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The relationship between statistics self-efficacy, statistics anxiety, and performance in an introductory graduate statistics course
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Schneider, William Ray
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Adult Education
Adult Learners
Attrition
Research Skills
Self-confidence
Statistics Self-efficacy
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ABSTRACT: The purpose of this study was to determine the relationship between statistics self-efficacy, statistics anxiety, and performance in introductory graduate statistics courses. The study design compared two statistics self-efficacy measures developed by Finney and Schraw (2003), a statistics anxiety measure developed by Cruise and Wilkins (1980), and a course performance measure. To view self-efficacy from two perspectives, the Current Statistics Self-Efficacy (CSSE) assessed student confidence in their ability to complete specific statistics tasks in the present, whereas Self-Efficacy to Learn Statistics (SELS) assessed student confidence in their ability to learn statistics in the future. The performance measure was the combined average of the midterm and final exam scores only, excluding grades from other course activities. The instruments were distributed to four sections of an introductory graduate statistics course (N=88) in a College of Education at a large metropolitan university during the first week of the semester during Fall 2009 and Spring 2010. Both of the statistics self-efficacy measures revealed a low to moderate inverse relationship with statistics anxiety and a low to moderate direct relationship with each other. In this study there was no correlation between statistics anxiety (CSCS), statistics self-efficacy (CSSE and SELS), and course performance. There was high internal reliability for each instrument's items making the instruments suitable for use with graduate students. However, none of the instruments' results were significant in relation to course performance with graduate students in this sample. Unlike prior research involving undergraduate-level statistic students that has reported a relationship between the CSSE and SELS, the present study, involving graduate students, did not find any significant correlation with performance. Additional research is suggested to investigate the reasons for the differences between the studies.
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Disseration (Ph.D.)--University of South Florida, 2011.
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by William Ray Schneider.
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The Relationship Between Statistics Self Efficacy, Statistics Anxiety, and Performance in an Introductory Graduate Statistics Course b y William R. Schneider A d issertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Adult, Career, and Higher Education College of Education University of South Florida Major Professor: Waynne B. James, Ed.D Jeffrey Kromrey, Ph.D. James Eison, Ph.D William Young, Ed.D. Date of Approval March 24, 2011 Keywords: adult education ad ult learners, research skills, self confidence, attrition, CSSE, CSCS, SELS Copyright 2011, William R. Schneider

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Dedication To my mother Christine for teaching me to read. To my wife Marge for her many hours working with me through the edits and changes and her love, encouragement, and support during this epic journey

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A cknowledgements I extend thanks to my committee members for their guidance. To Dr. Waynne James for planting the see d and being the best editor in th e world. To Dr. James A. Eison for helping me to discover. To Dr. William H. Young for all the encouragement, and to Dr. Jeffrey D. Kromrey for being my compass when I was out in the wilderness. And for Dr. John M. Ferron for his support and for acting as the outside chair for both defenses. Thank you also to the graduate students who participated in the study and the faculty in the Measurement and Research department who gave me access to their students. Special thanks go to Anfield for giving me the ti me I needed to complete my research.

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i Table of Contents List of Tables ........................................................................................................ iv List of Figures ....................................................................................................... v Abstract ................................................................................................................ v i Chapter 1 Introduction ......................................................................................... 1 Statement of the Problem .......................................................................... 4 Purpose of the Study ................................................................................. 4 Research Questions .................................................................................. 4 Theoretical Framework .............................................................................. 5 Significance of the Study ........................................................................... 8 Limitations .................................................................................................. 8 Assumptions .............................................................................................. 8 Definition of Terms ..................................................................................... 9 Organization of the Study ........................................................................ 10 C hapter 2 Review of the Related Literature ....................................................... 11 Social Cognitive Theory ........................................................................... 11 Self Efficacy .................................................................................. 29 Motivati onal Force and Expectancy Theory .................................. 29 Acade mic and Statistics Self Efficacy ...................................................... 16 Current Research in Self Efficacy ............................................................ 17 Goal Orientation ....................................................................................... 21 Researcher Preparation ........................................................................... 22 Statistics Anxiety ...................................................................................... 25 Summary ................................................................................................. 26 C hapter 3 Methods ............................................................................................ 28 Research Design ..................................................................................... 28 Population and S ample ............................................................................ 29 Sample S electi on .......................................................................... 29 Instrumentation ........................................................................................ 30 Demographic Questionnaire. ........................................................ 31 Statistic al Anxiety Rating Scale (STARS) ..................................... 31 Computation Sel f Concept Subscale of the STARS ...................... 32 Validity ................................................................................ 34 Reliability ............................................................................ 34 Administration ..................................................................... 35

