factors associated with dropping out of middle school and high school among Hispanic/Latino male students. Predictor variables investigated were: age, home language, retention history, SES, program of studies, suspensions, and GPA. Data were from a large urban school district in the state of Florida. A sample of 865 Hispanic/Latino male Latino students in the 8th grade in 1995-96 was followed longitudinally every year to the year 2000-01. Survival analysis and logistic regression were used to examine the data. The research questions were: 1) What is the relation between age, home language, retention history, SES, program of studies, suspensions, and GPA and dropping out of middle and secondary school by Hispanic/Latino males? 2) At what grade levels do the predictor variables begin to affect the male Hispanic/ Latino students' propensity for early school leaving? When are they at greatest risk? Of the predictor variables included in this research, age, retention history, program of studies, suspension, and GPA, were found to be statistically significant in the students' decision to drop out of school. This research also found that approximately 31% of this Hispanic/Latino male sample dropped out prior to completing their high school education during the 5-year span. Investigating the most hazardous time for dropping out of school, results suggested that for these students it is well into their secondary education, very close to when they would actually graduate, during their junior to senior years. It may be the time close to their eighteenth birthday that lets them legally choose to leave school that triggers this hazardous time period.
Dissertation (Ph.D.)--University of South Florida, 2005.
Includes bibliographical references.
Text (Electronic dissertation) in PDF format.
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
Title from PDF of title page.
Document formatted into pages; contains 119 pages.
Includes vita.
Adviser: John M. Ferron, Ph.D.
Grade retention.
School leavers.
Dissertations, Academic
x Measurement and Evaluation
t USF Electronic Theses and Dissertations.
4 856


Investigating the Hispanic/La tino Male Dropout Phenomenon: Using Logistic Regression and Survival Analysis by Dorian Charles Vizcain A dissertation submitted in partial fulfillment Of the requirementss for the degree of Doctor of Philosophy Department of Educational Measurement and Research College of Education University of South Florida Major Professor: John M. Ferron, Ph.D. Co Major Professor: Bruce W. Hall, Ed.D. Robert F. Dedrick, Ph.D. Carlos P. Zalaquett, Ph.D. Date of Approval: October 18, 2005 Keywords: education, race/ethnicity, gende r, grade retention, school leavers Copyright 2005, Dorian C. Vizcain


Dedication A Mi Madre Maria Ester y Mi Padre Jose Maria


Acknowledgements I would not have been able to complete th is extensive research if it had not been for the support of the members of the De partment of Educational Measurement and Research at the College of Education, Univ ersity of South Florida. Also greatly appreciated is the director a nd personnel of the large urban school district for granting access and collecting the requested data for this research. A special “gracias” goes to my committ ee, without whom the many obstacles encountered would have been insurmountable. To Dr. Bruce Hall, Dr. John Ferron, Dr. Robert Dedrick, and Dr. Ca rlos Zalaquett, “it has truly been an honor to work with you.” For their guidance, expe rtise in discussing, review ing, and editing the numerous drafts of my research, I will al ways be indebted to them. My very special thanks to Dr. Lou Ca rey, she was for me the sign post at the crossroads. A journey in pursuit of knowledge has been a dream come true. I will always have a warm place in my heart for the unexpect ed opportunity she made available to me. I must also acknowledge Dr. Bruce Hall who always had words of wisdom and guided me so as to have the winds at my back. My sincere thanks to Dr. Jeffrey Kromrey for the many informal chats that kept me focused on my goals and fueled my desire to be part of the academic research community. For expe riences with the enlightening world of education and the extraordinary people I’ve met and continue to meet, I have unending gratitude to them.


It is with enormous appr eciation that I acknowledge my fellow graduate students for their personal and professional support a nd encouragement. Tary, Jim, Kathy, Ron, Wendy, Cindy, Michela, Rich, Kr is, Patrick, John, Melinda, and Thomas, thank you for being so much fun to study with and sharing in intellectual queries that always included laughter. I am also very, very grateful to Lisa Adkins for her friendship, support, and always being there with words of encour agement, she truly is indispensable. My mother Maria, and my father Jose were instrumental in keeping me grounded. My parents never wavered as I co mmunicated those “bumps in the road” frequently encountered along the doctoral hi ghway. To my loving sister Mirta and her wonderful husband Mario, thank you for unde rstanding. You always had encouraging words, and with a wink Mirta would say “I know you can do it.” I would also love to share this accomplishment and acknowledge my youngest sister Annie, my brother Joey, nephews, Mario and David, and my niece Vanessa. Thanks for accepting the many changes in family plans and increasing in frequency the infamous “so when are you going to finish.” I am extremely fortunate to have had such wonderful people to work with and share my doctoral experience. Thank you all for your assistance and friendship. My encore acknowledgement is to my mother whose singing and laughter would transport me to places only a mother’s voice could take you.


v Table of Contents List of Tables iii List of Figures v Abstract vi Chapter One – Introduction 1 Statement of the Problem 3 Purpose of the Study 7 Research Questions 9 Method of Inquiry 9 Definitions of Terms 13 Importance of Study 16 Organization of the Study 17 Chapter Two – Literature Review 18 Background Information 19 National Level Studies 22 State Level Studies 30 Local Level Studies 37 Gender Differences 42 Survival Analysis: An Introduction 45 Studies in Education Using Survival Analysis 46 Summary 49 Chapter Three – Method 51 Participants 52 Procedures 53 Dependent Variable 54 Independent Variable 57 Analyses 61 Summary 66 Chapter Four – Results 67 Descriptive Statistics of Hispanic /Latino Male Student Sample 67 Logistic Regression Analysis 72 Logistic Regression Analysis Results 73 Survival Analysis 79 Univariate Categorical Predictor Analysis, Testing for Differences 84


vi Proportional Hazards Model Testing 89 Main Effects Analysis 89 Proportionality Assumption 91 Summary and Conclusion 94 Chapter Five – Discussion 96 General Findings 96 Statistical Methods Comparison 99 Conclusions 100 Limitations of the Study 100 Future Research 102 Recommendations 104 References 107 Appendices 113 Appendix A: Withdrawal Code s Available and Frequencies 114 Appendix B: ESE Codes Ava ilable and Frequencies 115 About the Author End Page


vii List of Tables Table 1 Correlation Coefficients of Achiev ement Predictor Variables 60 Table 2 Percentages of Hispanic/L atino Male Student Dropouts and National Status Dropouts 68 Table 3 Descriptive Statistics on Hispanic/Latino Male Student Status/Days Dependent Variable 69 Table 4 Descriptive Statistics on Hispanic/Latino Male Student Language and Retention Variable 70 Table 5 Descriptive Statistics on Hispanic/Latino Male Student F/R Lunch and Program Variable 70 Table 6 Descriptive Statistics of Hispanic/Latino Male Student Age Variable 71 Table 7 Descriptive Statistics on Hispanic/Latino Male Student Behavior Variable 71 Table 8 Descriptive Statistics on Hispanic/Latino Male Student Achievement Variable 72 Table 9 Logistic Analysis of Maximum Likelihood Estimates of Dropping Out 74 Table 10 Logistic Analysis of Maximum Likelihood Estimates with Interaction Predictors 76 Table 11 Estimates of Survival Func tion using the Lifetest Procedure and Kaplan-Meier Method 83 Table 12 Analysis of the Mode lÂ’s Main Effects using the Cox Proportional Hazards Model 90 Table 13 Proportionality Assumptions Testing using the Cox Proportional Hazards Model 92


viii Table 14 Non-Proportionality Te sting by Stratifying on the Retention Predictor 93 Table 15 Comparative of Logistic Analysis and Survival Analysis 100


ix List of Figures Figure 1 Probability of Dropping Out as a Function of Age 76 Figure 2 Odds of Dropping Out as a Function of Age 78 Figure 3 Estimates/Plot of survival Functi on using the K-M Method 83 Figure 4 Language Differences in the Surviv al Function 84 Figure 5 Retention Differences in the Survival Function 85 Figure 6 SES Differences for the Survival Function 86 Figure 7 Program of Study Differences for th e Survival Function 87 Figure 8 Cumulative Hazard Function for Retention 93


x Investigating the Hispanic/La tino Male Dropout Phenomenon: Using Logistic Refression and Survival Analysis Dorian C. Vizcain ABSTRACT This dissertation explored the factors associated with dropping out of middle school and high school among Hispanic/Lati no male students. Predictor variables investigated were: age, home language, re tention history, SES, program of studies, suspensions, and GPA. Data were from a larg e urban school district in the state of Florida. A sample of 865 Hispanic/L atino male Latino students in the 8th grade in 199596 was followed longitudinally every year to the year 2000-01. Surv ival analysis and logistic regression were used to examine the data. The research questions were: 1) What is the relation between age, home language, retention history, SES, program of studies suspensions, and GPA and dropping out of middle and secondary school by Hispanic/Latino males? 2) At what grade levels do the predictor variables begin to affect the male Hispanic/ La tino studentsÂ’ propensity for early school leaving? When ar e they at greatest risk? Of the predictor variables included in this research, age, retention history, program of studies, suspension, and GPA, were found to be statistically significant in the studentsÂ’ decision to drop out of school. This research also found that approximately


xi 31% of this Hispanic/Lati no male sample dropped out prior to completing their high school education during the 5-year span. I nvestigating the most hazardous time for dropping out of school, results s uggested that for these stude nts it is well into their secondary education, very close to when they would actually graduate during their junior to senior years. It may be the time close to their eighteenth birthday th at lets them legally choose to leave school that trigge rs this hazardous time period.


1 Chapter One Introduction Concern about the alarmingl y high percentage of Hisp anic/Latino students who drop out of high school began to crystallize in the late 1980s. Although the overall graduation rates from high school for all stude nts have increased while dropout rates have decreased (United States Department of E ducation, 2001), the rate for Hispanic/Latino students dropping out of school has remained the same or increased. Indeed, for this ethnic group the problem is getting close to epidemic proportions. An abundance of research information ex ists regarding education and school dropout in general, some of which specifi cally address the Hisp anic/Latino population (Battin-Pearson, Abbott, Hill, Catalano, Ha wkins, & Newcomb, 2000). The majority of dropout research attempts to identify the personal and soci al characteristics of the individuals that predict the o ccasion to drop out. This in turn may be used for identifying those at risk and possible intervention pr ograms. Among the factors that have been investigated in relation to dropping out are: academic achievement (Rumberger & Thomas, 2000); single-parent households (Pong & Dong-Beom, 2000); school transitions (Reyes, Gillock, Kobus, & Sanchez, 2000); recen cy of immigration (Driscoll, 1999); and school and community characteristics (Alspaugh, 1998). An article, written in the United States military newspaper known as the Stars and Stripes and published in 1989 said it very clearly. The article entitled, Hispanic dropout


2 rate skyrockets to 35.7% reported ; The high school dropout rate among the nearly 4 million Hispanic students in the United States ro se to 35.7 percent last year, almost triple that of white students and mo re than double that of blacks, according to a report by the Department of Education (New York Times, p.12). These findings marked the first time the government had conducted a detailed study of high school dr opout statistics and compiled and analyzed the data by race, age, sex, and location. The report, mandated by Congress in 1988, continues to be publishe d yearly and as of 2002, the high school dropout rate among young Hispanic/Latinos has now climbed to 38.6% (NCES, 2002, p.13). Kronick and Hargis (1998) suggested that one possible approach to investigating the problem of dropouts is to look at the char acteristics that diffe rentiate dropouts from graduates. Several of the characteristics th ey deemed critical in examining dropouts were: 1. Academic Ability – Dropouts have been found to have lower IQs than graduates, to be behind in readin g and math, and to be lacking in general academic skills. 2. Age – Dropouts tend to be held back in th eir schooling and to be one or two years older than their peers. 3. Socioeconomic Status – Dropouts tend to be of lower socioeconomic status than graduates. 4. Race – Dropouts tend to come from non-white, rather than white, racial backgrounds. 5. Gender – Males tend to dropout more often than females and for different but possibly related reasons Males often report dropping out for financial


3 reasons, either to help out at home or to support a family, while females report dropping out to start a home or because of pregnancy. 6. Family Background – It is reported that dropouts tend to come from families in which parents are not graduates of high sc hool. It is also reported that homes where mothers create an environment wh ere studying can be done have fewer dropouts than homes where this environmen t is not created (Kronick & Hargis, 1998). With these characteristics that differen tiate students who dr opout of school as compared to those who graduate as bac kground, the present study narrows the focus of the dropout phenomenon to Hispanic/Latino males exclusively. This specificity is designed to help in identifying the factor s contributing to the high dropout rates among this group of students. Statement of the Problem Data from the Census Bureau indicate that there were 29.2 million Hispanics in the United States, as of June 1, 1997. Between 1990 and 1997, the population growth was 6.6 million for Hispanics, 6.0 million for Wh ites, 2.8 million for Blacks, and 2.4 million for Asians. Between these same years, th e Hispanic population increased 29%, second only to the Asian/Pacific Isla nder population category increa se of 34%. In contrast, the rate of growth for Whites was 3% and fo r Blacks, 9.5%. Hispanic/ Latinos have now become the largest minority group in th e United States (Census Bureau, 2000). Another way to emphasize the critical nature of this problem is to report the ratio of Latino dropouts to the non-Latino dropout population. Latino stude nts make up 38.6%


4 of all dropouts although they represent 15.1% of the population overall. Despite changing immigration patterns and the influx of Latinos to the United States, the percentage has remained consistently higher than any other racial group for the enti re 29 years of data collection (NCES, 2000). This large percen tage of young people faces the prospect of social and economic disadvantages. Losing su ch high numbers of students produces an uneducated workforce that costs the nation bill ions of dollars in we lfare, unemployment, and lost output (Koshal, Koshal, & Marino, 1995). Yet another perspective is the high school completion rate. This is the proportion of 18 to 24 year-olds who have a high school diploma or an equivalent credential (e.g., General Education Development credential). NCES (2003) repo rted that Hispanic/Latino young adults are less likely than Whites and Blac ks to complete high school programs. In 2000, 64% of Hispanic/Latino 18 to 24 yea r-olds had completed secondary schooling, compared to 92% of Whites and 84% of Bl acks. Females were more likely to have completed high school reaching 88% compared to about 85% of male students (NCES, 2003, p. 42). A report by the De partment of Education entitled “ The Hispanic Dropout Project: No More Excuses ” (U. S. Department of Educati on, 1998), revealed that although the school dropout rates of severa l minorities have fallen over time, the rates for Hispanic students have remained high and in some ar eas of the country have actually increased (p. 5). Poverty, lack of English skills, lack of parents with knowle dge of the education system, and recent immigrant status are some of the factors that may have contributed to the results. One of the author s of the report stated that “R egardless of your position in society, if you are a Hispanic student, you are more likely to drop out of school and not


5 earn a diploma than if you are a non-Hispani c American in a similar position” (U.S Department of Education, 1998, p.6). Current population survey data (Census Bureau, 2002) of 14 to 24 year old high school students indicate a total of 27.367 m illion students. Of these, 3.375 million were dropouts (12.3%). Hispanic/Latino students numbered 4.918 million, in total, 2.707 million female (44%) and 2.211 million (55%) male. The dropouts numbered 1.479 million which translated to 30.1% of the Hi spanic/Latino population, a disproportionate 43.8% of the total number of dropouts. A closer look at the Hispanic/Latino dropouts reveals 565,000 were female (38.2%) and 914,000 were male (61.8%). Not only is there a problem in the number of Hispanic/Latino students not completing high school, but the number of male Hispanic/Latino students failin g to get a high school education is also of great concern. Definitions of Hispanic/Latino students differ across research studies as they focus on one or the other of the terms. Th e operational definition for the present study includes students who through self, parent or guardian reporting were classified as Hispanic/Latino on their school enrollment forms. These include any of the countries in which Spanish or Portuguese is the native language. The need for research of the Hisp anic/Latino dropout rate cannot be overemphasized. There are several critical implica tions to U.S. society as a result of this rapidly growing problem. Among them are: 1. Approximately one third of all Hispan ic/Latino students l eave school without graduating with a high sc hool diploma (U.S. Census Bureau, 2000). 2. Hispanics/Latinos have recently beco me the largest minority group in the


6 United States and by the year 2010 will comprise one of five Americans (U.S. Census Bureau, 2000; OERA, 1993). 3. A large subgroup of the labor force not having a high school e ducation could be a “disaster for the Un ited States” (Hispanic Dropouts, 1995). These data translate into a larger percentage of Hi spanic/Latino youth facing the prospect of social and econo mic disadvantages. The number of Hispanic/Latino dropouts starting in the middle school grades on thr ough to high school is not shrinking and the attrition rate increases until the end of secondary education. Failure in high school not only affects the individual, but also affects society. Dropping out of high school translates into a lost chance of a college education, lo wer paying jobs, political apathy, loss of tax revenue, health problems and strain on soci al services. Limited e ducation results in a person being more likely to suffer from poverty, engage in criminal activity and destructive behavior (McKi ssack, 1998; Rosenfeld, Richman and Bowen, 1998; Freeman, 1996; Jarjoura, 1996). Hispanic/La tinos are seen as a coming force in U.S. cultural and political life, but their low school completi on rates only enhance the thinking that they are missing out on opportunities for economic advancement. What is it that is causing so many yo ung Hispanic/Latino students to leave school? The High School and Beyond study, wh ich tracked a 1980 cohort of 30,000 high school sophomores over six years, found that socio-economic cla ss was the strongest predictor of who drops out (B arro, 1984; Fernandez, Paulsen, & Hirano-Nakanishi, 1989; Rumberger, 1995). Fernandez et al. (1989) made several observations from their research on Hispanic youth: 1) Hispanic youth are much more likely to drop out of school than non-Hispanic youth, 2) available evidence sugge sts that intra-Hispanic differential in


7 youth dropout rates is at l east as large as the Hispanic versus the non-Hispanic differential, and 3) although estimates of the Hispanic high school dropout rate vary widely across studies from a low 20% to a high of 40%, even the more conservative estimates tend to be substantially greater th an the dropout rates for non-Hispanic Whites. The authors conclude that educational atta inment is positively related to career achievement. From a status attainment perspective, high dropout rates among Hispanic/Latino students only serve as a barrier to the oppor tunities a higher education make possible. Some school districts are taking up reform s that don’t appear to be supported by empirical evidence. For example, despite resear ch that suggests that retention of students at the same grade level for consecutive year s "confers no lasting be nefit" to students, retention has become a very popular pract ice (Natriello, 1998, p. 15). Results from National Center of Education Statistics (N CES, 2000) do not back up the assertion that retention helps prevent st udents from dropping out. Purpose of the Study The purpose of this research is to exam ine the variables associated with dropping out of high school among Hispanic/Latino male students. Hispanics/Latinos are a diverse group of individuals comprised of different cultures and races. Mexicans make up the largest subgroup in the United States and as of 2000 were approximately (66%) of the Hispanic/Latino population. Ce ntral and South Americans made up about 15%, Puerto Ricons 9%, Cubans 4%, and a bout 6% from other countries (designated as “Other”) (NCES, 2003).