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ii Curren t Statistics Self Efficacy (CSSE ) and S elf Efficacy to Learn Statistic s (SELS) ............................................................ 3 5 Validity ................................................................................ 36 Reliability ............................................................................ 37 Administration ..................................................................... 38 Instrument Development P rocess ................................................. 38 Course Performance Measures .................................................... 39 Validity ................................................................................ 39 Reliability ............................................................................ 39 Administration ..................................................................... 40 Course Section Comparison ......................................................... 41 Data Collection ........................................................................................ 41 Time Line for Data C ollection ........................................................ 43 Data Analysis ........................................................................................... 43 S core R eliability ............................................................................ 44 Analysis by Research Q uestion .................................................... 45 C hapter 4 Results .............................................................................................. 48 Re sponse Rates for Participants ............................................................. 48 D emographic Characteristics of Participants ........................................... 49 Data Screening Methods ......................................................................... 54 The CSCS W ith P erformance ....................................................... 55 The CSSE W ith P erformance ........................................................ 55 The SELS W ith P erformance ........................................................ 55 ANOVA Results ............................................................................. 59 Means and Least Square Means .................................................. 60 Cronbach 's Alpha for Each I nstrument .......................................... 62 Findings and Results by Research Question ........................................... 63 Question 1 ..................................................................................... 63 Question 2 ..................................................................................... 65 Questio n 3 ..................................................................................... 66 Questio n 4 ..................................................................................... 66 Summary ................................................................................................. 69 Observations ............................................................................................ 73 Chapter 5 Summary, Concl usions, I mplications, and Recommendations ......... 75 Summary ................................................................................................. 75 Conclusions ............................................................................................. 78 Implications .............................................................................................. 82 Faculty .......................................................................................... 83 Students ........................................................................................ 86 Researchers .................................................................................. 86 Recommendations for Further Research ................................................. 88 R eferences ......................................................................................................... 91

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iii Appendices ......................................................................................................... 96 Appendix A Comparative Matrix for Self E fficacy Instruments ................. 97 Appendix B Demographic Questionnaire ............................................... 104 Appendix C Statistical Anxiety Rating Scale (STARS) .......................... 105 Appendix D Computational Self Concept Subscale (CSCS) .................. 108 Appendix E Current Statistics Self Efficacy (CSSE) ............................. 109 Appendix F Self E fficacy to Learn Statistics (SELS) .............................. 110 Appendix G Letter to Graduate Students ............................................... 111 About the Author ...................................................................................... End Page

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iv L ist of Tables Table 1 ANOVA and Coefficient of Determination Values for Course Section and Computational Self Concept Subscale ............................. 59 Table 2 ANOVA and Coefficient of Determin ation Values for Course Section and Current Statistics Self Efficacy .......................................... 59 Table 3 ANOVA and Coefficient of Determination Values for Course Section and Self Efficacy to Learn Statistics ........................................ 60 Table 4 Coefficient Alpha Estimates, Means, Standard Deviations, and Correlations of Study Measures ........................................................... 62 Table 5 Beta Weights and Uniqueness Indices Obtained in Multiple Regression Analysis Predicting Performance ....................................... 67

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v List of Figures Figure 1 R e lationship Between Efficacy Beliefs and Outcome E xpectations ......................................................................................... 6 Figure 2 Pie Chart of Percentages of Age Groups as Reported by Participants ......................................................................................... 50 Figure 3. Pie Chart of Percentages of Degree Programs in W hich Partici pants W ere Currently Enrolled .................................................. 51 Figure 4. Pie Chart of Percentages of Earned Degrees as Reported by Participants ......................................................................................... 52 Figure 5 Pie Chart of Percentages of Males and Females as Reported by Participants ......................................................................................... 53 Figure 6 Pi e Chart of Percentage of Race/Ethnicity as Self Reported by Participants ......................................................................................... 54 Figure 7 Scatter P lot of the Relationship Between Performance Scores and the CSCS (statistics anxiety measure) Total Score ..................... 56 Figure 8 Scatter P lot of the Relationship Between Performance Scores and the CSSE (current SE measure) Total Score 57 Figure 9 Scatter P lot of the Relationship Between Performance Scores and the SELS (future SE measure) Total Score ................................. 58 Figure 10. A Comparison of L east S quare Means for E ach of the Instruments by Course S ection ........................................................ 61