8 This investigation will attempt to identif y variables that are associated with Hispanic/Latino male students leaving school without obtaining a degree. In addition to examining such predictors, the aspect of time will be investigated to identify “critical moments” or high risk time periods in st udents’ educational lives, specifically as experienced by Hispanic/Latino male students. In discussing limits of theory and practice in student attrition, Tinto (1982) elaborated on several shortcomings of his own model of student disengagement from education. Although he was interested primar ily in higher educati on, his observations may be used in relation to all levels of educa tion. Of interest to this present research is Tinto’s observation that his m odel, “...fails to highlight the important differences in education careers that mark the experiences of students of different gender, race, and social status backgrounds”(p. 689) What is being advocated he re is the development of group-specific models of student disengagement. In addition to group-specific investigati ons on dropouts, Tinto also identified the need to take into account the longitu dinal character of dropout. He states: Although this appears to be self-evident in most studies, we have yet to ask to what degree different types of dropout beha vior vary over time. Past studies of dropout, with very few exceptions, have taken a quite limited time perspective. Most often they consider only two points in time: the point of entry, and some later time when dropout or pers istence is determined (p. 693). It is these two specific observations by Ti nto that are at the core of this present study. Group specificity is the Hi spanic/Latino male and this analysis is longitudinal in nature by looking at the educati onal careers of this sub-group for five years.


9 This study uses data from a large school district in west central Florida to investigate the Hispanic/Latino male student and the drop out phenomenon. Research Questions This study addressed the following questions: 1. What is the relation between age, home language, retention history, free/reduced lunch, program of studi es, behavior (disciplinary suspensions), reading achievement, mathematic s achievement, and GPA and dropping out of secondary school by Hispanic/Latino males? 2. At what grade levels do the predicto r variables begin to affect the male Hispanic/Latino studentsÂ’ propensity for early school leaving? When are they at greatest risk? In answering these questions, the resear cher hopes to address the gaps in understanding how dropout behavior develops. The focus is on a west central Florida school district population because of: (a) the hi gh number of Hispanic/Latinos included, (b) district is also one of th e largest school systems in the country and is similar to many other districts, and (c) there is a lack of empirical analysis of this phenomenon at the local level. Method of Inquiry Survival analysis will be one of the st atistical methods used in this study. The timing of events is at the center of this st atistical method, which has mostly been applied in biological and medical research where the event of interest is time to death. In such research, biostatisticians deve lop hazard models, hence the name survival analysis. It is also known by other names depending on the field of interest. Economists conduct


10 discrete time series analysis, engineers use failure time anal ysis, and sociologists call it event history analysis (Ronco, 1994) As Hougaard (2000) explains: Survival data concern times to some event. An event is typically defined as a transition from one of a few states to another state. The main emphasis is the timing of this event. It is a st andard requirement that at any one time, we observe whether the event has happene d at that specific time point. This should be satisfied for all times, until a time of end of observation (censoring)(p.33). Specifically, this study is exploring how surviv al analysis can assi st in estimating the probabilities of dropping out of school for Hi spanic/Latino male students. Willett and Singer (1991) have advocated the use of su rvival analysis for studying student dropout and teacher attrition. They have also advocat ed the use of survival analysis for major studies (Willett & Singer, 1994), in particular for use with NCES data. An important aspect of this analysis is th at variables in longitu dinal data can be examined with regard to change over time. The first step in survival analysis is to ascertain the survivor function or plot of the probability that a person, in this case a Hispanic/Latino male student, will stay in the group over time, in this case stay in school. Si nger and Willett (1991) write that the shape of the function is always about the same, at the beginning ev eryone is in the group so the survival probability is 1.0. With increased time, some individuals drop out of school and the survival rate declines toward 0.0, alt hough it never actually reaches 0.0 (this would indicate all students had dropped out). Theref ore, a plot of the function resembles an accelerating, negative curve (Denson & Schumacker, 1996).


11 The key to survival analysis is the cal culation of the hazard rate, which is “an unobserved variable, yet it controls both the oc currence and timing of events and it is the fundamental dependent variable in an even t history model” (Allison, 1984, p. 16). More clearly stated, the hazard rate would be th e probability of dropout. This is obtained by dividing the number of student s who drop out in a year by th e number enrolled in that year. For example, if 48 Latino students droppe d out of the tenth gr ade in a given year and there are 233 students enrolled in the 10th grade that year, the hazard rate is 0.20 which tells us that the students who stay in school each subsequent year are 20 percent likely to dropout (Blossfeld, Hamerle, & Mayer, 1989). Another key component in survival analysis is the risk set or the group of students who are at risk of dropping out over a set period of time. This study will examine the risk of dropping out for the group of students who enrolled in the 8th grade. Naturally, the risk set group decreases over time as some student s will dropout. The risk group is at its smallest when the most people have dropped out or at the last year of the study as the opportunities for dropping out have been maximi zed. It is here that the hazard function will have spikes if plotted, since a small change has a larger effect when the risk set is smaller. Censoring is also an important part of su rvival analysis. In survival analysis, a variable T (time), is typically the time of the occu rrence of an event of interest, in this study the event of intere st is dropping out. Censoring occu rs when observations are lost during the time frame of the study, a five year longitudinal study in this case, or reach the end of the study and the event has not occurr ed; these observations are considered rightcensored. Students who experienced the even t and dropped out would be the uncensored


12 observations. In describing calculations with right censored observations, a standard practice is to use an indicator variable S (status), being 1 if th e observation is an event and 0 when it is a censoring. For listing censore d data, the symbol + is typically used, so that t + denotes a censoring at time t In survival analysis right censoring does not influence model estimation as both uncensored and censored events can be incorporated (Ronco, 1995). There are several aims in us ing survival analysis as the inquiry method in this study. One of the major aims will be evaluati ng the effects of several covariates, in general. A second aim of the analysis will be prediction, in other words, determining the probability of dropping out for a single gr oup or individual, based on information collected before (this can be an overall probabi lity or based on some covariates). Lastly, in approaching dropping-out as a problem that is multi-faceted, combin ations of variables will be analyzed rather than analyzing them one at a time. Several models will be tested in considering which is “best” in identif ying variables for inclusion in the model (Hougaard, 2000). Research in education settings has often b een criticized for failing to consider the timing of events (Willett & Singer, 1988). W ith studies of dropout, the timing of the event is crucial. Other criticisms of exis ting methodologies that can be overcome with survival analysis are exclusion of subgroups, failing to consider censoring and combining incomparable groups of people (Denson & Schumacker, 1996; Willett & Singer, 1991).


13 Definition of Terms The following terms are the ope rational definitions for use throughout this study: Attrition Loss of students between the school years of eighth and twelfth grade without attainment of a diploma. Retention Students who repeat a grade due to unsatisfactory performance in the school year in which they are enrolled. Common Core of Data (CCD). The CCD is a program of the U.S. Department of EducationÂ’s National Center for Education Statistics that provides a comprehensive, annual, national statistical database of info rmation concerning all public elementary and secondary schools (approximately 95,000) and school districts (approximately 17,000). CCD is made up of a set of 5 surveys sent to state education departments. State education agencies compile CCD requested data in to prescribed formats and transmit the information to NCES (NCES, 2001). Censored. An event is censored if the researcher knows neither when the event will occur nor even whether it will happen. All that is known is that at the end of data collection, the event has not yet occurred. Observ ations do not experience the target event before data collection ends (Allison, 1995). Right Censoring An observation on variable T (the survival time of interest) is right censored if all you know about T is that it is greater than some value c (a censoring time which is independent of T) (Allison, 1995). Random censoring When observations are terminat ed for reasons that are not under the control of the i nvestigator (Allison, 1995).


14 Cumulative Distribution Function (cdf). One way of describing probability distributions; works for all random va riables. The cdf of a variable T denoted by F ( t ), is a function that tells us the probability th at the variable will be less than or equal to any value t that we choose. Thus, F ( t ) = Pr { T t }. Probability Density Function (pdf). Works with continuous variables, another way of describing their probability distributions. This function is defined as f ( t ) = 0() limtdFt dt = () dSt dt The pdf is just the derivative or slope of the cdf. Hazard Function. Works with continuous variable s and is another way of describing their probability distributions. The hazard function is defined as h ( t ) = 0limt Pr{tTttTt t Â…| The aim of the definition is to quantify the instantaneous risk that an event will occur at time t The proportion of the risk set who experiences the event in that period; are probab ilities over time (Allison, 1995). Discrete-Time Analysis. The value of the hazard function at time t is a probability. It is the probability that a random ly-selected member of the population will dropout in the interval between t and t+ 1, given the member has survived until the beginning of the same interval. Defined as: h(t) = Prob [ dropout be tween t and t+1 | survival until t. (hazard is defined differen tly in discrete and continuous time) (Allison, 1995). Dropout. All individuals who: (a) were enrolled at any ti me during the previous year; (b) were not enrolled at the beginning of the current year; (c) have not graduated from high school or completed a stateor district-approved educa tion program; and (d) do not meet any of the following exclusionary conditions: transferre d to another public


15 school district, private school or stateor district-a pproved education program; temporary absence due to suspension or school-approved education program; or death (NCES, 2001). Event Dropout Rate (National). Describes the proporti on of youths 15 through 24 years who dropped out of grades 10-12 in the 12 months preceding October of the reporting year (NCES, 2001). Status Dropout Rate (National). Represents the proporti on of youths ages 16 through 24 years who are out of school and w ho have not earned a high school credential (NCES, 2001). Hispanic/Latino. Students who through self, pare nt or guardian reporting were classified as Hispanic/Lati no on their school enrollment form s. These may include any of the following: Mexicans, Puerto Ricans, C ubans, Dominicans, Spaniards, Portuguese, and people from any of the Central American countries and any of the South American Countries whose native language is Spanish or Portuguese. Individualized Education Programs (IEP). The number of students with IEPs under the Individuals with Disabili ties Education Ac t (IDEA)-Part B. Race/Ethnicity. Categories used in the Common Co re of Data (CCD) at the time these data were collected, as approved by the federal Office of Management and Budget. They are mutually exclusive. Survival Analysis. A class of statistical methods for studying the occurrence and timing of events (Allison, 1995). Survivor Function. The proportion of an initial p opulation that survives through each of several successive time periods; probabilities over time. Defined as


16 S ( t ) = Pr { T > t } = 1 – F ( t ). Gives the probabil ity of surviving beyond t. The survivor function is a “list” of probabilities, one for each of the times of interest and is best displayed graphi cally (Allison, 1995). Time-dependent covariates. Time varying explanatory va riables that may change in value over the course of observation. Importance of the Study An empirical study of Hispanic/Latino male dropouts will assist educators, administrators, and educationa l policy makers decide which areas need their attention when considering preventive measures. Jarj oura (1996) acknowledged the difficulty in examining the dropout problem by noting in hi s discussion “This study makes it clear in more than one way that dropouts are hardly a homogeneous group and the consequences of dropping out of school are not one dimens ional”(p.249). If this is the case, a longitudinal look at the dropout problem within/among the student population with an interest in ethnicity and ge nder will be helpful in a dding to the knowledge base. As stated previously, one third of al l Hispanic/Latino students leave school without graduating with a high school diplom a, resulting in no opportunity of higher education. Since this group has recently become the largest minority in the United States, in addition to being the most rapidly growing population, and by the year 2010 is predicted to comprise one of five Americ ans (U.S. Census Bureau, 2000; OERA, 1993), it becomes self-serving to society as a whol e that this phenomenon be investigated and solutions be found. Education is of particular concern to this expa nding population as one third of Hispanic/Latinos are younger than 18 years old. Between 1972 and 2000 the


17 enrollment of Hispanic/Latino students in public elementary schools increased 157%, compared to 20% for Black students and 10% for White students ( NCES, 2003). Investigating the critical times that students experience dropping out of their education is important to assist teachers in identifying students who are at risk before problems arise. Looking at a specific gender and ethnicity, Hispanic/Latino males, may shed light on possible areas of future focus if differences are found to be of educational significance. In addition to helping educator s, this research will contribute to the educational knowledge base and therefore help those involved in pol icy development of dropout-prevention measures. Organization of the Study Chapter 1 introduces the study. Included in this chapter are th e statement of the problem, purpose of the study, research questi ons, method of inquiry, definition of terms, and organization of the study. Chapter 2 includes a review of literature related to Hispanic/Latino dropout rates and the review of the use of su rvival analysis in looking at time as an outcome variable and identifying factors that help predict thos e times that are the hi ghest risk for students terminating their education. Chapter 3, the methods section, describe s the research design population, sample, instrumentation, procedures, data an alysis, and a summary of the study. Chapter 4 presents the results from the data analysis. Statistical procedures are documented and the statistical findings are presented. Chapter 5 discusses the study findings and presents conclusions. Implications are reported as well as recommendati ons for further research.


18 Chapter Two Literature Review This literature review addresses the general back ground on the Hispanic/Latino dropout phenomenon. Many of the studies can be identified as looking at studentcentered, family-background, or school-centere d variables. Several have looked at all three types of variables simultaneously. Most data for dropout studi es are obtained or approached from four levels. These are the school, district, state, and national levels. Following will be a review of studies that have explored dropouts at these different levels. Many of the national level studies have us ed the National Education Longitudinal Study (NELS 88; 1998) data, and dropout informa tion is extrapolated. Also included in these studies are those using the High Sc hool and Beyond (HSB; 198082) databases, an earlier longitudinal study. At the state level, numerous studies have been done on dropouts and some have explored Hispanic/L atino dropout specifically ; those studies are reported and the states from which data were collected identified. Local level investigations are reviewed next and it is at the local level that this investigation will ultimately focus. Local level data combine school level and district level as one category in this current research. The review continues by in troducing survival analysis as a method of inquiry, and reports on studies in education that have utilized this met hod to investigate educational problems, with time as an important f actor to consider in studying dropping out.


19 Background Information As of 2000, Hispanic students made up approximately 15% of school-age children and that will increase to about 25% of th e total school-age populat ion by the year 2025. Since 1980, the enrollment of Hispanic stud ents in elementary public schools has increased over 150%, compared to 20% fo r African Americans and 10% for Whites (United States Department of Education, 2000). According to the Center for Education St atistics (NCES, 2000) during each of the last 10 years, approximately three million young adults between the ages of 16 and 24 years have either failed to complete high sc hool or have not comp leted middle school or enrolled in high school. In the year 2000 that number reached 3.8 million, which represents about 11% of young adults in the Unite d States. This figure is fairly consistent with those attained over the previous fi ve years. Even more disturbing is the disproportionate number of Hisp anic/Latino students who fail to complete a high school education. Of the three million pl us students not co mpleting high school, Hispanic/Latinos comprised a disproportionate 38.6% of th e dropout population, whereas they represent only 15.1% of the student popul ation. In contrast, Blacks as an ethnic group make up 14.6% of the student popul ation but are near ly proportionately represented with 17.6% in the number of dropouts. In contrast, those of European ancestry make up 66% of the student populati on, but account for only about 41.4% of all dropouts (NCES, 2000). Examining the dropout rates for Hispanic/La tinos reveals an important trend. In 2000, 27.8% of Hispanic young adults in the 16 through 24 age group had failed to complete high school or had failed to enroll in high school. This rate is nearly four times


20 that of white young adults. Despite changi ng immigration patterns and the influx of Hispanics to the United States, this number has remained consistently higher than any other racial group for the en tire 29 years of NCES data collection (NCES, 2000). Current dropout rates for the overall populat ion are lower than those reported in the 1970Â’s and 1980Â’s. Although this also holds true for Hispanic/Latino students, this subgroup tends to dropout at a higher rate than the White or Black subgroups. The decreasing number of dropouts in the overall popul ation may be due to the increased emphasis on a formal education in toda yÂ’s economy. With the Hispanic/Latino population now comprising the largest minority in the United States and expected to grow faster than any other ethn ic group, it is extremely impor tant to find solutions to the increasing number of Hispanic/L atino not graduating high school. A few general observations may serve to help shed some light on the dropout situation. In 1998-98, nine st ates had dropout rates lower th an 4.0%. These were in low to high order: North Dakota, Iowa, Wisc onsin, New Jersey, Maine, Connecticut, Massachusetts, Pennsylvania, and Oklahoma. There were two states (Louisiana and Arizona) and the District of Colombia with dr opout rates larger than 8.0%. The rest that reported event dropout rates fell somewhere in the middle. Unfortuna tely, data were not available for many of the states, some of which ar e of interest in this research due to their large number of Hispanic/Latino students (i.e ., Florida, Texas, Colo rado, California, and New York). The other states not reporti ng event dropout rates were North Carolina, South Carolina, Hawaii, Indiana, Kansas, Michigan, New Hampshire, and Washington (NCES, 2000).


21 There are currently few statistics on dropouts collected by states that are comparable. The NCES does collect some data, but not all states are submitting data and NCES recognizes that many st ates are not collecting data using the same methodology (Winglee, Marker, & Henderson, 2000). Th ese methodological prob lems encountered with education statistics are causing difficulties in data interpretation. High school dropout rates naturally carry over to higher education. The U.S. Census of 2000 reported that 29.3% of people between the ages of 25 and 29 years had completed a bachelors degree or higher, wh ile only 8.9% of Hispanics/Latinos had managed the same. Failure at the high school level not only affects the individual, but it also affects society. Dropping out of high school translates into a lost chance of a college education, lower paying jobs political apathy, loss of ta x revenue, health problems and strain on social services (McKissack, 1998; Rosenfeld, Richman, & Bowen, 1998). A recent U.S. Department of Labor study showed that 6.7% of adults with no high school diploma were likely to be unemployed, while only 3.5% of adu lts with a high school diploma were likely to be unemployed. With a bachelorÂ’s degree, only 1.8% of adults were likely to be unemployed (US Dep. of Labor, 1999). Further, immigration statistics reveal that as of 2000, a reported 16.9 million people had immigrated to the US from La tin America (Census, 2000). Two thirds of these immigrants came from Mexico and othe r Central American countries, specifically, 11.8 million from Mexico and Central America, 3.1 million from the Caribbean, and 2 million from South America. The number of La tino immigrants is likely to increase, and in turn so is the number of Latino children in American high schools. Such statistics demand that educators and policy makers take a closer look at th e demographics and


22 predictors of those students dropping out of school, as many Latinos ar e likely to be left behind economically and socially if this trend continues. Many empirical studies on high school dropout rates among minorities focus overwhelmingly on the same types of factors. These include characteristics of students and their families, such as, socioeconomic st atus, marital status of parents, education level of parents, immigrati on status, and number of sib lings. Further, many of these studies use the same national longitudinal data sets (e.g., Alsp augh, 1998; Natriello, 1986; Rumberger & Larson, 1998; Rumberger, 1987). This is advantageous on one hand but it also has its downside. On the positive side, these studies have established consistency in dropout patterns across time, but only looking at nati onal data can obscure possible local trends. For instance, high dropout rates among students in Florida could be offset by lower dropout rates in Connecticut. National Level Studies In specifically looking at dropout among Hispanic youth using data from the sophomore cohort of the HS& B data, Fernande z, Paulsen, and Hira no-Nakanishi (1989) found that grades were a strong predicto r of dropping out. Lo oking at non-Hispanic whites, Blacks, and Hispanics by gender, this was true for all three groups. White males also demonstrate a significant effect of bot h marriage and children on dropping out but only marriage was significant for Hispanic males. So not only is taking on adu lt responsibilities a detriment for female students while attending school, but the study show ed that white males also had a higher propensity to dropout if marriag e and/or parenthood was a fact or. The authorsÂ’ also noted that both male and female black and wh ite students who pe rformed better on the


23 achievement test were less likely to drop out than students who performed poorly on the test. For Hispanics, the same pattern was iden tified but it was only statistically significant for the males. Fernandez et al. (1989) concluded that th eir findings pointed to the importance of separating analyses of dropping out by race/e thnicity and gender. They demonstrated some important differences in the proce sses that lead student s to dropout by these subgroups. There was an excepti on though; decisions of male Hispanics appear to have been more sensitive to family size than for the other groups. No matter what subgroup they were in, scholastic perf ormance and grade delay affect ed students’ decisions to remain in school or dropout. Among males, achievement is a stronger deterrent to dropping out for Hispanics and non-Hispanic Bl acks than for non-Hispanic whites. These findings support the thinking that remedies to grade de lay and policies designed to improve Hispanic scholastic achievement are likely to produce the biggest rewards. Exploring race and academic disident ification, Osborne (1997) reported significant findings relating to Hispanics. He wrote, “identification with academics is the extent to which one’s self evaluation in a pa rticular area (e.g., academics) affects one’s overall self-evaluation (global self-esteem)” (p. 728). Using St eele’s (1992) definition of disidentification as the lack of a relationship between acad emic self-esteem and global self-esteem, the study examined how Hispanic s’ academic performance and self esteem compare with that of African American and White students. Data were from the National Education Longitudinal Study (NELS ) and only those participants who participated in the base year (1988), first follow-up (1990), a nd second follow-up (1992) were part of the analysis.


24 The scores for self-esteem were hi ghest among African-Americans across the three time points. Whites remained very st able across time, whereas African-Americans self-esteem increased from eighth to tenth gr ade, and then decreased by twelfth grade. An interesting trend was that for Hispanic s, who showed that although they had the lowest self-esteem at eighth grade, by tw elfth grade their self-esteem was higher than whites. But as the self-esteem of these Hisp anic students was incr easing, their grades were also dropping. The trends illustrate a potential disconne ct between academic reality and self-view for these minority groups, and set the stage for the assertion that these trends may reflect disidentification in pr ogress for the two minor ity groups (Osborne, 1997). Using the data collected from the Nati onal Educational Longitudinal Study (19881994) Kramer, (1998) examined dropout cau ses among race-ethnic and gender groups. The race-ethnicity variable categories used in the study we re Asian/Pacific Islander, Hispanic, Black, White, American Indian/Alask an Native. Factor analysis was used to categorize the 20 items into workable factor s. The extracted factors were named: 1) academic problems, 2) family issues, 3) school disciplinary problems, 4) economics, 5) interpersonal psychosocial, and 6) peer infl uences. Results of the study found that gender differences varied significantly across five of the six factors used in an analysis of variance of group mean factor scores. The interpersonal factor was the only factor not statistically significant. Males cited the academ ic factor, school discipline, and economics as the main reasons they left school. Fema les also cited academics problems first and then family factors as their main reason for dropping out.


25 The recency of immigration seems to be an important factor in the study of high school dropout rates. Driscoll (1999) us ed National Education Longitudinal Study (NELS) data to examine this relationship. Fo r purposes of this study, first-generation Latinos were identified as those born outside the Unite d States; second-generation Latinos were defined as thos e born in the United States wi th one or both parents born elsewhere; and third-generation Latinos were those born in th e United States as were both parents. Prior to this stud y, Rumberger (1995) concluded that second generation Latinos were higher dropout risks than third generation Latinos. Dr iscoll (1999) also included socioeconomic and other demographic variable s as factors affecti ng dropout rates. She distinguishes between early a nd late dropouts with early drop out meaning prior to being a second semester sophomore in high school. Using a set of logistic regression models, Driscoll (1999) determined that first and second generation Latino students who comple ted two years of high school were less likely to drop out than third generation students who completed two years of high school. This finding remained significan t when socioeconomic and family background variables were held constant. Third generation students were more likely to drop out of school at any point compared to first or second generation students. This finding replicates that of Varled eÂ’s (1987) study where she found that Mexican students who were born in Mexico were less likely to drop out than Mexican students born in the United States. This result is su rprising given that these students had the advantage of learning English at a young age and having parents who were more likely to be fluent English speakers.


26 Driscoll (1999) suggests that the finding may reflect thir d generation studentsÂ’ notion that their chances of succe ss are limited given discrimina tory practices and cultural beliefs that do not view education as the key to economic success. The author also identifies the importance of previous academic success on high school completion. She suggests that educators should focu s on encouraging academic success early on and to work with students who are strugg ling, without negatively affecting their perceptions of thei r own abilities. Using the NELS school effectiveness study data from 1988, Rumberger and Thomas (2000) looked at dropouts as a measur e of school performance and investigated the role of student turnover. The authors point out that student turnover has been neglected in the lite rature, yet a 1993 study f ound that 75% of children in the US change schools at least once before the age of 18, a nd 10% moved at least six times (Rumberger & Thomas, 2000, p. 42). Turnover in some schoo ls has been found to be as high as 30% to 40%. Low-achieving student s impede the improvement of schools overall performance on standardized tests. Although their low acad emic performance is not stated as the reason, such students may be dismissed from schools for various other reasons, contributing to high turnover rates. These st udents are not typically included in dropout statistics, but in reality they probably should be. Results from Rumberger and ThomasÂ’s ( 2000) study indicate that turnover rates varied more than dropout rates, and much of the variation in both variables could be accounted for by differences in student charact eristics. Further, the characteristics of schools, such as high teacher/student rati os, accounted for much of the change in


27 turnover rates. The authors suggest that changes to school po licies and a focus on retention would decrease th e dropout rate and increase academic performance. Also using NELS:88 data, RumbergerÂ’s (1995) multilevel analysis examined the factors that influence studentsÂ’ decisions to leave school and the f actors that influence rates of dropping out among schools. In the firs t part of the study, a student-level model of dropout behavior was deve loped and tested with logi stic regression using only individual-level variables. In the second part of the study, a hierarchical linear modeling (HLM) analysis was performed using both st udent-level and school-level variables. As part of the student-level, logistic regression analysis, separate regression estimates were derived for Blacks, Hispanics, and whites. Controlling other variables in the model, females had significantly higher dropout rates among Blacks and Whites, but not among Hispanics. Family socioeconomic st atus was highly predic tive of student drop out, twice as likely to drop out as students from average social class families. At the student-level, the single most powerful predictor was whether a student was held back in an earlier grade (Rumberg er, 1995). The effect of single parent households on risk of dropout has been examined extensively in the literature with many studi es establishing a direct link between the two variables (Pong & Dong-Beom, 2000). There ha s also been some examination of the effects of a reduction in income with regard to family structure. There is some debate on this issue, with one side arguing that low in come could result in gr eater divorce rates and subsequently cause children to drop out of school, and the other side arguing that divorce leads to lower income and subsequent dropout. It has been establis hed in other studies


28 that the income of a divorced wife decreases fa irly dramatically after a divorce (Peterson, 1996). Proposing that income levels drop after divorce and lead to subsequent higher dropout rates for children of divorce, Pong and Dong-Beom (2000) examined student data from the National Education Long itudinal Study (NELS) of 1998 and focused on students whose parents were t ogether at the beginning of ei ghth grade and then were divorced some time in the following four y ears. Results indicated that when family structure changed to a mothe r-headed household, income signi ficantly decreased and risk of dropout was significantly incr eased. At the same time, a two-parent family structure did not significantly reduce th e dropout risk among Latino students. Nonetheless, the dropout rate increased even more for Latino students when family instability occurred. This dropout rate for Latinos was two times mo re than that for black students, and three times more than that for White or Asian st udents with the same levels of family instability. Interestingly, when family instabil ity resulted in the a ddition of stepparents, the rate of Latino dropout increased even further to nearly 30%. Shu (1988) investigated the determinan ts of dropping out of high school for several Hispanic subgroups. Th is study was unique in that it looked at three specific groups: Mexicans, Puerto Ricans, and Cubans, groups that make up a majority of Hispanics usually included in the “Hispanic” category of most educ ational research of the United States. High School and Beyond (HSB) data were used to develop models to discriminate dropouts from non-dr opouts for the national, Hispanic, as single groups, and then a Mexican, Puerto Rican, and C uban model as three distinct groups.


29 As the dependent variable, dropout, is dichotomous in nature, discriminant analysis was the statistical procedure used. The independent factors used in the seven discriminant analyses were: st udent characteristic (i.e., ag e, sex, high school program, changed schools since grade 5), family b ackground, educational attainment, school related problems, students’ aspirations and expectations, students’ perception of the school, and out of school work/a ctivities. Those f actors deemed most influential were then applied in various models related to the three subgroups. Shu (1988) in reporting differences in student characterist ic variables among dropouts from various groups found about half of the dropouts were male for the national sample compared to approximately 53% male for the Hispanic sub-sample. When it came to age (categorized into 15 or younger, 16, 17, 18 or older), th e dropout rates were much higher for the Hispanic subgroups than for the national sample in all but the 17 year olds. It needs to be noted that there was a higher percent of older students (17 years old and older) in the Hispanic sub-samples th an in the national sample. The probability of a Hispanic student dropping out was much greater than that of a student in the national sample regardless of age. In reporting the results of the comprehensive models, comparisons were made for each of the factors among the models. Within the aspirations and expectations factor, the variable “Expected to leave high school” wa s a very important predictor in all five models. “Age,” under student characteristics was an extrem ely powerful discriminator for all but the Cuban model. Looking at the educ ational attainment factor, “Grades,” existed in all the models but the Cuban m odel. Shu (1988) report ed that the five comprehensive models were quite different from each other. First, the national model


30 differed from the Hispanic model and th e three Hispanic sub-samples differed significantly from each other. Although the Mexican-American model and the Puerto Rican model shared some discriminative va riables, the Cuban American model was different from all other models. It was also the least reliable of all models from a predictive point of view. In summarizing the historical trend of recent dropout studies, Shu (1988) concluded that two manifest characteristics had emerged. The first is that due to computer technological advances which helped in the creation of national databases, a number of models and theories have b een put forth on dropping out of school. The second is the awareness of the high dropout rates among Hisp anic youth. Unfortunately, few theories on Hispanic dropouts have been developed and even fewer that focus on Hispanic subgroups. State Level Studies Griffin (2002) examined the relation ship between high school grades and dropping out for Asian, Black, Hispanic, a nd White students. The approach was to examine students’ ability to identify with academics by looking at th e factors associated with academic identification. To identify the discrepancy on the importance put on academics among these ethnic groups, two possi ble explanations were looked at. One was cultural inversion (Ogbu, 1992), which o ccurs when minority group members behave in a manner not in-line with the dominant cultur e. The other was stereotype threat (Steele, 1997), which exists when a student’s performa nce could confirm a negative stereotype about their ethnic group, possi bly having an effect on academic performance. Griffin hypothesized that, “if either cu ltural inversion or stereotype threat plays a role in


31 academic disidentification, the Black and Hi spanic students, who often face both negative academic stereotypes and peer pressure to adopt anti-academic behaviors, should place less emphasis on academic performance when de ciding to leave school than either Asian or White students.” (p.75). Data for the 1990-1991 school year, grades 9 through 12, were provided by the Florida Department of Education. The st udy looked at a random sample of 75 high schools from 14 school districts. The variable s of interest were dropout status, grade point average (GPA), and race. Results show ed the dropout rate was highest for Blacks, closely followed by Hispanics, then Whites, and then Asians. Male s had a higher dropout rate across each racial group except for Asia n students. For racial groups for which a negative stereotype or oppositional subculture (i.e., peer-pressure to resist schooling and academic success) applies, the dropout rate was higher, supporting the disidentification hypothesis (Griffin, 2002). Shedding some light on the plight of ethnic minority males, Graham, Hudley, and Taylor (1998) examined, in two studies, mi ddle school students’ ach ievement values. The participants in study 1 were all African-Am ericans. In study 2, a middle school in Los Angeles, California, comprised of an ethnically diverse samp le of 401 students, was used. The breakdown was 50% Latino, 30% African American and 20% White although there were small numbers of Asians, Persians and biracial stude nts included also. The data for boys nominating other b oys as a function of ethnicity and achievement level were quite surprising. St udents were asked to nominate classmates who they most admired, respected, a nd wanted to be like. Latino nominators overwhelmingly valued other Latinos (76%) compared with Afri can Americans (13%)


32 and White males (11%), and low achiever s (39%), over average (33%), and high achievers (28%). The most va lue nominations (35%) were allocated to low-achieving Latinos. The African American males had sim ilar results as the Latino males. The group receiving the most nominations for admire d, respected, and someone the nominator wanted to be like was the low-achieving Afri can American boys (27%), compared with average (15%) and high-achieving African American classmates. White nominators valued high achievers (67%) ove r average (23%) and low achievers (10%). These results clearly show that males of Latino and Afri can American ethnicity are placing a higher value on other intangibles and not on academics in responding to who it is they admired among their fellow classmates (Graham et al., 1998). Using data from Chicago area schools Reyes, Gillock, Kobus, and Sanchez (2000) examined how the school transitions of a group of minority youth relate to academic achievement and dropout. Changing sc hools is a significant life transition for adolescents and can have a lifel ong impact. Previous studies ha ve indicated that a single transition results in higher dropout rates ( Blyth et al ., 1983; Eccles & Midgely, 1988; Seidman et al., 1996). By not relying on nati onal data, this study portrays what school transitions are really like fo r urban minority youth from low socioeconomic backgrounds, without these experience s getting lost in aggregate data The study looks at self-reported changes in self-perceptions from eighth to ninth grade, soci al support networks, perceptions of school and also academic performance. Reyes et al. (2000) hypothesized that t hose students who co mpleted school would have had smoother transitions from middle school to high school and also have more positive self-perceptions. Results obtained from a series of multivariate analyses of


33 variance (MANOVA) revealed that fewer tran sitions lead to higher achievement and therefore, lower dropout rates. Students who experienced fewe r transitions from middle to high school also had better academic grades than those students who experienced dramatic changes (either positive or negative). On the whole, minority students were found to be extremely sensitive to school tr ansitions. The authors comment that this sensitivity may be cultural. Minority students of ten must fit into two cultures at once. The dominant culture is inherent in our school systems, while a student from a minority background has his or her own cultural values to conform to as well. Reyes et al. add that Latino children are taught to respect authority and therefore are likely to be less vocal in classes. The lack of participation impacts how teachers view their abilities. AfricanAmerican children for example, are taught interdependence and cooperation, yet the dominant culture in schools focuses on i ndependence and individual achievement. In response to Reyes et al.Â’s ( 2000) findings, the Chicago scho ol system is working to minimize school transitions by having student s attend K-8 schools a nd then ninth-grade through twelfth-grade schools. The transition to and from middle school is thus avoided. Approaching school dropouts from a differe nt angle and using locally based data, Alspaugh (1998) looked at dr opouts among students in Misso uri. Although he did not break his analysis up into ethni c groups, his findings are of interest to this research. Most studies on high school dropout focus on family bac kground, personal problems and school related factors, such as academic success. Alspaugh (1998) suggests that there is a relationship betw een school organizational char acteristics and dropout and also community well-being and dropout. Co mmunity well-being was measured in the study by unemployment rates, average family income and also crime rates. School


34 organization was measured us ing the size of the schools, units of high school credit (i.e., subjects offered) and al so extracurricular activities. Using some basic relationship technique s of data analysis, Alspaugh (1998) found that larger high schools have much hi gher dropout rates than smaller schools, a phenomenon that may be attributed to inte rpersonal relationships developed between teachers and students at smaller schools. Second, there was also a strong correlation between high community crime rates and high dropout rates. Third, a decrease in participation in extracurricular activities also led to higher dr opout rates. This is probably due to school size, since ther e are fewer opportunities for st udents to participate in extracurricular activities when there are more students with which to compete. Together, these present a multiple factor model for high Latino dropout rates. Another interesting finding was that broad course o fferings did not decrease dropout rates (Alspaugh, 1998). Many school o fficials have tried to offer a broad range of courses hoping that students would find the addi tional subjects interesting and therefore would stay in school longer. AlspaughÂ’s fi nding is in agreement with PittmanÂ’s (1991) study and also Pittman and HaughwoutÂ’s (1987) study. However, other studies have found that increasing the amount of homework and increasing the level of course-work do prevent dropout (e.g., Rumberger, 1995). Alspaugh found that the lowest high school dropout rates were found in sma ll, rural schools. These are schools that are predominantly white. Latino students are more likely to be in schools that are large, and are located in lowincome communities with high crime rates (Pittman, 1991).


35 Alexander, Entwisle and Horsey (1997) propose that tendency to drop out is developed over the life course. Using a sample of students from Baltimore, a city that has high proportions of minorities and many pe ople in low socioeconomic groups, the authors tracked studentsÂ’ academic progress from their first day of school until high school completion or dropout. Baltimore has a very high dropout rate; the 1997 NCES data estimate this at 30%. The authors maintain that looking at students early on in their academic life is important, given that acad emic performance and attitudes toward academics, as well as conduct, are all established in the first grade. Further, school officials often slot or "tra ck" students into categories at an early age, and this categorization tends to follow stude nts through their sc hool experience. Alexander et al. (1997) us ed variables measuring a childÂ’s person resources, family context and school experiences, in a ddition to the usual demographic variables. Items asking about attitudes toward self and school were posed to measure personal resources. Family context measures focused on family stressors, and parentsÂ’ attitudes, values and socialization practices. School e xperiences were measured using items that asked studentsÂ’ about their a cademic achievement, such as test scores and grades in mathematics and reading, and also whether there were track placements in the school. Several measures of dropout were used in the study. Using logistic regression models, Alexander et al. f ound that parentsÂ’ attitudes toward education were highly significant, as were family stressful conditions. Among the studentsÂ’ school experiences, academic perfor mance, reading level, track placement and other academic achievements were also extr emely important predictors of dropout. These variables were all statistica lly significant independent of demographic variables. The


36 demographic variables that had a signif icant impact on dropout rates were: low socioeconomic status, being male, having a large number of siblings, being born to a young mother and coming from a single parent household. Ethnicity wa s not a significant focus in this study, since the researchers only compared black to white dropout rates. Further, the small differences in dropout by ethnicity were obscured when socioeconomic status (SES) was controlled for. Th e authors concluded th at the process of academic disengagement is an area that needs to be further studied, and they criticized current studies for failing to examine this long-term social process. In a qualitative study, Hebert and Reis (1999) looked at high achieving minority students in urban schools. This study examined the opposite side of the fence, in that, instead of focusing on why youth drop out of school, the focus was on why youth stay in school and what motivates them to achieve. Their findings indicate that although there is a difference in how students rated the following factors in importance, they all contributed to student s being successful. These factor s were: a strong belief in self, supportive adults, a network of achieving peer s, extracurricular program, challenging learning experiences, personal characteristics, resilience, and family support. Such factors can be used to help motivate other students. This was one of seve ral qualitative studies identified during the course of this literature review. In another, involving focus group intervie ws with Chicano/La tinos (appropriated by many Mexican descendants as reflective of their unique culture) who had dropped out of high school, Aviles, Guerrero, Howarth, and Thomas (1999) found several areas where students reported difficulties. These problematic areas included attendance, participation


37 in school activities, alternativ e educational programs, expecta tions of teachers and staff, and personal situations. As the authors re ported in their resu lts of the study: Possibly the most important finding in this study was the view that Chicano/Latino students who left high school were not dropouts. Rather, group members consistently and distinctly reporte d what can best be described as being facilitated out. The combination of lowered teacher expectations and encouragement on the part of school personne l to opt out of mainstream education facilitated a steady exodus of Chicano/La tino students out of the school system (p. 469). The qualitative approach of research is in formative in that it deviates from the many other studies that focus on national data th at tend to obscure local trends (Chiricos, 1987). Local Level Studies Using a sample of high-ability students from a northeastern, urban high school, Hebert and Reis (1999) investigated relati onships and support systems that help youth stay in school and the most important f actors in achieving academic success. The high school where the study occurred was described as looking similar to an industrial plant (i.e., few windows and in need of repair). The student population was 60% Puerto Rican, 20% African American, and 20% white Asian and other ethnic groups. Almost all students in the sample were fr om families of low socioeconomic status and half lived in subsidized housing. Most of the students also cam e from families with multiple siblings. Thus, many of the risk factors for dropout were present. However, these students all exhibited superior academic performance. All students in this study credited


38 an adult role model with mo tivating him or her to strive for academic honors. These adults were usually teachers and coaches and, occasionally, ment ors from community programs. Several students commented that te achers who gave the students some choice in their curriculum captured student interests, and students subsequently performed much better in those classes. Unfortunately, such choices move school officials away from focusing on standardized testing and other mean s of developing cons istent and reliable data (Herbert & Reis, 1999). Other students in this study cited high e xpectations and positive comments from teachers as motivators behind achievement. This finding concurs with many years of teacher research that reports teachers w ho project high expectations on students eventually see those expectations reflected in pe rformance (Good, 1980; Rosenthal & Jacobsen, 1968). Another importa nt finding from the Hebert and ReisÂ’s (1999) study is the role parents play in stude ntsÂ’ academic success. Most students in the sample had extensive social support from their parent s and usually this amounted to emotional support only as financial support was impossi ble. One student cited his parentÂ’s tremendous sacrifice to allow him to su cceed and he felt obligated to do so. Many of the studies discuss cultural beliefs and practi ces among Latinos, yet few discuss what those beliefs and practices actua lly are. CarterÂ’s (1983) study for example, although written to explain Lati no cultural clashes with the criminal justice system in Texas, offers some other important insights about Latino culture. These insights can be applied to the educational se tting and may help explain w hy Latino males have such a high likelihood of dropout.