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vi Abstract The purpose of this study was to determine the relationship between statistics self efficacy, statistics anxiety, and performance in introductory graduate statistics courses The study design compared two statistics self efficacy measures developed by Finney and Schraw (2003), a statistics anxiety measure developed by Cruise and Wilkins (1980), and a course performance measure. To view self efficacy from two perspectives, the Current Statistics Self Efficacy (CSSE) assessed student confidence in their ability to complete specific statistics tasks in the present, whereas Self Efficacy to Learn Statistics (SELS) assessed student confidence in their ability to learn statistics in the future. The performance measure was the combined average of the mi dte rm and final exam scores only, excluding grad es from o ther course activities The instruments were distributed to four sections of an introductory graduate statistics course ( N Both of the statistics s elf efficacy measures reveal ed a low to moderate inverse relationship with statistics anxiety and a low to moderate direct re lationship with each other In this study there was no correlation between = 88) in a College of Education at a large metropolitan university during the first week of the semester during Fall 2009 and Spring 2010.

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vii statistics anxiety (CSCS), statistics self efficacy (CSSE and SELS), and course performance. There was high internal reliability for each instruments items making the instruments suitable for use with graduate students. H owever, none of the instruments results were significant in relation to course performance with graduate students in this sample. Unlike prior res e arch involving undergraduatelevel statistic students that has reported a relationship between the CSSE and SELS, the present study, involving graduate students, did not find any significant correlation with performance. Addi ti onal research is suggested to investigate the reasons for the differences between the studies

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1 Chapter 1 I ntroduction There are many reasons why doctoral students fail to complete their degree programs. According to Haynes (2004), Smallwood (2004), and Bair and Haworth (1999), nationwide the attrition rate in doctoral programs of study is as high as 40 to 50%. Although attrition and persistence rates vary by field of study and program, the main reasons given for the high attrition rates were lack of satisfaction with program of study, unsupportive department culture, lack of satisfactory dissertation progress, academic achievement in dicators, and employment and financial factors (Bair & Haworth, 1999). The reasons associated with student satisfaction with program of study as an indicator of degree completion described by Bair and Haworth are satisfaction with degree programs, required courses, and instructional quality. Bair and Haworth assert that students who believed the coursework was valuable and relevant, and who saw their own work as satisfactory, were more likely to complete their degrees. Since a series of research and stati stics courses are required for candidacy and eventually degree completion, student perceptions of confidence in their performance in statistics and statistics anxiety in those courses may co ntribute to doctoral attrition. Another contributing factor to wh ether or not students complete their doctoral programs may be their level of personal self efficacy beliefs in statistics and research related courses. Self -

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2 efficacy, or student perception of personal competence, may reduce the effects of statistics anxie ty, a major cause of attrition in statistics and research programs. According to Onwuegbuzie (2003), Between two thirds and four fifths of graduate students appear to experience uncomfortable levels of statistics anxiety. Indeed, for many students, stati stics is one of the most anxiety inducing cours es in their programs of study. . levels of statistics anxiety experienced by students can be so great that undertaking research methodology and statistics classes has come to be regarded by many as extremely negative (Onwuegbuzie, 1997a), and perhaps, more important, a major threat to the attainment of their degrees. (p. 1023) Onwuegbuzie (2003) suggests that students regularly delay taking courses related to statistics or research until they can no longer avoid it. . often waiting until the final t erm which is not ideal Although the exact number of statistics and research courses vary by discipline and institution, these required statistics and research courses may create a stumbling block that not all s tudents overcome. Based on a review of the universities classified as doctoral degree granting, large metropolitan university with very high research activity in the southeastern U.S. listed in the Carnegie Classification of Instit utions of Higher Educati on (2011), the number of statistics and research courses varies by college and program. The typical number of credit hours required in statistics and research is between 9 and 24. For example, Purdue University requires a minimum of 9 credit hours in foundations and research competencies. The University of Florida requires 22 credit hours of research coursework in their Higher Education Administration Ph.D. program. Auburn University requires 12 hours of research coursework, while the Educational Leader ship Specialization at Colorado State University requires 1518 credit hours of research core courses.