39 Carter (1983) identified four cultural el ements: 1) familial roles and norms, which include a centralized family st ructure with a male authorit y figure; 2) a “personalistic” sense of loyalty and honor, defense of which is a necessity; 3) arrant sensitivity to insults, that includes an exaggerated sense of m achismo; and 4) immediate dominion which refers to reacting to a situation with little long-term view of the consequences. With regard to familial roles and honor, academic failu re may be seen as a sign of weakness, so it is theorized, instead of attacking the problem, Latino ma les may drop out of school to save face. All of these cultural elements, pa rticularly regarding English fluency, are frequently misinterpreted by the dominant culture and these mis understandings can lead to interpersonal conflicts and systemic conflicts. Teachers and school officials are, more often than not, part of the dominant Anglo-culture. Such officials often misread la nguage differences in Latinos as a sign of low intelligence; they may see sensitivity to failure as bad temperament, and upholding Latino cultural values as “un-Am erican.” Any one of these th ings could result in conflict between the teacher/ official and the student, and could have long-term consequences on the student’s education and future economic opportunities. Carter ( 1983) concluded that in this context, better unders tanding of Hispanic/Latino culture is an essential part of making education possible. Hess and D’Amato (1996) took a unique approach at examining some of the potential differences between high school dropouts and persisters among MexicanAmericans. Their sample consisted of 80 Mexican-American children in grades 3 through 5, and although no specific place is men tioned, the size of the sample would suggest it is derived from a small geographical area. Half th e children had at least one or


40 more older siblings who had dropped out of high school while the other half had one or more older siblings who were considered to be high school persisters. Many studies on dropouts use data from students who have already dropped out. By using children in elementary school, risk indicators may be id entified early on in a student’s schooling. The results of the study found that for elem entary age Mexican-American children, school absences and expectations of high sc hool completion were significant factors in differentiating siblings of persiste rs from siblings of dropouts. In a study conducted by the Latino Coalit ion (University of South Florida’s Florida Mental Health Institute, and th e Children’s Board of Hillsborough County, 2000), some major findings on the Latino dr opout phenomena are re ported. Although the major focus came from qualitative methods, de scriptive statistics for demographics on “all students identified as Latino” and school characteris tics are also reported. The exploratory study aimed to gain an understanding of the factors contributing to the high attrition rate of Latinos in the school dist rict. Focus groups and semistructured in-person and te lephone interviews were conduc ted with three groups of students: high achieving st udents, at-risk students, and dropout Latino students. Community representatives, school system pers onnel, principals, and teachers were also involved in the information gathering process. From the data on Latino students in the school system database, the researchers developed a profile of Latino st udent risk factors for those wh o drop out or ar e at risk of dropping out. The sample size for this analys is was 19, 350 students, attending one of 79 elementary schools, 33 middle schools, 19 high schools, or 9 ex ceptional education schools. As already discussed, only socio-demographic factor s and school factors were


41 selected for analysis. The findings revealed that Latino students had a higher probability of leaving school if they were: 1. Eligible to receive free meals. 2. Classified as monolingual or predominantly Spanish speaking. 3. Included in Exceptional Education a nd Alternative Educati on or placed in disciplinary programs, juvenile justice programs, or substance abuse programs. 4. Identified as having irregular attendance, frequent tardiness, having been retained in grade, and assessed as being low achievers (Latino Coalition, 2000). The Latino Coalition (2000) suggested th e need for more focus on middle-school dropout prevention programs where there is a high ratio of Latino students to Latino administrators and teachers. Their conclusions agree with studies that report students’ perceptions of “not belonging” and “no one to talk to,” th e feeling of “no connection to school,” found in previous dropout research. The study recommended that in addressing th e attrition rate of Latino students, causes must be understood to be multi-faceted and this fact needs to be understood by those involved in finding solutions. The aut hors conclude, “…stakeholders of this issue share responsibility for addr essing the need for consistent parental and professional support, outreach and improved dissemination of information, and awareness of the cultural issues that impact on students' decision to leave scho ol” (Latino Coalition, 2000). Another local study addressed one of the f actors considered to affect the dropout phenomena, that of out-of-school susp ensions. Conducted for the Hillsborough Constituency for Children (Raffaele, 2000), the study aimed to gain greater


42 understanding of factors relate d to excessive out-of-school suspensions in the county and how schools, families, and communities can work together to find better ways to combat this problem. Using the data from the 199697 school year, with a sample size of 145,903 students, 33,620 of them experienced out-of-sc hool suspensions, an overall rate of 23%. Looking at gender, although boys and girls are equally represented in the school district, 73% of the suspensions were boys while 27% were girls. Latino students were proportionately represented; they made up 18% of the student population and were responsible for 17% of the suspensions. The study noted common characteristics of students with multiple suspensions. These were identified as: 1. Low parental support / Family dysfunction 2. Disrespect for authority / Poor attitude 3. Self-esteem problems 4. Poor achievement / Not involved in school 5. Truancy /Tardiness / Inconsistent attendance 6. Gang involvement / Juvenile delinquency 7. Behavior and/or Social problems 8. Low SES 9. Substance abuse Behavior and/or social pr oblems were the most reported characteristic at all school levels. Over 50% of the schools at each level reported this characteristic. Disrespect for authority, poor achievement, and low parental support we re also frequently reported by the schools.


43 Gender Differentials This research is primarily interested in the factors that are related to the large number of Hispanic/Latino males not finishi ng their high school educ ation. It has been well documented in the numerous studies that are included in this review that there are a multitude of variables that contribute to young students’ decisions to drop out of school. It seems that ethnicity and gender play a si gnificant role in dropping out of school and the following is some of the empirical evidence that has been reported. In an American Association of Univ ersity Women study (2001), although their aim was to bring forth publicly the “Troubling Label for Hispanics: Girls most Likely to Drop Out,” awareness, it was compared to othe r group of girls in the United States. It was reported that, “according to government data, 26 percent of Hispanic girls leave school without a diploma, compared with 13 percen t of Black girls and 6.9 percent of White girls. The only group that ha s a higher dropout rate among all students is Hispanic boys. Thirty-one percent of Hispanic boys drop out compared with 12.1 percent of Black boys and 7.7 percent of White boys” (p. 13 ). (see also McGlynn, 2001, p. 30). In a study to show race-ethnicity and ge nder differences in reasons for dropping out of school, Jordan, Lara, and McPartland ( 1996), found that across the race-ethnicity groups and the gender groups, school related fact ors were the most cited reasons for early dropout. Using the NELS: 88 database, a factor analysis categorized the various dropout reasons into a smaller number of measures. Th e extracted 7 factors from the original 21 items were: Family-related, School-Relat ed, Work-Related, Safety, Suspensions, Mobility, and Friendship reasons.


44 Hispanic and White males reported job -related reasons for dropping out second to school-related reasons although for African American males, the second most reported reason was suspension or expulsion. For the fe males, the family re lated factor was the second most reported although for the White females, job related reasons was second with family related a very close third. The biggest differences in the study were gender differences although several ethni c/racial differences were also found. Males reported the primary reasons for dropping out were school-related, job-rela ted and, suspension and/or expulsion. Females reported school-related, family-related and, j ob-related as their primary reasons for leaving sc hool (Jordan et al., p.76). Hall and Rowan (2001) wanted to determ ine the characteristic differences of Hispanic-American males and institutions of higher education which enable academic failure. Here again, although the researchers’ interest for their study differed in that their purposes were aimed at higher education, many of the described differential status for Hispanic-American males and the reasons they give for dropping out or graduating from college may be useful in looking at the younger student population. In their review of literature, citing Hall (1994), Rowan and Hall (2001) state, “...over 40 percent of Hispanic-American male s separate from school before completing the requirements for promotion to the tenth grad e.” This figure alone is one that should be a wake-up call to education practitioners. To allow this many stude nts to fall through the cracks of the schooling system needs to be addressed. Concluding, Hall and Rowan lament, “Given the current state of higher educ ation, the ultimate sacrifice will be borne by the society in the loss of their human development a nd productivity” (2001, p. 572).


45 In attempting to create a comprehens ive model of the sc hool leaving process among Latinos, Velez and Saenz (2001) iden tified and reported on three clusters of factors: individual factors, fa mily factors and, structural factors. The authors concluded that modeling the school dropout process requires a theore tical approach that incorporates all three types of predictors. Several recommendations regarding research and data needs were presented for the bene fit of future studies. As they stated: Despite the serious nature of the La tino dropout phenomenon not only for the Latino community but for the nation as a whole, there continues to be an absence of data for the study of Lati no dropouts. One of the most serious problems plaguing research based on th e Latino population in general is the absence of historical data to assess changes over time. Another important area with policy implications that begs for em pirical attention is the issue of gender and education (p. 461). Specifically, the ways that would enhance our understanding of the school leaving process of Latinos are reported as: 1. Development of a nationally representative longitudinal survey to capture the school leaving process of Latinos. 2. Development of inventories to compile information about successful programs that have made advances in re ducing the dropout problem of Latino youth. 3. Development of a clearinghouse that ca n compile and organize our knowledge about Latino dropouts.


46 These suggestions are not only helpful in identifying the difficulties that Latino students are having but also in the design and development of interventions to keep these students in schools. Survival Analysis : Introduction Survival analysis is used to determine the time taken before a pa rticular event occurs. Therefore, it not only examines the occurr ence of an event, but also its timing. Originally used in medical research, surviv al analysis was often applied to examining the effects of new treatment procedures on mortality, hence its name (DesJardins & Moye, 2000). In the social scien ces, this technique is often referred to as event history modeling or hazard modeling. It has been used extensively in sociology, but has only recently been introduced to education research (DesJardins & Moye, 2000; Denson & Schumacker, 1996). Survival analysis usually re lies on logistic regression modeling if the technique is parametric and the Kaplan-Meier Method if the technique is nonparametric (Satten & Somnath, 2001). Logistic regression is used wh en the dependent variable is dichotomous and the independent variables are measured at least at the interval level. Models are estimated using maximum likelihood rather th an ordinary least squares as in linear regression (Neter, Kutner, Nach tsheim, & Wasserman, 1996). In looking at the timing of educational ev ents using survival analysis, there are several methods. Schumacker and Denson (1994) reported on an approach to interpret interaction of predictor va riables with time in a disc rete-time method. Previous continuous-time methods did not allow for the use of both time-invariant and time varying predictor variables.


47 Studies in Education Using Survival Analysis In a study that examined attrition among college students, DesJardins and Moye (2000) used data from the High School a nd Beyond/ Sophomore Cohort, and conducted a survival analysis. The initial model containe d several variables such as gender, academic resources and whether the student was a parent at a given time. Subsequent models added financial aid variables, grade point aver ages and different components of academic resources such as academic intensity, high sc hool rank and senior ye ar test score. By running time comparison models and models th at did not consider time, DesJardins and Moye found that the models incorporating time were better predicto rs of graduation as some predictor variables had less effect ove r time while others had more (p. 18). The authors advocate that this last finding is ve ry important since it highlights the importance of examining variables over time, rather than examining them as unchanging events. Ronco (1995) used competing risks surviv al analysis to investigate whether students who enroll at a university will graduate withdraw or transfer. Data used for this study were taken from Texas Department of EducationÂ’s database of first time enrolled college students. Competing risks referred to the different types of exits from the institution. Predictor variables examined in cluded ethnicity, gende r, enrollment status, GPA and major. Note that some of these variables are time varying, for example, enrollment status and GPA, and others are not. Ronco us ed ordinary least squares regression to select the variables for the logi stic regression model a nd excluded those that were not significant. Results from this study indicated that th e hazard rates for withdrawal or transfer were highest after the second semester. Rate s remained fairly high until the seventh


48 semester upon which time some students be gan to graduate. After graduation began, hazard rates peaked, but are only artificiall y high since the risk pool has decreased substantially by this point. Ethnicity was the only stable variable to remain significantly related to all three types of exit. Latino stude nts were less likely to transfer to another four-year school or dropout, but also were mu ch more likely to tran sfer to another twoyear school (p. 16). Ronco (1995) proposes th at this may be because Latino students move to find a college that better suits their needs. Willet and Singer (1995) used a technique known as multiple-spell discrete-time survival analysis to study the sequential occurrence of exit from, and reentry into the teaching profession. They explored the occurrence of this pair of alternating events in the lives of special educators, the events of leaving, and then returning to teaching. Twelve years of longitudinal data that described up to four spells for each e ducator were: (a) first spell in teaching, (b) second sp ell out of teaching, (c) third spell in teaching, and (d) fourth spell out of teaching. Their results were promising for the use of multiple-spell discrete-time survival analysis although difficulty was found in conf orming to the independence assumptions. As they concluded: The lack of independence is a problem that is not unique to multiple-spell discrete-time survival analysis. In fact the same dependence also occurs across consecutive time periods within a single spell. Hence, both discrete-time and continuous-time survival me thods designed for the anal ysis of single spells including the popular Cox continuous -time proportional-hazards modelsuffer from exactly the same drawback (Willet & Singer, 1995, p. 61).


49 In a study that examined stude nt dropout among first time 9th graders in Dallas Public Schools, Denson and Schmacker ( 1996), followed students over a four year period. Again, this study used competing risks which were: wi thdraw, dropping out, graduation, still enrolled af ter four years, no-show, a nd unknown. Predictor variables examined were such factors as gender, et hnicity, special educ ation enrollment, poor English skills and overage. Results from this study indicated that the hazard rate for graduation was 81% for any stude nt remaining in the risk poo l after the second semester of 12th grade. Dropping out and withdrawing were greatest until the senior year. All ethnic groups were at the greatest risk of dropping out during the 9th grade. This effect was particularly strong for Latino students. Further, those with lower proficiency in English were also more likely to drop out than proficient English speakers. Summary This review addressed many variables, bot h singly and in combination, that can positively or negatively affect dropout among middle and high school students. The demographic conditions that had a significant impact on dropout rates were: low socioeconomic status, being male, having a large number of siblings, being born to a young mother, and coming from a single parent household. Among the studentsÂ’ school experien ces, poor academic performance, low reading level, lower track placement and ot her poor academic achievements were also extremely important predictors of dropout. Al so included are attit udes toward education and expectations of the students, numb er of school transitions, school/classroom environment, size of the schools and the av ailability of extrac urricular activities. Regarding the value one puts on fellow cl assmates, males of Latino and African


50 American ethnicity are placing a higher value on low achievers and other intangibles and not on academics. Negative effects on students’ ability to continue with thei r education include family stressful conditions, large schools, and high crime rates of communities. Some factors surprisingly may not have much of an effect on the dropout phenomenon. For example, recency of immigration had unexpected results in that third generation students had higher dropout rates than second or first generation students. Th e expectations were that the children of immigran ts having most recently a rrived would encounter more difficulties and therefore dropout at a higher rate than those of second or third generation families. Other factors that have been shown to contribute to the high attrition rate of Latino students are eligibility to receive free meals, cla ssification as monolingual or predominantly Spanish speaking, inclusion in Exceptional Education and Alternative Education programs or placement in disciplinar y programs, juvenile justice programs, or substance abuse programs, identified as havi ng irregular attendance, frequent tardiness, having been retained in gr ade, and low achievement. This investigation looks sp ecifically at Hispanic/Lati no male students’ age, home language, retention history, pr ogram of studies and, beha vior. In addition, various academic achievement variables are studied, in cluding: reading scale scores, math scale scores, and students GPA. In addition to id entifying whether these variables may be good predictors, the aspect of time is investigated to see when it is that “critical moments” or high risk time periods occur in st udents’ educational lives, firs t of all as students and then specifically, as experienced by Hi spanic/Latino male students.


51 Chapter Three Method This study is a secondary an alysis of public school data from a large urban school district in the state of Florida. A long itudinal approach was employed; a sample consisting of Hispanic/Latino male students in the 8th grade in 1995-96 was followed every year to the year 2000-01. Although the graduating year for th is group of students was 1999-00, data were collected until the year 2000-01 to provide information on students not graduating “on time.” The goal of this investigation, utilizing logistic regression and survival analysis as the method of inquiry, is to report survival probabilities of Hispanic/Latino male student s. In other words, when are students at “greatest risk” for dropping out of school ? What are the students’ achievement characteristics as they re late to student dropout? The research questions this study addresses are the following: 1. What is the relation between age, ho me language, retention history, free/reduced lunch, program of studies behavior (disciplinary suspensions), reading achievement, mathema tics achievement, and GPA and dropping out of secondary school by Hispanic/Latino males? 2. At what grade levels do the predic tor variables begin to affect the male Hispanic/Latino students’ propensity for early school leaving? When are they at greatest risk?