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3 Self efficacy has been defined by Bandura as the self beliefs students hold about their ability to complete specific tasks or actions successfully (1997) Self efficacy theory acknowledges the diversity of human capabilities. Thus, it treats the efficacy belief system not as an omnibus trait but as a differentiated set of self beliefs linked to distinct realms of functioning. Moreover, efficacy beliefs are differentiated across major systems of express i on within activity domains. . Efficacy beliefs are concerned not only with the exercise of control over action but also with the self regulation of thought processes, motivation, and affective and psychol ogical states (Bandura, 1997, p. 36) Self efficacy beliefs play a major role in a students confidence in the ability to complete advanced research (Unrau & Beck, 2004). By identifying the levels of statistics self efficacy of graduate students and the relationship to completion of doctoral level statistics coursework, faculty should be able to enhance the research skills of those graduate students who are identified as lacking specific levels of self efficacy by providing more help and encouragement in learning statistics. Statistics anxiety is defined as the negative thoughts and feelings experienced by an individual when encountering statistics in any form (Bandalos, Finney, & Geske, 2003; Onwuegbuzie, 2003; Wei & Tang, 2005). Finney and Schraw (2003) in their study found a negative correlation between statistics self efficacy as measured by the Current Statistics Self Efficacy (CSSE) scale and statistics anxiety. This suggests that where personal self efficacy is high, statistics an xiety is low or n on existent. In other words, when students are confident in their ability to complete certain statistics tasks or problems they will not experience high levels of statistics anxiety prior to taking a statistics exam.

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4 Statement of the Problem Little resear ch has been conducted on the relationship between statistics self efficacy, statistics anxiety, and performance for graduatelevel students Currently many graduate students may struggle with statistics courses because they do not have the personal self e fficacy to perform at the required level; and, therefore, students may delay their progress in statistics coursework --or leave the doctoral program altogether Onwuegbuzie (2003) states students expectations of their performance are an important manifest ation of their levels of self efficacy (p. 1023). Onwuegbuzie succinctly restates Banduras approach in a passage: Simply put, self efficacy theory predicts that an individuals belief system influence behavior choices, effort invested, persistence, and task success. According to this conceptualization, people tend to engage in activities that they believe they can undertake, control their efforts, persevere until this level of performance is accomplished, and then evaluate their performance according to previous expectations. (pp. 10221023) Purpose of the Study The purpose of this study was to investigate the relationship between statistics self efficacy, statistics anxiety, and performance in introductory graduate statistics courses. This study was concerned with the confidence of students who take the required statistics courses and who may have statistics self efficacy and statistics anxiety issues that impact their performance in statistics classes. Research Questions Research questions relat ed specifically to this study include:

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5 1. What is the relationship between statistics self efficacy and statistics anxiety? 2. What is the relationship between the Current Statistics Self Efficacy (CSSE) and Self Efficacy to Learn Statistics (SELS) and perform ance in a graduate introductory statistics course? 3. What is the relationship between statistics anxiety and performance in a graduate introductory statistics course? 4. What is the relationship between statistics self efficacy, statistics anxiety, and performance? Theoretical Framework The theoretical framework for the study encompasses social cognitive theory which, according to Bandura (1989), sees humans as self regulating organisms influenced and shaped by behavioral, personal, and environmental fac tors rather than reactive organisms shaped and shepherded by environmental forces or driven by concealed inner impulses (Pajares, 2002, p. 2). The relationship between behavioral, personal, and environmental factors is termed triadic reciprocal causation. It is believed that any of the factors that comprise the triad can be altered through varied teaching methods, support systems, and counseling services (Pajares, 2002). The theoretical framework of self efficacy (SE) and its application to statistics s kill development in doctoral student coursework provides the direct ion for this study.