52 In addition to computing and plotting the estimated survival functions, differences between the covariates on surv ival probabilities were interpreted. In the final analysis, this investigation tested the model to examin e which predictors were “best” for predicting dropout. All statistical analyses were computed using the Statistical Analyses Software package (SAS, 2000-2004). Participants The population from which the sample wa s drawn was contained within one of the school districts in the stat e of Florida. From the most recent data available on this district, the total number of Hispanic/La tino male students ente ring eighth grade was obtained. The data were collected from a ll public middle schools in the district (37 schools). The starting year was 1995 when th e student population was in eighth grade. These middle schools then funnele d the students into the dist ricts’ 19 high schools. Data were obtained for the subsequent years of the study, 1996 through 2000, from these schools. Although the projected graduating year for this group of students was 2000, data were collected until 2001 to be sure to in clude those students for which extra time was necessary for graduation. The students’ demographic information reco rds were used to identify the sample for this study (Hispanic/Latino males). In addi tion to individual va riables considered as predictors, multiple variables acting in concert to affect dropping out were analyzed. Differences in duration times of dropouts were investigated to identify the variables associated with leaving school.


53 Procedures A letter requesting student data from the sc hool district was sent to the head of the county school assessment and evaluation department. The importance of the research was noted in that information on the local situa tion of the dropout problem may be useful in acquiring resources to help thos e at risk and acquire funding for possible interventions. In order for the study to proceed, appr oval from the Institutional Review Board (IRB) indicating the st udy met federal guidelin es for the protection of human subjects was requested and obtained. This approval incl uded an agreement to participate in the study from the school district from which the data were obtained. The countyÂ’s approval was given under the following conditions: 1. The data to be used were fo r the years 1995-1996 through 2000-2001. 2. No additional data could be collected or used. 3. Confidentiality had to be assured for all pa rticipants. That is, all data had to be aggregated such that the district could not be iden tified as well as any other participant including parents, students, and administration. 4. Student data had to be destroyed wh en the project has been completed. The sample for this research was taken from the population of public school eighth graders in the district in the 1995-1996 school year. These st udents were in the 37 public middle schools in the dist rict. From the entire population of eighth graders in the county, using withdrawal c odes as criteria, the sample was made up of only those students who reported being Hisp anic/ Latinos and male and a ttended public school in the school district. The total number of Hispanic/Latino male stud ents in the collected sample was 1,076.


54 The data were coded by an identifica tion numbers only; this number was required to follow the student for the five year duration of the study. No names were used to insure anonymity. The data were collected from all middle schools in the district (37 schools); this sample was co mprised of Hispanic/Latino male students enrolled in the eighth grade during the 1995-96 academic year and followed for the subsequent five years. These middle school s fed students into th e districtsÂ’ 19 high schools. Data were obtained for the subs equent years of the study, 1996-97 through 2000-01, from these schools. As stated pr eviously, although the projected graduating year for this group of students was the 1999-2000 school year, da ta were collected through Spring 2001 to be sure to include those students for which up to one year extra time was necessary for graduation. Operational definitions and codes of the variables follow in the next section. Dependent Variable The dependent variable, time in days enrolled in this study, was calculated by adding the maximum number of days students we re enrolled for each of the six years of the study period. The years included in th is study are 1995-96 through to 2000-01. For the 1995-1996 school year the maximum number of days enrolled was 180 days. For 1996-97 and 1997-98, ninth and tenth grade, re spectively, the school year was made up of 180 days enrolled also. In the school years of 1998-99, and 1999-2000, the maximum number of days enrolled was 179 days. The la st year of the study was included as stated previously to include students needing an extra year to complete their education. This last year of 2000-01 had 184 days enrolled maki ng up the school year. Summing up the days enrolled for these six years results in a total of 1082 days in school.


55 Dropout or non-dropout (po ssibly censored), the status variable, is identified by the withdrawal codes used by th e school district. This district has 29 different withdrawal codes, of these, 17 were used as identific ation codes for this study sample. The first seven codes correspond to students who have dr opped out and the rema inder of the codes to the censored students. Those students w ho were defined as dr opouts were coded 1 and non-dropouts were coded 0. To identify the dropout students, the 17 withdrawal codes used are listed below: 1. W05 – Any student over compulsory attendance age who leaves school voluntary with no intention of returning. 2. W13 – Any PK-12 student withdraw n from school due to court action. 3. W15 – Any PK-12 student who is withdrawn from school due to non-attendance. 4. W21 – Any student who is withdraw n from the rolls due to being expelled from school. 5. W22 – Any PK-12 student whose whereabouts is unknown. 6. W24 – Any PK-12 student who is withdrawn from school to attend a home education program. 7. W26 – Any student who leaves to enter the Adult Program within the district prior to completion of graduation requirements. 8. W01 – Any PK-12 student promoted or transferred to another attendance reporting unit in the same school. 9. W02 – Any PK-12 student promoted or transferred to another school in the same district.


56 10. W2A – Any student who was withdrawn following an expulsion hearing resulting in a change of placement in lieu of expulsion. 11. W03 – Any PK-12 student who w ithdraws to attend another public school in or out-of-state. 12. W04 – Any PK-12 student who withdraws to attend a non-public school in or out-of-state. 13. W06 – Any student who graduated from school with a standard diploma. 14. W07 – Any student w ho graduated from school with a special diploma based on option one-mastery of st udent performance standards. 15. W08 – Any student who left school with a certificate of completion. 16. W12 – Any PK-12 st udent withdrawn from school due to death. 17. W27 – Any student w ho graduated from school with a special diploma based on option two-mastery of employment and community competencies. The censored students comprised the rema ining withdrawal codes that include codes identifying censorship such as graduati ng with a standard diploma, graduating with a special diploma, leaving school with a certif icate of completion, tr ansferring to another school, and other codes that identify the reas ons for students no longer “in” the school system. These are the students considered cen sored for the study. In other words, none experienced the event of intere st. They completed their education in some way or left and were accounted for by the school di strict’s withdrawal codes.


57 Independent Variables The independent variables for the study are the following: 1) age, 2) home language, 3) retention history, 4) free/reduced lunch, 5) program of studies (four levels), 6) behavior (disciplinary susp ensions), 7) GPA (State), 8) FCAT writing scores, 9) FCAT reading achievement scores and 10) FCAT mathematics achievement scores. The age variable, a continuous variable, was converted to months and then years for the analyses as a decimal to record yearly progress more accurately; this approach was used to better identify a more precise point in which events occurred. The home language variable was dichotomized fro m information gleaned from the data file. StudentsÂ’ school record applications ask two questions pertaining to language; one asks about a stud entÂ’s home language and a se cond asks about a studentÂ’s native language. For purposes of this study, if a studentÂ’s report identified Spanish in either the native or home category, then the language variable was noted as Spanish being the studentÂ’s language. If Englis h was noted in both the home and native categories, then the language variable was noted as Englis h being the studentÂ’s language. Spanish was coded 1 and English is coded 0. The retention history variable was also dichotom ized. Each individualÂ’s grade was reported and identified for the 5 years span, the duration of the study period. For those students whose grade was reported as the same for consecutive years, they were noted as having been retained. All others show ed that they were in eighth grade in 1995 and the twelfth grade in 1999. This variable wa s coded 1 for yes, at least once, and 0 for never retained.


58 Social Economic Status was determined by the meal status variable. District identifiers used in this study were: 0 – Did not apply 2 – Free Lunch 3 – Reduced Lunch 9 – Free Meals Direct Students identified with distri ct codes for free lunch, reduced lunch, and free meals direct were combined to identify the free/reduced lunch dichotomized variable. All others comprised the no free/reduced lunch category; for this study, non participation was coded 0 and participation was coded 1. The Program of Studies variable had 9 codes in the district. These were designated as follows: AS Academic Scholar, AT Academic Scholar / Technical Prep, CP College Prep, CT College / Technical Prep, GE – General, IB International Baccalaureat, TC Technical / Career, TP Technical Prep, and VO – Vocational. For this study, four categories were formed. Th e college preparatory category, coded 1, included the AS, AT, CP, CT, and IB program s. The technical preparatory category, coded 2 was made up of the TC, TP, and VO programs. The genera l studies category, coded 3 comprised the GE program of studies The fourth category, unclassified, was made up of the students without any classifications and was coded 4. This variable was then dummy coded for the analysis with the general studies as the reference category. Behavior (suspensions) was a continuous variab le and represents total incidents


59 reported. The district uses th ree separate variables to iden tify problematic behaviors by the students although this study used suspensions as the vari able of interest. Using the longitudinal data totals for the three variable s-disruptive behavior, disciplinary referrals, and suspensions-a correlation analysis wa s performed. Due to high correlation coefficients between suspensions and disr uptive behavior, r = .95, suspensions and referral history, r = .92, and disruptive behavi or and referral history, r = .86 respectively, the researcher used total number of suspen sions as the identifying behavioral variable. Achievement (GPA) was the first of the achievement predictor variables. Although the district records a district GPA and a state GPA, only the state was used for this analysis. The district incorporates a s cale that exceeds 4.0 due to specialized courses and therefore the researcher decided to keep the uniform 4.0 as the maximum for this study. The recorded GPA in 10th grade was used for this variable. For students missing a GPA for 10th grade, GPA in 11th or 12th grade was used for this study, if available. The three remaining achievement variab les (FCAT Writing, FCAT Reading, and FCAT Mathematics), were analyzed using th e districts FCAT scores for these subject specific variables. The Writing scores were repo rted on a scale of 1 to 6 scale in half unit increments. Although two types of writing are assessed, expos itory and persuasive, these were reported as one since too few students ha d scores for both. The FCAT Reading scale and the FCAT Math scales used the same s cale, 100-500. All FCAT scores were from the 10th grade administration of these standardi zed tests. A correlation analysis was performed to see the relationship of thes e three achievement variables and GPA (see Table 1).


60 In the Pearson correlation analysis, th ere were moderate to moderately high correlation coefficients ranging from .48 to .75 among the four achievement predictor variables of GPA, FCATWRIT, FCAT READ, and FCATMATH. As the FCAT achievement test scores go up, the state GPA sc ores tend to increase also and vice versa. The researcher used GPA as the identifying ach ievement variable due to the sample size being diminished considerably by including the FCAT achievement scores. All three FCAT scores cut the sample si ze nearly in half and so it wa s decided to use GPA as the sole achievement variable. Table 1 Correlation Coefficients of Achievement Predictor Variables _______________________________________________________________________ __ GPA FCAT FCAT FCAT________ Writing Reading Math GPA 1.00000 865 FCAT .49 1.00000 Writing 520 532 FCAT .52 .56 1.00000 Reading 495 471 496 FCAT .58 .48 .75 1.00000 Math 495 471 472 495 _______________________________________________________________________ Note: All correlations were statistically significant (x< .0001). This being a secondary analysis of collect ed data of public school students, there is the question of data accuracy. Prior to re aching the final database where the data are stored, student data are record ed and inputted by numerous in dividuals. Therefore there is no surefire certainty that all data entry was without error. This being the case, there is difficulty in establishing with absolute certa inty, the accuracy of the data in the study.


61 Hope and good faith acceptance that the data collection followed social research procedures properly and wit hout human input errors is acknowledged and warranted. Analyses The first data analyses were descriptive to ascertain the characteristics of the sample. Sample sizes of Hispanic/Latino male students, means, standard deviations and ranges were calculated. Differences betw een dropouts and non-dropouts were examined as well as those differences among the covari ates. Relationships and associations among demographic and achievement variables were re ported. Finally, surv ival probabilities and hazard rates were calculate d and interpreted. The independent/predictor vari ables are those listed belo w which were selected in a more heuristic method from those availabl e at the school district. Several survival models were developed and separate analyses performed to identify variables for inclusion. Time was the dependent variable a nd those “best” predicto rs were incorporated into the several models formulated. Models were developed to predict which students graduate and which do not graduate. The mode ls also examined whether the variables that predict dropping out at some specific ti me-point for some Hispanic/Latino male students were the same as those used to pr edict dropping out at a later time-point for other students. This survival analysis was conducted using longitudinal da ta on a cohort of Hispanic/Latino studen ts in grade 8 in 1995-1996 and followed for 6 years to 2000-2001. The event of interest was dropping out of school This study investigat ed the probabilities and hazard risks of this event the students’ success or failure to graduate from high school.


62 Description of the sample as a whol e was done by analyzing the duration of school engagement indirectly through two mathematical tran sformations of duration: (a) the survivor function and (b ) the hazard function. Thes e transformations remain meaningful in the face of censoring; in this study, censoring would include graduation or leaving the study prior to its 5 years span for “other” reas ons. The survival-probability distribution function at time t is the probability that a randomly-selected member of the population will “survive” beyond t : S(t) = Pr ob [survival beyond t]. The hazard function is the probability that a randomly-selected member of the populat ion will “dropout” in the interval between t and t + 1, give n that the individual has survived until the beginning of that same interval: h(t) = Pr ob [“dropping out” between t and t + 1 / survival until t ] (Anderson et al., 1980, p.205). This is followed by identifying survival probability times and predictors of duration by comparing survivor plots com puted separately for students who share specific values of the pr edictors in this study. The proportional hazards model, consid ered semi-parametric, has several advantages over parametric approaches in that it does not require the researcher to choose a particular probability distributi on to represent survival times, as do parametric methods. Second, the Cox regression, as it is ofte n called, can incorporate time-dependent covariates (i.e., those variable s that may change in value over the course of the study). Lastly, the proportional hazards model can readily accommodate both discrete and continuous measurement of event times.


63 As a foundation to understanding this pro cess, an explanation of the three different ways of describing probability di stributions will be introduced. First, the cumulative distribution function (cdf) of a variable T, denoted by F(t), is a function that tells us the probability that the variable will be less than or equal to any value t that is chosen. As an equation, it would look like this, F(t) = Pr{T t}. Knowing the value of F for every value of t, gives us all there is to know about the distribution of T. More commonly used in survival analysis is the closely related functi on called the survivor function, defined as S(t) = Pr{T>t} = 1 F(t). One can intuitively see the similarities. The survivor function gives the probability of surviving beyond t, a specific point in time (Allison, 1995). One of the research goals in the pres ent analysis was to compare survivor functions for the cohort of Hispanic/Latino ma le students in this sample. If the survivor function for certain individuals is higher or lower than the survivor function for other individuals, then these differe nces must be investigated. If the survivor functions among these individuals cross though, interpretations may be unspecifiable. A second way of describing probability distributions with continuous variables is the probability density function( pdf ). This function is defined as f (t) = ()()dFtdSt dtdt the p.d.f. is just the derivative or slope of the c.d.f.. The well established normal curve or bell-shaped curve as it is al so known to be associated w ith the normal distribution is given by its pdf, not its cdf (Allison, 1995). The major functions being used to relay th e results of this st udy are the survivor function and the hazard function. This latt er distributional func tion is called the


64 hazard function and has become more popular then the p.d.f. in describing distributions. This function is defined as h (t ) = 0limt Pr{tTttTt t …| instead of h (t ); some authors denote the hazard by (t) or r (t), (Allison, 1995). With this background on some basic understanding of three different ways of describing probability distributions, a more speci fic detail of the survival analysis method of this study can now be told This analysis incorporates a mathematical model most commonly used for analyzing survival data the Cox proportional hazards (PH) model. Of interest in this analys is is the survival experien ce of this cohort of eighth graders as they progress in their education. This study i nvestigated whether certain variables have confounding effects on student dropout in addition to interaction effects among several variables on student dropout Are these explanatory variables good predictors of surviving to graduation. Survival time T, denotes “days enrolled in school.” The explanatory variables were labeled X1, X2, X3,..,Xp. The variable X1 was the primary, “dropout variable.” The variables X2-X3...Xp were the extraneous variable included as possible confounder or in teraction covariates. The formula for the Cox Proportional Hazards model is usually written in terms of the hazard model fo rmula as follows: 10(,)()p ii iBXhtXhte this model gives an expression for the hazard at time t for an individual with a given specification of a set of expl anatory variables denoted by X, which represents a collection of predictor variables that is being modeled to predict an individual’s hazard. The Cox model formula says that the hazard at time t is the product of two qua ntities. The first of


65 these is the baseline hazard function, 0()ht. The second quantity is the exponential expression e to the linear sum of BiXi, where the sum is over the p explanatory X variables (Kleinbaum, 1996). The model contains 7 predictor variable s (i.e., age, home language, retention history, free/reduced lunch, program of studies (four leve ls), behavior (disciplinary suspensions), and GPA (State). The independe nt variables, as not ed above, summarize the joint influence among these variables on th e hazard-rate and allow for interactions to be evaluated. To evaluate the possible effects of the various variables on Hispanic/Latino dropouts, in addition to interpretation of potential interaction e ffects, a number of statistics were reported. These include: re gression coefficients corresponding to each variable in the model, standard errors of the regression coe fficients, p-values for testing the significance of each coefficient, and h azard ratios for the effect of each variable adjusted for other variables in the model. The last piece of information to be interp reted in this preliminary analysis is the P(PH). This information is used to evaluate the proportional hazards assumption. The value given is a p-value derived from a st andard normal statistic computed from the model output. Non-significance w ould be interpreted from a p-value larger than 0.10, indicating that the PH assumption is satisfied, whereas a small p-value, say less than 0.05, would indicate that th e variable being test ed does not satisfy this assumption (Kleinbaum,1996). In addition to the above analysis, survival curves for the sample of students were plotted, as well as survival curves adjusted for the effects of the various variable in the


66 different models. These curves give additional information describing model comparisons over the time period of the study. It is the surviv al curves along with hazard ratios which are of primary importance in survival analys is. Having survival times and the possibility of censoring are the reasons it is the preferred method over logistic regression, which considers only a dichotomous outcome. Summary The research design employed a longit udinal approach. The data were from a large urban school district in the state of Florida. The sample, consisting of Hispanic/Latino male students in the 8th grade in 1995-96, was follo wed every year to the year 2000-01. This investigation, using a local level data set, which included only Hispanic/Latino male students in the district, emphasized a focused look at the longitudinal data and put into perspective how the Hispanic/Latino male was affected by the variables and covariates under investigation. Specifical ly, this study looked at how Hispanic/Latino males and achievement characteristics relate to student dropout. In the final analysis, this investigation reported on the finding of the “best” model, the most predictive regarding which predictors have the greatest effects on students’ decisions to complete high school or dropout of school.


67 Chapter Four Results The goal of the analysis is to report surv ival probabilities of male Hispanic/Latino students of an urban school di strict in the state of Flor ida. Using SAS (9.01, 2004), a survival analysis is performed on data from the 1995-96 through 2000-01 study sample. Although conventional statistical methods (i.e ., linear regression, l ogistic regression) have difficulty in dealing with censoring, a logistic regression is applied to glean information for the last school year of the st udy in addition to the su rvival analysis on the longitudinal six years of the study. The chapter is divided in to three main sections with subheadings. Section one contains descriptive statistics of the data fo r both statistical analys es. Section two reports results of the logistic regression and section three reports the survival analysis using the proportional hazard method. These three sections are followed by a summary of the research findings. Descriptive Statistics of His panic/Latino Male Student Sample The time variable that was used for the study was measured and reported in days. The researcher decided to use da ys enrolled as the time to event variable since using days present for each year would then lead to brin ging the days absent as another covariate and clarity and simplicity of the data were important goals.


68 The data sample consisted of 1076 Hi spanic/Latino male students in 8th grade in the 1995-96 school year. Due to missing values on the achievement variable GPA, the sample size was reduced to 865 Hispanic/La tino male students. Of these 865 students, 268 (30.98%) dropped out of school and 597 (69. 02%) stayed in schoo l or withdrew for legitimate reasons (see wit hdrawal codes under dependent variable section and a frequency table of withdr awal codes in Appendix A) Although exceptional student education (ESE) was not a focus in the study, available codes of the study sample and frequencies are found in Appendix B. To illustrate the study sample in referen ce to the national status dropout statistics, the percentage of dropping out were slightly hi gher in the study than the national status dropout statistics (see Table 2). Whereas the national dropou t percentage for Hispanic/Latino students wa s reported to be 27%, the pr esent studyÂ’s Hi spanic/Latino male dropout percentage was 31%. Also of intere st in the national statistics is that male students are dropping out of school at a higher rate than female students, 57% to 43% respectively. Table 2 Percentages of Hispanic/Lati no Male Student Dropouts and Na tional Status Dropouts ________________________________________________________________________ National Status Dropouts (in millions) ________________________________________________________________________ Dropped Total Nation Ethnicity Gender Out of Sample (All) (W B H ) ( M F ) School (N) ________________________________________________________________________ Yes 268 31% 3.8 11% 7% 11% 27% 57% 43% No 597 69% 31.4 89% 93% 89% 73% 43% 57% Summary 865 100% 35.2 100%.......................... _______________________________________________________________________ Note: NCES, 2004, Status Dropout Rate in 2001, (16-24 year olds out of high school without a credential)


69 The independent variables in the model are: X1 = age, X2 = language, X3 = retention, X4 = free/reduced lunch, X5 = program of study 1 (Coll. prep), X6 = program of study 2 (Tech. prep.), X7 = program of study 4 (Unclassified), and X8 = behavior by suspension, X9 = GPA,. Three predictors are continuous a nd four are categorical with one of these (program of study) having several levels indicati ng the created dummy variables in the analysis. The mean number of days enrolled in school was 681.98 with a standard deviation of 223.89; the range of days enrolled was 781082 days (see Table 3). Summary statistics of the number of censored and uncensored values (the status variable) are as follows. Of the 865 students, 597 (69%) were censored a nd 268 (31%) were uncensored, in other words, 268 students experienced th e event, dropped out of school. Table 3 Descriptive Statistics on His panic/Latino Male Student Stat us/Days Dependent Variable _____________________________________________________________________________________ Dropped Total ______ Days___ __ Out of Sample M SD Skewness Kurtosis School (N) _______________________________________________________________________ Yes 268 31% 582.47 187.55 -0.03 -0.53 No 597 69% 726.66 224.62 -1.11 0.01 Summary 865 100% 681.98 223.89 __-0.67____-0.69___________ The distribution for the language variable was 490 (57%) Spanish speaking students and 375 (43%) English speak ing students (see Table 4). The retention distribution was 417 (48%) of the students were retained at so me point in their education while 448 (52%) of the student s were never retained.


70 Table 4 Descriptive Statistics on Hi spanic/Latino Male Student L anguage and Retention Variable _____________________________________________________________________________________ Dropped Total Language Retention Out of Sample Span Eng Yes No School (N) _______________________________________________________________________ Yes 268 31% 153 57% 115 43% 225 84% 43 16% No 597 69% 337 56% 260 44% 193 32% 404 68% Summary 865 100% 490 57% 375 43% 418 48% 447 52%______ The free/reduced lunch predictor had a distributio n of 588 (68%) of students taking part in the free/reduced lunch progr am while 277 (32%) were not in the lunch program (See Table 5). Program of study had four levels and the distribution of the categories was Table 5 Descriptive Statistics on Hispanic/Lati no Male Student Free/Reduced Lunch and Program Variable _____________________________________________________________________________________ Dropped Total Free/Reduced Lunch Program of Study out of Sample Hi Lo Col Tech Gen Uncl School (N) _______________________________________________________________________ Yes 268 31% 76 28% 192 72% 74 28% 134 50% 57 21% 3 1% No 597 69% 201 34% 396 66% 287 48% 218 37% 88 15% 4 1% Summary 865 100% 277 32% 588 68% 361 42%_ 352 41%_145 17% 7_<1% as follows: college preparatory was 352 ( 41%), technology preparatory was 361 (42%), general study was 145 (17%), and unclassified was 7 (<1%). The age predictor ranged from 15.83 to 20. 37 years, with a mean age of 17.69 and standard deviation of 0.64 years (see Table 6).


71 Table 6 Descriptive Statistics on Hispanic/ Latino Male Student Age Variable _____________________________________________________________________________________ Dropped Total _____________Age___ Out of Sample M SD Skewness Kurtosis School (N) _______________________________________________________________________ Yes 268 31% 17.85 0.69 0.57 0.47 No 597 69% 17.62 0.61 0.72 0.73 Summary 865 100% 17.69 0.64 0.69 0.65 _________ The next predictor variable was behavior. It ranged from 0 to 70 reported total suspensions with a mean score of 8.84 and a standard deviation of 10.43 suspensions (see Table 7). Table 7 Descriptive Statistics on Hispanic/Lati no Male Student Behavior Variable _____________________________________________________________________________________ Dropped Total __ __ Behavior________________ Out of Sample M SD Skewness Kurtosis School (N) _______________________________________________________________________ Yes 268 31% 15.09 12.05 1.03 1.29 No 597 69% 6.03 8.19 2.49 8.02 Summary 865 100% 8.84___10.43___ 1.77____ _3.63__________ The achievement predictor is GPA with a range of 0.33 to 4.00 state GPA. The mean GPA was 2.36 and the standard deviation was 0.60 (see Table 8).


72 Table 8 Descriptive Statistics on Hispanic/Lati no Male Student Achievement Variable _____________________________________________________________________________________ Dropped Total ________________GPA_________________ out of Sample M SD Skewness Kurtosis School (N) _______________________________________________________________________ Yes 268 31% 1.99 0.51 0.49 1.71 No 597 69% 2.52 0.56 -0.04 0.06 Summary 865 100% 2.36 0.60 0.10 __-0.03__________ As summary statistics are be ing reported, there is one mo re statistic that should be identified, graduate numbers. Of the sample total of 865 students, 344 Hispanic/Latino male students graduated with a standard di ploma, 3 with a special diploma based on option one-mastery of student performance st andards, 1 with a special diploma based on option two-mastery of student performance standards, and 1 with a certificate of completion. Adding these as an overall completi on of secondary education statistic, of the 865 Hispanic/Latino male students in the sixyear longitudinal study, 349 (40%) students completed their education by receiving a standa rd diploma, special diploma or certificate of completion. Logistic Regression Analysis A logistic regression was applied in this phase of the investigation. Whereas in the survival analysis the depende nt variable is time, specifica lly it will be days in school for the students, here in the logistic regr ession the dependent vari able is dichotomous, dropout or non-dropout. To assist in a sound interpretation, the assessment of the model will include an overall evaluation, tests of i ndividual predictors, goodness-of-fit-statistics, and predicted probabilities of the model.


73 Logistic Regression Analysis Results Overall Evaluation. The results of the overall eval uation testing th e global null hypothesis (all effects are null) i ndicates that the model is a better fit than the base-line (intercept-only) model. The test reports signifi cance in the model bein g a better fit to the data than the null model. Looking specifi cally at the likeli hood ratio statistic, significance was found with a, X 2 (9) = 326.4328, p <.0001. Tests of Individual Predictors. The logistic regression re sults for the longitudinal data showed that Predicted Logit of (D ropout) = -9.5709 + (0.5671) Age + (-0.1769) Language + (1.7165) Retention + (0. 3871) Free/Reduced Lunch + (-0.7152) College Preparatory + (-0.4164) Technica l Preparatory + (0.5947) Unclassified Program + (0.0513) Behavior + (-1.0873) GPA. The log of the odds of a student dropping out of school is positively related to a studentÂ’s retention history, positively related to a studentÂ’s behavior by suspension, negatively related to GPA, positively related to a studentÂ’s age, and negatively re lated to the college preparatory program of study (see Table 9). Five of the nine predictor variables were found to be statistical ly significant in the logistic regression model. Ke ying on odds ratios, retention history was a strong predictor in the model. Students made to repeat a gr ade had odds of dropping out that were 5 to 6 times the odds of those who were never retain ed during their educati on after adjusting for all the other variables in th e model. The second significant variable was GPA, this variable was negatively related to droppi ng out. A lower recorded state GPA for a student, resulted in a higher probability of dropping out of school, holding constant all other variables in the model. Next predictor of significance was positively related to


74 Table 9 Logistic Analysis of Maximum Likelihood Estimates of Dropping Out ____________________________________________________________________________________ Parameter Coefficient Standard Wald Odds /Predictor DF Estimate (B) Error (B) Chi-Square Pr > ChiSq____Ratio_ Intercept 1 -9.5709 2.5284 14.3288 0.0002 Age 1 0.5671 0.1376 16.9933 <.0001 1.763 Language 1 -0.1716 0.1900 0.8674 0.3517 0.838 Retention 1 1.7165 0.2130 64.9529 <.0001 5.565 F/R Lunch 1 0.3871 0.2142 3.2664 0.0707 1.473 College Prep 1 -0.7152 0.2667 7.1895 0.0073 0.489 Tech Prep 1 -0.4164 0.2532 2.7038 0.1001 0.659 Unclassified 1 0.5947 0.8752 0.4618 0.4968 1.813 BehSus 1 0.0513 0.00924 30.8434 <.0001 1.053 GPA 1 -1.0873 0.1930 31.7550 <.0001 0.337 _______________________________________________________________________ n = 865 dropping out. Students with behavioral pr oblems as reported by the number of suspensions they accumulated during thei r education had a significantly higher probability of dropping out of sc hool than those with few or no behavioral problems after controlling for all other va riables in the model. The age of a student was also found to be significant in rela tion to staying in school. The analysis indicates that the older a student is, the higher probability of the student dropping out before gr aduation, holding constant all other variables. Also of significance was the program of study variable, students decl aring a college preparatory had a lower probability of dropping out of school than students declaring general studies (the referenced group). Predicted Probabilities. The association of predicte d probabilities and observed responses show the extent to which high pr obabilities are associat ed with dropping out and low probabilities with staying in school. The c statistic, one of several measures of association, is 0.85. This tran slates to 85% of all possible pa irs of students with different


75 observed outcomes, one dropout and one non-dr opout, the model corr ectly predicted a higher probability for those students who dr opped out of school than the probability for those who stayed in school. Goodness-of-Fit-Statistics. In assessing the goodness of fit of the model to the outcome of staying in school or dropping out, the results are as follows. The HosmerLemeshow goodness-of-f it test yielded a 2 (8) of 14.0172 and was not significant with a value of p = .0813. This indicates the null hypot hesis of good fit can not be rejected at the .05 level. Although not significan t at the .05 level, the researcher felt compelled to investigate further the po ssibility of the interaction effects on the model. To investigate the possibility of a “better model” being available, several interaction variables were introduced to th e model. The goal is to see if adding the interaction variables will result in better f it as shown by Hosmer-Lemeshow test statistic and also to observe if the c statistic raises the predicted probability of the model. The first investigation incorporated inte ractions of all statistically significant predictor variables, comprising the following: age*retention, age*behavior, age*GPA, retention*behavior, retention*GPA and behavior*GPA. In the results of the model with the additional interact ion predictors, the Hosmer-Lemes how goodness-of-fit test yielded a 2 (8) of 8.1136 with a value of p = 0.4224, but many of the predictor variables were no longer statistically significant in the model. Eliminat ing the interaction predictors in order of non-significance resulted in a “best model” which inco rporated two of the six interaction variables (rete ntion*age, retention*behavio r) and provided adequate goodness-of-fit with a yielded 2 (8) of 8.0989, p=0.4239, at the .05 significance level. The model fit was better and the predicted probability c statistic was slightly higher at


76 0.86, almost identical to the previous model which had no inte raction predictors included in the model (see Table 10). Table 10 Logistic Analysis of Maximum Likelihood Estimates with Interaction Predictors ____________________________________________________________________________________ Parameter Coefficient Standard Wald /Predictor DF Estimate (B) Error (B) Chi-Square Pr > ChiSq_ Intercept 1 -21.6944 5.1645 17.6459 <.0001 Age 1 1.2101 0.2816 18.4640 <.0001 Language 1 -0.1953 0.1904 1.0515 0.3052 Retention 1 18.1978 5.8195 9.7783 0.0018 F/R Lunch 1 0.3777 0.2156 3.0692 0.0798 College Prep 1 -0.7160 0.2685 7.1118 0.0077 Tech Prep 1 -0.4012 0.2540 2.4947 0.1142 Unclassified 1 0.8080 0.9172 0.7761 0.3783 BehSus 1 0.1001 0.0229 19.1142 <.0001 GPA 1 -0.9936 0.1953 25.8885 <.0001 Age*Retention 1 -0.8915 0.3221 7.6621 0.0056 Retention*Beh 1 -0.0604 0.0248 5.9523 0.0147 _______________________________________________________________________ n = 865 Contrasting the results of the model in Table 9 and the model with interactions in Table 10 reveals several observations. The pred ictor variables which were found to be of significance in the model with no interaction variables were also found to be significant in the more complex model which included two interactions. Specifically, the variables which positively related to dr opping out were the same in both models. These variables were age, retention, and behavior. Contra sting the significant variables which were negatively related to dropping out, these we re also identical in both models. These predictor variables were the college preparatory program of study and the student GPA. It appears that the effects of retent ion are moderated by the age and behavior variables. To explore these interactions Fi gure 1 was created to show the probability of


77 dropping out as a function of age for four gr oups (retained students with low behavior problems, where low was defined as 0 on the be havior scale which ranged from 0 to 70; retained students with high behavior probl ems, where high was defined as 50 on the 70 point scale; non retained stude nts with low behavior proble ms; and non retained students with high behavior problems). Figure 1. Probability of Dropping Ou t as a Function of Age_(n=865)________________ Series 1 (Circles) are students not re tained with low behavior problems. Series 2 (Stars) are students not reta ined with high behavior problems. Series 3 (Squares) are students reta ined with low behavior problems. Series 4 (Triangles) are students reta ined with high behavior problems. The previously discussed main effects can be seen in the graph of Figure 1. Namely retained students are more likely to drop out, as are older students, and students with behavior problems. Perusal of the gra ph also reveals the rela tive position of the non retained high behavior problem group change s at different ages. The probability of dropping out for this group increases with ag e at a greater rate than the other three


78 groups. At age 16 the effects of retention a nd behavior problems are both notable but by age 18 the effects of behavior seem much more pronounced than the effects of retention. Another view of these results is to in terpret the odds of dropping out for these students. As the graph in Fi gure 2 shows, as a studentÂ’s behavior reports increase in numbers, it appears that the risk of dropping out for the student increases, and this general pattern exists whethe r a student is retained or not retained. For example, the odds of dropping out for a Hi spanic/Latino male student at age 16, retained, and with high behavior problems is approx imately 1.5 to 1, which stead ily increases to 2.5 to 1 as they reach 18 years of age. By contrast, a 16 year old student not retained with high behavior problems has lower odds of approxima tely .5 but has a steeper climb and results in odds of approximately 7 to 1 of dropping out by the time a stude nt is 18 years old. Also of note is the distance s hown in the series at the th ree age levels. The groups are much wider at 18 years of age than at 16 y ears of age although ag ain, the effects are nearly parallel for the retain ed groups as their odds of dr opping out slightly increase with age. As with the probabiliti es, the odds of dropping out among Hispanic/Latino male students not retained with high behavior problems show a st eeper and non parallel curve regarding behavior problems.


79 Figure 2. Odds of Dropping Out as a Function of Age_(n=865)_____________________ Series 1 (Circles) are students not re tained with low behavior problems. Series 2 (Stars) are students not reta ined with high behavior problems. Series 3 (Squares) are students reta ined with low behavior problems. Series 4 (Triangles) are students reta ined with high behavior problems. The behavior variable appears to have a st rong effect on dropping out whether in the non retained student group or the retained gr oup. Because the investigation of possible interactions was exploratory in nature, further investigation of the relationship among and between these variables and the effect it has on dropping out of sc hool is warranted. Survival Analysis The DURATION (time in days) variable was identified as days enrolled for each year. To get a total for each individual in the sample, days enrolled for each year were added for a sum total. Two other variables we re available for possible analysis, days


80 present and days absent but it wa s the decision of the researcher to use days enrolled for the overall attendance dependant variable. Of the six procedures that SAS software ut ilizes for survival analyses, this current study used the lifetest procedure as a starting point. Th e main portion of the research was completed using the phreg procedure which utilizes the proportional hazard model method of survival analysis. For each stude nt in the sample, the duration variable (DAYS for this study) contained either the time th e event of interest o ccurred (dropout) or, in censored cases, the last time the student wa s academically engaged (in school). This variable is the total sum of the days the student reported being enrolled for each year, 1995-96 through to 2000-01. A second variable (STATUS) indicates the status of the student at the time recorded in the DAYS variable. A widely used practice is to notate STATUS=1 for uncensored individuals (dropouts) and STATUS=0 for censored individuals. The data record also contains the values of the predictor variables: AGE, LANGUAGE, RETENTION, FREE/REDUCED LUNCH, PROGSTU (Program of study), BEHSUS (disciplinary suspensions), and GPA. This comprised the basic data structure for the survival analysis. The LifeTest Procedure Us ing Kaplan-Meier Estimator The lifetest procedure produces estimates of survival functions using two methods: the Kaplan-Meier method and the life-table or actuarial method. The K-M method is better suited for smaller data sets and precisely measured event times and the life-table method better for large data sets with event times measur ed crudely. As this data sample is fairly large and the even t times measured precisely, and there are no


81 constricting criteria on the KM method being used with larg e data sets, this method was utilized. The Kaplan-Meier (KM) estimator (als o known as the product limit estimator) is a popular method for estimating survival functions The collected sample consisted of 1076 Hispanic/Latino male students. Since there are no predictor va riables in this analysis, the entire sample was used in calculating survival functions. Since previous analyses used the sample consisting of 865 students, survival function estimates were calculated for this sample also. Due to the similar estimates in both, the sample consisting of 865 students were reported. Using the lifetest procedure, SAS produced the following results: at 78 days, which would coincide with approximately half a year of enrollment, the observation was censored, the KM survival estimate is undefined. At 181 days, which would coincide with approximately one year of enrollment the KM survival estimate is .9965. This means that the probability a student will surviv e for 180 days or more is estimated to be .9965 (see Table 11). The year and a half mark is approximately 272 days and the probability of survival KM estimate is .9834. At 362 days, approximately two years of enrollment, the probability of surviving this far or beyond KM estimate is .9565. Taking this same pattern of looking at th e KM estimates for the remaining years at half yearly intervals, the following probabilities are produced. At 452 days, approximately two and a half school years, th e KM survival estimate is .9075. Continuing with the next event time with an uncensored observation close to the three-year total of 541 produced a KM survival estimate of .8606 at 541 days. At the three and a half year mark, approximately 631 days, the KM estimate is .7964. Year 4 showed an estimated


82 probability of .7249 at 720 days, and at four and a half years a KM estimate of .6626 at approximately 810 days. Year 5 translated to approximately 899 days, the standard graduation time for this cohort produced a KM es timate of .5998. As can be seen in Table 10, this is the point in time that the risk set decreases from 34 8 students to 30 students due to graduation. The last se veral survival functions need to be interpreted with the knowledge that the sample now includes a sma ll number of students in the risk set. The last dropout occurred at 1076 days with a su rvival estimated at .1131. At 1082 days, the largest censoring time, the KM estimate is undefined. The next statistic to report is Failure, which is just 1 minus the KM estimate. This is the estimated probability of dropping out prior to the speci fied time. At 122 days or approximately half a year, the estimated pr obability of dropping out is about .00116; at 181 days, approximately one year of enrollme nt, it is .00351, less than one percent. At 272 days, which coincides with approximately one and a half year of enrollment, the failure statistic is .0166; at 362 days, the tw o year enrollment, it is .0435. At 452 days, coinciding with the two and a ha lf year of enrollment point, th e failure statistic is 0.0925; at 541 days, approximately three years of enrollm ent, it is .1394. Three and a half years of enrollment is at approximately 631 days and the failure statistic is .2036; at 720 days, the four year enrollment, it is .2751. At 810 days, approximately half way through this cohortÂ’s senior year in high sc hool, the failure statistic is .3 374; at 899 days, the standard graduation time, it is .4002; and at 1076 days, the last recorded dropout time, it is .8869.