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6 According to Bandura (1997), the outcome expectations include the physical, social, and self evaluative effects derived from a given course of action. Bandura (1997) st ated: In given domains of functioning, efficacy beliefs vary in level, strength, and generality (p. 22). The combination of the varying levels of SE of individuals produce specific outcomes. These SE beliefs have a greater influence on outcome expectat ions than ability alone (Bandura, 1997). Figure 1 depicts the influence that SE beliefs have on a persons outcome expectations. Figure 1. Relationship between efficacy beliefs and outcome expectations. Self efficacy theory suggests that personal beliefs effects behavior, level of personal effort, resolve, and task attainment in specific learning outcomes (Bandura, 1997). Bandura continues his explanation that: Perceived self efficacy is a judgment of ones ability to organize and execut e given types of performances, whereas an outcome expectation is EFFICAC Y BELIEFS Level Strength Generality OUTCOME EXPECTATIONS Physical Social Self evaluative PERSON BEHAVIOR OUTCOME

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7 a judgment of the likely consequences such performances will produce. Outcome expectations can take three major forms (Bandura, 1986a). Within each form, the positive expectations serve as incentives, the negative ones as disincentives. One distinct class of outcomes is the positive and negative physical effects that accompany the behavior. These include pleasant sensory experiences and physical pleasures in the positive forms and aversiv e sensory experiences, pain and physical discomfort in the negative forms. Human behavior is partly regulated by the social reactions it evokes. Positive and negative social effects form the second major class of outcomes. On the positive side, they inc lude such social reactions of others as expressions of interest, approval, social recognition, monetary compensation, and conferral of status and power; on the negative side, they include disinterest, disapproval, social rejection, censure, deprivation of privileges, and imposed penalties (1997, pp. 2122) Later Bandura writes This third major class of outcomes includes the positive and negative self evaluative reaction to ones own behavior (1997, pp. 2122) Physical effects, social effects and self evaluative reactions are the three forms of outcome expectations In a study conducted by Onwuegbuzie using a model of statistics achievement and anxiety called the Anxiety Expectation Mediation The importance of expectation in t he Anxiety Expectation Mediation (AEM) model suggests that the social cognitive theory (Bandura, 1977, 1986) in general, and the self efficacy theory in particular (Bandura, 1977, 1982, 1986, 1997), are pertinent to the processes underlying the learning of statistics because expectation is a manifestation of self efficacy. Self efficacy theory predicts that ones belief system influences behavior choices, effort invested, persistence, and task success in the learning of a foreign language (Bandura, 1977, 1982, 1986, 1997). Furthermore, the finding that expectation predicts statistics achievement suggests that a self fulfilling prophecy prevails, in which students who have low expectations of their statistics ability exhibit behaviors that may lead to under achievement (Onwuegbuzie, 2003, p. 1033) (AEM) model, he indicates:

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8 Significance of the Study Accor ding to Bair and Haworth (1999), traditional academic indicators are not reliable predictors of persistence to the doctoral degree (p. 18). Thes e indicators include undergraduate i nstitution attended, holding a masters degree, length of time between degrees, bachelors or masters degree major, amount of time taken to complete the masters, and GPA for the last two years of undergraduate study (Bair & Haworth, 1999). The traditional indicators mentioned previously measure a construct different than that of personal self efficacy beliefs in graduatelevel statistics classes, and do not tap into students self beliefs about their capacity to complete certain tasks and goals required to successfully pass graduate statistics coursework. Limitations This research design was limited to participants who were graduate students at a doctoral degree granting, large metropolitan university with very high research activity in the s outheast ern U .S These graduate students cannot be interpreted as being representative of graduate students at all universities. Three of the measurement tools used in this study may not have been appropriate for College of Education graduate students as anticipated. Possible differences in age, education and/or experiences may have impacted the results of the three instruments. Assumptions It was assumed that all students answer ed the instrument items accurately and truthfully to the best of their ability.