83 Table 11 Estimates of Survival Function using the Li fetest Procedure and Kaplan-Meier Method. ____________________________________________________________________________________ Product-Limit Survival Estimates Non-Dropout Days NonStandard Dropout Risk Enrolled Dropout Dropout Error Number Set____ 0.00 1.0000 0 0 0 865 78.00* . 0 864 122.00 0.9988 0.00116 0.00116 1 861 179.00 0.9977 0.00233 0.00165 2 851 180.00* . 2 850____ 181.00 0.9965 0.00351 0.00202 3 848 203.00 0.9941 0.00586 0.00261 5 844 272.00 0.9834 0.0166 0.00440 14 820 325.00 0.9676 0.0324 0.00613 27 794 _360.00* . 35 767____ 362.00 0.9565 0.0435 0.00710 36 757 410.00 0.9361 0.0639 0.00858 52 726 450.00* . 73 690 452.00 0.9075 0.0925 0.0103 74 689 540.00 . 108 614____ 541.00 0.8606 0.1394 0.0124 109 613 570.00 0.8380 0.1620 0.0133 125 593 630.00* . 153 550 631.00 0.7964 0.2036 0.0147 154 549 720.00 0.7249 0.2751 0.0166 202 451____ 741.00 0.7053 0.2947 0.0171 214 423 760.00 0.6950 0.3050 0.0174 220 402 777.00 0.6827 0.3173 0.0177 227 387 794.00 0.6755 0.3245 0.0179 231 372 810.00 0.6626 0.3374 0.0182 238 348____ 899.00 0.5998 0.4002 0.0272 259 30 900.00* . 259 28 903.00 0.5758 0.4242 0.0351 260 24 1013.00 0.3393 0.6607 0.0821 266 6 1053.00* . 266 3 1070.00 0.2262 0.7738 0.1074 267 2 1076.00 0.1131 0.8869 0.0963 268 1 1082.00* . 268 0____ n = 865 NOTE: The marked* survival ( non-dropout) times are cen sored observations. Estimated probability (dr opout) of dropping out, prior to the specified time. In Figure 3, the estimates of the Kaplan-M eier survival function are plotted. As seen in the diagram, it is near the end of the studentÂ’s educa tion (close to graduation) that events most affect their school completion.


84 Kaplan-M eier M ethod Estim ated Survivor D istribution Function 0.00 0.25 0.50 0.75 1.00 SU R VIVAL TIM E IN D AYS 020040060080010001200 Legend:Product-Lim it Estim ate C urveC ensored O bservations Figure 3. Estimates/Plot of Survival Function using the K-M Method (n=865) Univariate Categorical Predictor Analysis, Testing for Differences The next analysis reported is a univariate analysis on the variables of interest. For the categorical variab les, it is recommended that one gr aphs and looks at the KaplanMeier curves for each of the gr oups. This will show the shape of the survival function for each of the groups and tell whether or not the groups have proportional hazards. This helps in determining whether there is a difference between levels of categorical predictors. Language. Does language have any effect on the survival experience of this student population? To test the null hypothesi s that there is no difference between the language groups, the Mantel-Haenszel Test (also known as the log-rank test) was calculated. Interpretation of the log-rank test of equality across strata resulted in no


85 differences found. The obtained Chi-squa re value for the predictor variable Language was not statistically significant, 2 (1)= 0.03, p= .86, at the .05 significance level. The similarity in the survival function for the 2 language groups [English coded 0, Spanish coded 1] can be seen in the gra ph (see Figure 4). The survival function are almost identical except for at the very begi nning and at the very end of the study time. Figure 4. Language Differences in the Survival Function (n=865) Retention. In addressing the question of whethe r retaining a student at any point between eighth and twelfth grade had an effect on staying in school, statistical significance was found. The chi-square value for the log-rank test of equality across strata statistic was statistically significant, 2 (1)=190.83, p<.0001. This indicates student retention negatively affected the studentÂ’s ove rall probability of re maining in school until graduation.


86 The graph of the survival function of each group of Retention (see Figure 5) displays survival curves that overlap at the beginning and then diverge for the remainder of the study. These separate and distinct paths of this variab le may suggest some violation of the proportional hazards assump tion. The consequences of this may be problematic in later analysis since proportionality is an assumption in the Proportional Hazards Model. An approach to address this possible violation will be further explained in the Proportionality Assumption section. Figure 5 represent the visual plots of su rvival functions testing for differences in the retention predictor groups [Not-reta ined code 0, Retained coded 1]. Students who Figure 5. Retention Differences in the Survival Function (n=865) had been retained at some point in their education had a higher probability of dropping out than students who had not been reta ined during their educational experience.


87 F/R Lunch. The next predictor variable free/reduced lunch, was also significant. There seems to be a significant effect on st aying in school or dr opping out whether the students participate or do not participate in the free/reduced lunch program. The chisquare value for the log-rank test of equality across strata statistic was statistically significant, 2 (1)=4.08, p=.04, at the .05 level. This indicates studentÂ’s participation affected the studentÂ’s overall probability of remaining in school until graduation. The survival curves for the two groups of the free/reduced lunch predictor (see Figure 6), shows an overlap in the beginni ng of the study but then separate out to somewhat proportional curves for the remai nder of the study [Nonfree lunch coded 0, Free lunch coded 1] Figure 6. F/R Lunch Differences fo r the Survival Function (n=865) The proportionality assumption proportional haza rds appears to have been met in this variable.


88 Program of Study. The program of study predictor variable was also significant. There seems to be a significant effect on st aying in school or dr opping out whether the students have decided on their long term e ducational goals. In th is analysis, the chisquare value for the log-rank test statistic was statistically significant, 2 (3)=119.27, p<.0001, at the .05 level. This indicates st udentÂ’s chosen program of study affected the studentÂ’s overall probability of remaining in school or dropping out. The graph of the survival curves (see Figur e 7) shows that thr ee of the four groups are somewhat proportional although one group (U nclassified) stands ou t with a distinct survival curve. Of the predictor variables anal yzed thus far, along with retention, this one has shown the second greatest effect. Figure 7. Program of Study Differences for the Survival Function (n=865)

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89 Proportional Hazards Model Testing The prediction model will now be analyzed with the goal of obtaining a model relating to dropping out of school for Hispanic/Latino male students. The model to be tested is one in which all the continuous and dummy coded categorical variables (age, language, retention, free/reduced lunch, coll ege preparatory, tec hnical preparatory, unclassified program, behavior and GPA) are entered simultaneously as predictors. Main Effects Analysis The next analysis is the modelÂ’s main effects (see Table 12). The age predictor variable is significant with a p-value of <.0001, holding all other variables constant. The retention variable, is also significant with a p-value of <.0001. The program of study predictor variable identifying college preparat ory educational goal, is significant with a p-value of .0016. The program of study vari able identifying thos e students choosing a technical preparatory educationa l goal, is also significant w ith a p-value of .0201. The program of study variable identifying those st udents not having been classified with an educational goal, is significant with a p-valu e of <.0001. The next predictor variable of significance is behavior, and it has a p-value of <.0001 and the achievement predictor variable GPA is also signifi cant at the p-value of <.0001. Further interpretation of Table 12 focu sed on the hazard ratios. This can be interpreted for dichotomous vari ables as the ratio of the estim ated hazard for those with a value of 1 to the estimated hazard of those w ith a value of 0, holding constant all other covariates. It can be interpreted for a conti nuous variable as the ra tio of the estimated hazard for those one unit higher on the predicto r relative to those one unit lower on the

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90 predictor. Looking at the age predictor, as a studentÂ’s age increases by one unit, and the remaining variables are held constant, the hazard rate of droppi ng out approximately Table 12 Analysis of the ModelÂ’s Main Effects using the Cox Proportional Hazards Model ____________________________________________________________________________________ Analysis of Maximum Likelihood Estimates Parameter Standard Pr > Hazard Vars DF Estimate Error Chi-Square ChiSq Ratio___ Age 1 0.72080 0.09716 55.0377 <.0001 2.056 Language 1 -0.17400 0.12793 1.8498 0.1738 0.840 Reten 1 0.01672 0.19079 28.3987 <.0001 2.764 F/R Lunch1 0.19157 0.14275 1.8008 0.1796 1.211 ColPrep 1 -0.57194 0.18073 10.0147 0.0016 0.564 TechPrep 1 -0.37144 0.15985 5.3993 0.0201 0.690 Unclass 1 4.13108 0.65158 40.1963 <.0001 62.245 BehSus 1 0.01925 0.00487 15.6064 <.0001 1.019 GPA 1 -1.42672 0.15324 86.6775 <.0001 0.240 n = 865 doubles. Regarding retention, for those students having been retained, while holding all the other variables constant, the hazard rate of dropping out was approximately two to three times greater than stay ing in school (i.e., it increase d by 276.4%). For the program of study predictor, college preparatory, holding all other variables constant, those students who chose a college preparatory prog ram, their hazard rate of dropping out was approximately half as likely as those in the general program of studies (referenced group), hazard ratio = .567 For the progr am of study technical preparatory, holding all other variables constant, the hazard rate of dropping out was approxima tely two-thirds as likely as the genera l program of study (referenced group), hazard ratio = .69. The behavior predictor, holding all others consta nt, as the studentsÂ’ behavior disciplinary reports increased by one unit ( on a 70 point scale), the h azard rate of dropping out

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91 increased by 2.0%. Finally, looking at the predictor GPA, the model indicates that as a studentÂ’s GPA decreases by one unit, and the remaining variables in the model are held constant, the hazard rate of Hispanic/Lati no male students dropping out of school was approximately four times as great. In ot her words, as GPA increases by one unit the hazard rate was reduced to about one quarter of what it was. Proportionality Assumption To verify that the model satisfies th e assumption of proportionality, the following analysis checks proportionality by including time-dependent covariates in the model. These time dependent covariates are the interactions of the predictor variables with time. Interpretation of the proportio nality test resulted in signi ficance of one time dependent covariate, as well as the covariates collec tively. The collectivel y obtained Chi-square value was statistically significant, 2 (9)= 27.94, p<.0001. Due to this significance, the assumption of proportionality has not been sa tisfied. Testing the i ndividual variables as time dependent covariates resu lted in retention*days being significant with a p-value of <.0001. The remaining time dependent covariat es were not significant with p-values greater than .05 as shown in Table 13.

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92 Table 13 Proportionality Assumptions Testing usi ng the Cox Proportional Hazards Model ____________________________________________________________________________________ Analysis of Maximum Likelihood Estimates Parameter Standard Pr > Hazard Vars DF Estimate Error Chi-Square ChiSq Ratio___ Age 1 0.74313 0.09822 57.2419 <.0001 2.103 Language 1 -1.20395 2.20747 0.2975 0.5855 0.300 Reten 1 -11.77982 2.67346 19.4147 <.0001 0.000 F/R Lunch1 -2.34047 2.70220 0.7502 0.3864 0.096 CollPrep 1 -4.14494 3.61647 1.3136 0.2517 0.016 TechPrep 1 3.03332 2.85112 1.1319 0.2874 20.766 Unclass 1 13.10893 13.77387 0.9058 0.3412 493330.5 BehSus 1 -0.02041 0.00483 17.9155 <.0001 1.021 GPA 1 -1.34986 0.15366 77.1731 <.0001 0.259 Lang_D 1 0.16594 0.35007 0.2247 0.6355 1.180 RET_D 1 2.04268 0.43010 22.5555 <.0001 7.711 SES_D 1 0.40665 0.42770 0.9040 0.3417 1.502 CollP_D 1 0.55631 0.56902 0.9558 0.3282 1.744 TechP_D 1 -0.54431 0.45413 1.4366 0.2307 0.580 Uncls_D 1 -1.66230 2.55390 0.4237 0.5151 0.190 n = 865 A solution to a non-proportional predictor is to stratify on th e predictor with a new model. This fits separate models for each level of retention, specifically, having been retained or never been retained. The model is under the constraint that the coefficients are equal but the baseline hazard functions are not equal. Running this an alysis resulted in the results shown in Table 14. Note this includes all predictors but retention. The parameter estimates for these predictors are al most identical to the values presented in Table 12, and thus the interp retation of the effects of t hose variables on dropout remains the same. Since the parameter estimates are al most identical to those in the model with retention as a proportional predictor, it can be co ncluded that it is not necessary to stratify on the predictor.

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93 Table 14 Non-Proportionality Testing by Stratifyi ng on the Retention Predictor (n=865) ____________________________________________________________________________________ Analysis of Maximum Likelihood Estimates Parameter Standard Pr > Hazard Vars DF Estimate Error Chi-Square ChiSq Ratio___ Age 1 0.72658 0.09757 55.4555 <.0001 2.068 Language 1 -0.17151 0.12811 1.7924 0.1806 0.842 F/R Lunch1 0.22052 0.14300 2.3780 0.1231 1.247 ProgS1 1 -0.57196 0.18091 9.9952 0.0016 0.564 ProgS2 1 -0.38147 0.15983 5.6964 0.0170 0.683 ProgS4 1 4.03335 0.67148 36.0797 <.0001 56.450 BehSus 1 0.01942 0.00483 16.1914 <.0001 1.020 GPA 1 -1.36567 0.14908 83.9134 <.0001 0.255 To further elaborate on the effects of rete ntion, a graph was used to illustrate the effects. Results of the retention predictor show the cumulative hazard of the retained group appears to rise at an in creasing rate (see Figure 8). As time advances, the hazard risk of students dropping out of school is gr owing greater whereas the risk of students never retained increases at a constant and lower rate.

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94 Log-Survival Function for R etention / D ays G roup 0.0 0.5 1.0 1.5 2.0 2.5 3.0 SU R VIVAL TIM E IN D AYS 020040060080010001200 STR ATA:R ETEN TIO N =0R ETEN TIO N =1 Figure 8. Cumulative Hazard Function for Retention. Summary and Conclusion The first section described the sample of Hispanic/Latino male students. Descriptive statistics on the predictor variable s and the dependent vari able were reported. In section two, a logistic regression analysis was performed and results interpreted. As stated earlier, significance was found in several of the predic tor variables. Of the seven variables of interest in th e research, all but language a nd free/reduced lunch were found to have a significant effect on whether Hi spanic/Latino male students dropped out of school or completed their education and gra duated. The effects on a student dropping out of school is positively related to a studentÂ’ s retention history, positively related to a studentÂ’s behavior by suspension, positively related to a studentÂ’s age, negatively related to GPA, and negatively related to the college preparatory program of study.

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95 Section three described and reported on su rvival analysis using the proportional hazard model method. There was significance in five of the seven variables in the analysis using the SAS Language phreg proc edure. The only variab les that were not statistically significant (p>.05) were the la nguage predictor and the free/reduced lunch predictor variables. In the survival analysis using th e proportional hazards method, the event of interest, dropping out of school, was positively related to a studentÂ’s age, positively related to a studentÂ’s retention hist ory and, positively related to a studentÂ’s behavior by suspension. Dropping out of school for this cohor t of Hispanic/Latino male students was negatively related to GPA, and ne gatively related to the college preparatory program of study. The results from the analyses will be discussed in the following chapter.

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96 Chapter Five Discussion Many empirical studies on high school dropout rates among minorities focus overwhelmingly on the same types of factors. These include characteristics of students and their families, such as, socioeconomic st atus, marital status of parents, education level of parents, immigrati on status, and number of sib lings. Further, many of these studies use the same national longitudinal data sets (e.g., Alsp augh, 1998; Natriello, 1986; Rumberger & Larson, 1998; Rumberger, 1987). This is advantageous on one hand but it also has its downside. On the positive si de, these studies have established patterns across time, but looking at only national data can obscure possibl e local trends. For instance, high school dropout rates among stude nts in Florida could be offset by lower dropout rates in Connecticut. General Findings General findings are organized in terms of the following research questions: 1. What is the relation between age, ho me language, retention history, free/reduced lunch, program of st udies, behavior (disciplinary suspensions), reading achievement, mathema tics achievement, and GPA and dropping out of secondary school by Hispanic/Latino males? 2. At what grade levels do the predic tor variables begin to affect the male Hispanic/ Latino studentsÂ’ propensity for early school leaving? When are they at greatest risk?

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97 First, this research found that approxim ately 31% of this Hispanic/Latino male sample dropped out prior to completing thei r high school educati on during the 5-year span. This is slightly higher than the na tional reported average of Hispanic/Latino dropouts of 27% for both genders but much highe r than the national average of 12.3% for all dropouts (Census Bureau, 2002). The most hazardous time for these students is well into their secondary ed ucation, very close to when th ey would actually graduate, during their junior to senior years. It may be the ti me close to their eighteenth birthday that lets them legally choose to leave school that triggers this hazardous time period. The significance of the age predictor in th is study reinforces the research of Shu (1988) which also found that the older the student, the higher probability of dropping out of school. Although language was not signi ficantly related to time to dropout, significance was reported in the retention variable at the 0001 alpha level. This is consistent with the findings of the Latino Co alitionÂ’s (2000) study reve aling that students had a higher probability of leaving school if they were identified as having been retained in grade. This is not just a Hispanic/Lati no male phenomenon. It is well documented that retention is an influence on st udentsÂ’ ability and desires to continue with their academic life (Rumberger & Thomas, 2000; Rumberger, 1995). The free/reduced lunch predictor in this study was comprised of whether a student was receiving free-lunch assistance or not part of this financia l assistance. Here as in the language predictor, there was no significan ce found in how this variable related to dropping out or staying in school. Although Rumberger (199 5) and others have found significance in the soci oeconomic variable, it may have been the categorical method of identifying SES for this study (free lunch) that produced the discrepant finding.

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98 To investigate the choices students make regarding their educa tional plans in high school, this group of Hispanic/Latino males was divided into four categories. These categories were college preparatory, technica l preparatory, general education, and those students who were not specified (unclassifie d). After creating dummy variables for this categorical variable, with ge neral education as the referenced group, the results were significant. This study found signi ficance in choosing college prep aratory, as it related to general education. Hispanic /Latino male students declar ing a college preparatory program of study were the group less likely to drop out of school. Significance was also found in choosing a technical preparatory pr ogram of study as it related to general education. This group was also less likely to drop out of school than the general education group. With the unc lassified group, students which had not declared any program of study, although also significant, it was negatively related to dropping out as it related to the referenc ed group. Students in the unclassi fied group were more likely to drop out of school. These findings are consistent with the fi nding of Alexander et al. (1997) who found that track placement was an extremely important pr edictor of dropout. This study looked at suspensions as a pred ictor in the model and found it also to be significant. As studentsÂ’ reported disciplinary problems increased, thei r likelihood of dropping out also increased at a significant le vel. Kramer (1998) examined dropout causes among race-ethnic and gender groups. The finding of the research coincide with the findings of the present analysis in that males reported school di sciplinary problems, academics, and economics as the main reasons they dropped out of school. In the Aviles, Guerrero, Howard, and Thomas (1999) study, attendance was one of several problematic

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99 areas reported by students who had dropped out of school, coin ciding with the results of the present study. The achievement variable for the study, GP A, was also found to be significant in predicting whether Hispanic/La tino males dropped out of school or stayed in school. The findings in this research agree with the findings of Fernandez, Paulson, and HiranoNakanishi (1989) who in their investigation of non-Hispanic whites, Blacks, and Hispanics by gender reported grades as a strong predictor of dr opping out for all three groups. Rumberger and Thomas (200) suggested that changes in school policies and a focus on academic performance would decreas e the dropout rate in their study of the NELS 88 school effectiveness study data. In addressing the time element of the rese arch, it was found that the greatest risk of dropping out occurred at appr oximately the eleventh grade. This period coincides with the student turning of age at which a student ma y drop out willingly. It is also the period that work may begin to play a larger role in a studentÂ’s responsibility to either family or personal relationships. Statistical Methods Comparison Both methods, the logistic regression and the proportional hazards model found statistical significance in identifying pred ictors of Hispanic/Latino male dropouts (see Table 15). Logistic regres sion analysis found age, retention, suspension, GPA, and college preparatory of the program variable to be statistically significant. Neither the technical preparation nor the unclassified program of study groups were found to be of statistical significance.

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100 The proportional hazards model also found ag e, retention, suspension, GPA, and college preparatory to be statistically si gnificant. In addition to finding statistical significance in the identical pr edictors found in the logistic regression, the proportional hazard analysis also found the technical prep aration and the unclassified group to be statistically significant. It appears the proportional hazard s model approach was more sensitive in detecting relationships in its calculations. Table 15 Comparative of Logistic Anal ysis and Survival Analysis ________________________________________________________________________ Logistic Regression Survival Analysis Parameter Odds Hazard /Predictor DF Pr > ChiSq Ratio_ Pr > ChiSq Ratio______ Age 1 <.0001 1.763 <.0001 2.056 Language 1 0.3517 0.838 0.1738 0.840 Retention 1 <.0001 5.565 <.0001 2.764 F/R Lunch 1 0.0707 1.473 0.1796 1.211 Coll Prep 1 0.0073 0.489 0.0016 0.564 Tech Prep 1 0.1001 0.659 0.0201 0.690 Unclass 1 0.4968 1.813 <.0001 62.245 BehSus 1 <.0001 1.053 <.0001 1.019 GPA 1 <.0001 0.337 <.0001 0.240 ________________________________________________________________________ n = 865 Conclusions StudentsÂ’ age, retention history, behavior problems program of study, and GPA are important factors in pr edicting whether students drop out of school. Although at the present time, and for several previous decades, holding a student back and having the student repeat a grade they ha d difficulty in completing has been the standard practice, this solution may be an area of educational practices that needs to be revisited. Age, retention, behavior, program of study, and GPA all seem to have an effect on whether a student decides to stay in school or drop out of school. This research found

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101 evidence that individually, these variable are im portant in investigating factors related to student dropout and it also found that the re tention effect is some what moderated by the age of the student and their behavior as re ported by disciplinary probl ems. More attention may need to be focused on such variables as we assess and eval uate how students are performing in school to better assist them and keep them from dropping out. The findings of this longitudinal analysis of fact ors affecting dropping out of school among Hispanic/Latino males will hopefully assist in coming up with remedies to this national problem. Limitations of the Study This study focused only on one school dist rict. Most student data are reported by schools and collected by district s. There are several other li mitations of this study which follow. First, due to the various definitions of variables and statisti cal computations used by districts, the results may not be generalizable beyond this school district and may in fact be unique to this school district (Hammack, 1986; Ekst rom, Goertz, Pollack, & Rock, 1986). Second, the variables examined are t hose which the school district uses for identification and academic performan ce purposes. Although some interesting relationships among certain variables would have been advantageous to this research to investigate (e.g., methods of instruction, p eer group interactions, intervention programs) it was not possible to obtain such data. According to Morro w (1986), there is no standard system for data collectio n and keeping track of students moving among schools or leaving the state. Many student s who have dropped out of sc hool show up as having left the district or state and there is no way to confirm what has actually happened to these “missing” students.

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102 A third area of concern to the present rese arch is the operational definition of the socio economic status predictor variable. A mo re precise description of the family and their socio economic status may have had a more pronounced effect had it been better defined and with several categories. Alt hough using meal program participation as a dichotomous predictor as was used in this study can be informative, limitations were present in the study. Another limita tion to the study was that it did not look at barriers or access to education issues for students. Barr iers such as inadequate school/district funding along with applying a holistic accomm odation process instead of considering individual circumstances need to also be investigated. Factors l ooking at students that refuse to or are unable to assimilate coul d also shed light on the dropping out problem. Access to the better performing schools is also worth a look to identify successful approaches to graduation. Lastly, since data collection and data en try involve many people, human error is likely somewhere along the process. Therefor e, unless one collects and enters all data personally, which would not automatically elim inate all errors, data quality may itself be a limitation. Future Research Additional studies would be he lpful to confirm some of the findings in the present investigation. The present study used a corr elational approach and replicating this research may result in added evidence to these findings. Replication studies on other schools from different districts may be looke d at and time frames may be lengthened or shortened depending on research queries of in terest. A continuation of this study may be comprised of comparing local da ta to other locales in the st ate. This study focused on one

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103 school districtÂ’s student level factors of demographics and ac hievement, future research could include school level factor s such as classes within scho ols, schools within districts, and districts within states for a more complex and thorough investigation. Also, having collected longitudinal data at the student, cla ss, local district, and state levels, multi-level statistical models may be applied to ascertain best fit and investigate those predictors solely and in combination having the largest e ffect on dropouts. This could lead to further study of including both male and female Hispanic/Latino students. In addition, future studies could include all st udents by ethnicity for a bett er understanding of student dropout. To further the study of the dropout phe nomena, all factors mentioned may be investigated using more comple x statistical analyses such as hierarchical linear modeling (HLM) and structural equation modeling (S EM). Also available are mixed methods approaches, a combination of qualitative and quantitative approaches, for a more robust description of the factor s associated with stude nts dropping out of school. One possible avenue to explore could be a more effective representation of the socio economic status (SES) predictor. This variable has been found to be a significant predictor of dropping out of school by several researchers (Alspaugh, 1998; Reyes, Gillock, Kobus, & Sanchez, 2000; Rumber ger & Larson, 1998; Rumberger, 1995). As this variable is widely used in educational research, a more comprehensive operational definition would be helpful in identi fying its effects with more precision. In addition, state level data may be inve stigated in relation to other states and aggregated national data that may be availa ble. Lastly, the dropout phenomena of all our

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104 students across our Nation needs to be addressed as we enter into the 21st century requiring competition for job and resources on a global level. This study reports the condition of Hispan ic/Latino male dropouts at the local level with data from one school district in the stat e of Florida. The population of males in eighth grade in 1995 was followed for 5 years to analyze their academic experience. Only a small number of variables were used in th is survival analysis that included age, language, retention, free/reduced lunch, program of studies, behavior, and GPA. Expanding on this research should include ot her empirically signifi cant variables as well as interaction effects of various combinati ons. More complex models are required and a deeper investigation of all factors that play a part in studentsÂ’ academic lives should be investigated. Recommendations In this study, the variables of interest we re those that a school district already had available. This limitation extends to an obvi ous recommendation to expand on the type of data collected by districts for future use in research. Continuing this thought would be to expand on the length of time used in the longitu dinal approach to the study. Results from the study showed that it may be much earlier than middle sch ool and high school that the problems of at risk students may be be ginning to develop. Al though the problems may start earlier, it manifests itself in 11th and 12th grade. It may very well be that 5 years worth of data is not enough to pinpoint problematic periods in studentsÂ’ lives for a better understanding of the dropout phenomenon. Although there is much discussion on both si des of the issue for the instituting of national standards, it would at least give res earchers the opportunity of looking at how

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105 the nation is doing educationally. Presently there is such vari ation in high school graduation requirements from state to state that it is difficult to get a clear picture not only of graduates but also of dropouts. The phrase “comparing apples to oranges” comes to mind but it is exactly what researchers are being asked to do in attempting to find solutions to the ever increasing number of dropouts across the United States. More research is needed on what keeps students in school and motivat es their learning in addition to what causes others to leave school. Solutions for the long term are necessary. They may be more difficult to implement but if chosen correctly, they may/will be the ones to produce the desired effects. Involvement in their children’s educati on by parents is a must for the academic success of students, especially those having difficulty due to th e various factors that have been explored in this re search (Pong & Dong-Beom, 2000; Peterson, 1996). Educators also need to be aware that these students are experiencing a rough time in the process of getting an education. The concept of empat hy, although easy to understand is much more difficult to implement in the everyday classroom In this specific in stance, we need to reach out to the Hispanic/Lati no communities if there is to be success in the education of Hispanic/Latino students. In reaching all of the stude nts having difficulty with completing their education, we need to re ach out to learn the reasons why they are deciding to drop out of school instead of graduating and ta king advantage of the new opportunities that are now available to them. The NCES data on the curre nt condition of dropouts repo rt approximately 11% of the students in the United States drop of school before graduating (NCES, 2003). The picture was fairly even when the issue of gender was investigated. Although males seem

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106 to dropout at a slightly highe r rate than females, there was no discernable difference. When looking at the ethnicity breakdow n, the alarming trend of Latinos disproportionately having such a large dropout percentage should not be overlooked. High school dropout survival rates naturally carry ove r to higher education opportunities. The U.S. Census of 1997 reporte d that 28% of people between the ages of 25 and 29 had completed a bachelorÂ’s degree, while only 11% of Latinos had managed the same (Driscoll, 1999). In 2002, Hispanic/Latinos of th is age group comprised 19.3% of the population with 10.3% completing a bach elorÂ’s degree (NCES, 2003). If we can increase the numbers of Hisp anic/Latino youth staying in hi gh school, we may likely see a decrease in other social problems, such as poverty and crime, and an increase in employment prospects and earning potential. To this end, this research is aimed at contributing to the empirical knowledge base of the Hispanic/Latino dropout phenomenon.

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112 Rumberger, R. W. & Thomas, S. L. (2000). The distributi on of dropout and turnover rates among urban and suburban high schools. Sociology of Education, 73, (1), 39-67. Sattin, G. A. & Somnath, D. (2001). The Ka plan-Meier estimator as an inverseprobability-of-censoring weighted average. The American Statistician, 55, (3), 207-210. Schumacker, R. E. & Denson, K. B. (1994). Interpreting significant discrete-time periods in survival analysis. Paper presented at the annual meeting of the American Educational Research Associat ion, New Orleans, La., April 4-8, 1994. Shu, G. J. (1988). The Determinants of Dropping Out of High Schools for Cuban Americans, Mexican Americans and Puerto Ricans. Dissertation, University of Wisconsin-Milwaukee. Seidman, E., Aber, J. L., Allen, L., & French, S. E. (1996). The impact of the transition to high school on the self-esteem and pe rceived social cont ext of poor, urban youth. American Journal of Community Psychology, 24, 409-515. Staman, E. M. (1979). Predicting Student Attrition at an Urba n College. Dissertation, The College of William and Mary in Virginia. Steele, C. (1997). A threat in the air: How stereotypes shap e intellectual identity and performance. American Psychologist, 52, 613-629. Tinto, V. (1982). Limits of theory and practice in st udent attrition. Journal of Higher Education, 53, (6), 687-700. United States Department of Education (1998). No More Excuses: The Final Report Of the Hispanic Dropout Project. Washington, DC. United States Bureau of the Census (2001). Current population survey, March 2000. Washington D.C.: Govern ment Printing Office. United States Bureau of the Census (2000). Statistical Abstract of the United States. Washington, DC: U.S Gove rnment Printing Office. U.S. Department of Educa tion (2003). National Center for Education Statistics. Projections of Educatio n Statistics to 2013. NCES 2004 – 013, by Debra E. Gerald and William J. Hussar. Washington, DC: 2003.

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113 U.S. Department of Educa tion (2003). National Center for Education Statistics. Status and Trends in the Education of Hispanics. NCES 2003 – 008, by Charmaine Llagas. Project Officer: Thom as D. Snyder. Washington, DC: 2003. U.S. Department of Educa tion (2001). National Center for Education Statistics. Dropout Rates in the United States: 2000. NCES 2002 – 114, by Phillip Kaufman, Martha Naomi Alt, and Christopher D. Chapman. Washington, DC: 2001. U.S. Department of Educa tion (2001). National Center for Education Statistics. Dropout rates in the United States:1999. Retrieved June 28, 2001, from U.S. Department of Educa tion (2000). National Center for Education Statistics. Information on public sc hools and school districts. Retrieved September 14, 2001 from U.S. Department of Educa tion (2000). National Center for Education Statistics. Key indicators of Hispanic student ac hievement: National goals and benchmarks for the next decade [on-line]. Available: Varlede, S. A. (1987). A comparative st udy of Hispanic high school dropouts and graduates: Why do some leave sc hool early and some finish? Education and Urban Society, 19, (3), 320-329. Velez, W. & Saenz, R. (2001). Toward a co mprehensive model of the school leaving process among Latinos. School Psychology Quarterly, 16, (4), 445-467. Willet, J. B. & Singer, J. D. (1995). It’s dj vu all over again: Using multiplespell discrete-time survival analysis. Journal of Educational and Behavioral Statistics, 20, (1), 41-67. Willet, J. B. & Singer, J. D. (1988). Doing data analysis with proportional hazards models: Model building, interpretation and diagnosis. Paper presented at the annual meeting of the American Educationa l Research Association, New Orleans, La, April 5-9, 1988. Winglee, M. (2000). A recommended appro ach to providing high school dropout and completion rates at the state level. Technical report, National Center for Education Statistics, Ja nuary 2000. NCES 2000-305.

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114 Appendices

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115 Appendix A: Withdrawal Code s Available and Frequencies Frequency: DNE – Any PK-12 student who was expected to attend a school but did not enter as expected for unknown reasons 617 W01 – Any PK-12 student promoted or transferred to another attendance reporting unit in the same school 164 W02 – Any PK-12 student promoted or tr ansferred to another school in the same district W2A – Any student who was withdrawn fo llowing an expulsion hearing resulting in a change of placement in lieu of expulsion 113 W03 – Any PK –12 student who withdraws to attend another public school in or out-of-state 7 W04 Any PK –12 student who withdraw s to attend a non-public school in or out-of-state 4 W05 – Any student over compulsory attendance age who leaves school voluntarily with no inte ntion of returning 376 W06 – Any student who graduated fr om school with a standard diploma 2 W07 – Any student who graduated from school with a special diploma based on option one-mastery of student performance standards 1 W08 – Any student who left school with a certificate of completion W09 – Any student who left school with a special ce rtificate of completion W10 – Any student who left school with a State of Florida High School Diploma (GED) W11 – Any PD-12 student withdraw n from school due to hardship 1 W12 – Any PK-12 student withdr awn from school due to death 2 W13 – Any PK-12 student withdraw n from school due to court action

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116 Appendix A (continued) W14 – Any student who withdraws from school to enter the military 98 W15 – Any PK – 12 student who is wit hdrawn form school due to nonattendance W16 – Any student who withdr aws from school to get married W17 – Any student who withdraw s from school due to pregnancy W18 – Any student who withdr aws due to medical reasons W19 – Any student who is withdrawn fr om school because exceptional student education programs are unavailab le due to the student’s age W20 – Any student who w ithdraws from school due to failing the Statewide Student Assessment Test, Parts I or II and who does not receive any of the certificates of completion 19 W21 – Any student who is withdrawn from the rolls due to being expelled from school 36 W22 – Any PK – 12 student whose whereabouts is unknown W23 – Any PK – 12 student who withdr aws from school for any reason other than those given above 7 W24 – Any PK – 12 student who wit hdraws from school to attend a home education program W25 – Any PK – 12 student who w ithdraws from school who is under compulsory attendance age 111 W26 – Any student who leaves to enter th e Adult Program within the district prior to completion of graduation requirements

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117 Appendix B: ESE Codes Available and Frequencies Frequency: 13 2010 Educable Mentally Handicapped (EMH) 3 2020 Trainable Mentally Handicapped (TMH) 3 2030 Severe / Profoundly Me ntally Handicapped (SPMH) 2031 Traumatic Brain Injury 2032 Other Health Injury 2038 Hospital Group – DU 2039 Hospital Group 2 2040 Physical Therapy 3 2041 Occupational Therapy 92 2050 Speech Impaired Part-Time 1 2051 Language Impaired Part-Time 2052 Hearing Impaired Part-Time 2060 Speech Impaired Full-Time 2061 Language Impaired Full-Time 2062 Hearing Impaired Full-Time 2068 Established Condition 2069 Developmentally Delayed 2070 Visually Handicapped Part-Time 2080 Visually Handicapped Full-Time 32 2090 Emotionally Handicapped Part-Time

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118 Appendix B (Continued) 29 2100 Emotionally Handicapped Full-Time 2101 Emotionally Handicapped Modified Day 85 2110 Specific Learning Disabilities Part-Time 45 2120 Specific Learning Disabilities Full-Time 2121 Specific Learning Disa bilities Modified Day 2122 Language Learning Disabilities Full-Time 58 2130 Gifted Part-Time 3 2140 Hospital / Homebound Part-Time 2143 Hospital / Homebound Tel 1-1 2144 Hospital / Homebound Tel l-2 2148 Hospital / Homebound PT Dual Enrolled 2150 Profound Health Care 14 2151 Severely Emotionally Disabled 2152 Multiple Handicaps Hard-of-Hearing & Blind 2153 Autistic

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119 About the Author Dorian Charles Vizcain received a Bachel orÂ’s Degree in Music Performing Arts from New Jersey City University in 1979 a nd a MasterÂ’s Degree in Education from the University of South Florida in 1995. Since en tering the Ph.D. program at the University of South Florida in 1995, he has taught measurement and statistics courses to undergraduates at all USF campuses and Hillsborough Community College. While in the Ph.D. program at the Univers ity of South Florida, he coauthored and published in the Florida Journal of Educational Research. Dr. Vizcain investigated numerous educational research problems as a member of research teams and solo projects. The results of these papers were presented at annua l research conferences that included, the Florida Educational Research Association (FERA), th e Eastern Educational Research Association (EERA), Association for General and Liberal Studies (AGLS), American Anthropological Asso ciation (AAA), and, the American Educational Research Association (AERA).


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