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9 Definition of Terms The following terms used throughout this study are defined as follows: Computational Self Concept subscale (CSCS) of the Statistics Test Anxiety rating Scale (STARS) subcomponent of instrument designed to measure the anxiety level of students in relation to their concern about taking statistics tests. Current Statistics Self Efficacy (CSSE) Instrument designed by Finney and Schraw (2003) to measure students personal beliefs about their current ability to comp lete specific statistics tasks. Grad uate student A student enrolled in a graduate program of study at an accredited university. Introductory statistics The introductory statistics course in the College of Education (COE). This course is typically taken first in the series of statistics cou rses and is either tak en as a required course or as an elective. On line course Course delivered via internet using Blackboard with instructors guidance. Performance measure The performance measures for this s tudy were based on the combined midterm and final exam scores in the introductory statistics course. The actual value of the performance measure is derived from the c ombined scores divided by two. Self efficacy The personal beliefs held by individual s that t hey possess the capacity to complete cer tain tasks in certain domains of functioning, under certain conditions (Bandura, 1997). Self Efficacy to Learn Statistics (SELS) Instrument designed by Finney and Schraw (2003) to measure a students personal beliefs in their ability to learn to complete specific statistics tasks in the future Statistics anxiety The physical, psychological, and emotional triggers experienced by a student when confronted with assignments, tests, or other deliverables (Bandalos, Finney, & Geske, 2003). Traditional classroom course Course delivered in the usual oncampus classroom setting.

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10 Organization of the Study Chapter 1 is an introduction to the study and establishes a framework for the research, including the problem, purpose, research questions, theoretical framewor k, limitations, assum ptions, and definition of terms Chapter 2 is a review of the literature related to social cognitive theory, academic and statistics self efficacy, current research in self efficacy, goal orientation, researcher preparation, statistic s anxiety and summary. Chapter 3 reports the research design, population and sample, instrumentation, data collection, and data analysis. Chapter 4 is the prese ntation of the research finding s which includ es an explanation of participant response rates, a description of the characteristics of the participants, data screening methods, findings and results of the research questions, and a summary Chapter 5 includes the summary, conclusions, implications, and recommendations for further research .

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11 Chapter 2 Review of the Related Literature The purpose of this study was to investigate the relationship between statistics self efficacy, statistics anxiety, and performance in an introductory graduate statistics course. The parts of this chapter include a review of social cognitive theory, academic and statistics self efficacy, current research in self efficacy, goal orientation, researcher preparation, statistics anxiety, and summary Social Cognitive Theory Self efficacy and human agency are components of soci al cognitive theory. Social cognitive theory also includes two causal components: the development of competencies and the regulation of action (Bandura, 1997, p. 34). Bishop and Bieschke (1998) studied the development of research interests using social cognitive theory. They suggest that, based on a model of social cognitive theory, students will engage in research based on their perceptions of the rewards or punishments for engaging in such research activities. Shivy, Worthington, Wallis, and Hogan ( 2003) state that when students conduct research they may feel rewarded or punished depending on their experiences. According to Pajares (200 2), the classes of determinants ( behavioral, personal, and environmental factors ) are the foundations of social cognitive theory. Pajares believes that the behavioral factors influence the personal

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12 factors and the environmental factors. Each influences and shapes the others. Pajares writes : Human functioning is viewed as the product of a dynamic interplay of personal behavioral, and environmental influences. For example, how people interpret the results of their own behavior informs and alters their environments and the personal factors they possess which, in turn, inform and alter subsequent behavior. This is the foundation of Bandura's (1986) conception of reciprocal determinism, the view that (a) personal factors in the form of cognition, affect, and biological events, (b) behavior, and (c) environmental influences create interactions that result in a triadic rec iprocality (2002, p. 1) Graduate students work to develop the knowledge and skills to become producers of original research. In the pursuit of this goal, students exert some control over how they learn. Their beliefs in their ability to learn are relat ed to their past educational experiences, their support systems, and their ability to persevere in challenging situations such as graduate study. These belief systems are a part of what Bandura (1997) calls human agency. Human agency is defined as a pers ons ability to carry out a course of action intentionally. According to Bandura (1997) effects are not the characteristics of agentive acts; they are the consequences of them (and). . the power to originate actions for given purposes is the key fe atur e of personal agency. . Beliefs of pers onal efficacy constitute the key factor of human agency (1997, p. 3) Self Efficacy Self efficacy is defined as a persons level of confidence in his ability to perform specific tasks under specific conditions or situations. Personal beliefs of performance precede outcomes ( Bandura, 1997). Bandura states that the outcomes people anticipate depend largely on their judgments of how well they will be able to per form in given situations (p. 23). Prior

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13 experiences personal beliefs, and vicarious experiences are all influential in a persons development of personal self efficacy. The causal relationship between beliefs of personal self efficacy and outcome expectations was previously discussed (Bandura, 1997). By influencing the choice of activities and the motivational level, beliefs of personal efficacy make an important contribution to the acquisition of the knowledge structures on which sk ills are founded (Bandura, 1997 p. 35). Bandura postulates that perceived self efficacy is concerned with an individuals judgment of his ability to achieve a desired level of performance. Bandura (1997) states that performance expectations (outcomes) are affected by the important part self efficacy plays in social cogniti ve theory. There are three levels of self efficacy (SE) generality assessment. At the most basic level, SE is measured for a particular performance under a specific set of conditions (Bandura, 1997, p. 49). At the second highest level, SE is measured for a class of performances within the same activity domain under a class of conditions sharing common properties (Bandura, 1997, p. 49). And at the highest level (or global level), measures of perceived SE are taken without specifying the activities or the conditions under which they must be performed (Bandura, 1997, p. 49). Bandura (1997) states that the optimal level of generality at which self efficacy is assessed varies depending on what one seeks to predict and the degree of foreknowledge of the situational demands ( p. 49). The current study will be assessed at the specific or basic level of SE: statistics tasks under a specific set of conditions.

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14 Motivational Force and Expectancy Theory Scholl (2002b) defines motivation as the force that: En ergies Behavior -What initiates a behavior, behavioral patterns, or changes in behavior? What determines the level of effort and how hard a person works? This aspect of motivation deals with the quest ion of "What motivates people? ( para. 2) Directs Behavior -What determines which behaviors an individual chooses? This aspect of motivation deals with the question of choice and conflict among com peting behavioral alternatives. (para. 3) Sustains Behavior -What determines an individual s level of persistence with respect to behavioral patterns? This aspect of motivation deals with how behavior is sust ained and stopped. (para. 4) Motivational force and expectancy t heory are influenced by personal self efficacy (Scholl, 2002 b ). According to Bandura (1997), self efficacy beliefs affect the nature and intensity of emotional experiences: through the exercise of personal control over thought, action, and affect (p. 137). Bandura (1997) states: The thought oriented mode in the regulation of affective states takes two forms. Efficacy beliefs create attentional biases and influence whether life events are construed, cognitively represented, and retrieved in ways that are benign or emotionally perturbing. The second form of influence centers on perceived cogniti ve abilities to control perturbing trains of thoughts when they intrude on the flow of consciousness. In the actionoriented mode of influence, efficacy beliefs regulate emotional states by supporting effective courses of action to transform the environme nt in ways that alter its emotive potential. The affect oriented mode of influence involves perceived efficacy to ameliorate aversive emotional states once they are aroused ( p. 137) According to Scholl (2002 a ), certain situations cause individuals to ex perience emotional states or reactions. Scholl continues Emotional reactions are in reality, physiological states (e.g., changes in blood pressure, heart rate,

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15 chemical secretions) that we feel under certain situations (2002 a p ara. 2). These reactions under certain situations influence individual beliefs about the ability to complete certain tasks and/or achieve specific goals. And these tasks choices are further influenced by the expectancy value individuals place on effort to achieve these chosen tasks and goals (Scholl, 2002a ). Expectancy theory describes how individuals make choices based on various behavioral options. Expectancy theory postulates that personal beliefs about ones ability to achieve specific desirable outcomes can increase the mot ivation to perform particular tasks or activities (Bandura, 1997). Motivational force is the mechanism to achieve desired outcomes and e xpectancy value theory is a component of m otivational force. Scholl (2002b) states that there are three components of m otivational force Expectancy theory is one component. The other two components are instrumentality and v alance. Instrumentality is the belief by the performer that high performance will lead to a desired outcome. Valance is an individuals belief in t he value of a desired outcome. If individuals believe the reward to be great, they will invest more effort in the performance and goal achievement. Expectancy theory is the belief that an individuals effort will lead to good performance. Self efficacy, goal difficulty, and perceived control all influence the individuals expectancy beliefs and goal performance (Scholl, 2002 b ). Bandura asserts : In expectancy value theory, motivation is regulated by the expectation that a given course of behavior will produce certain outcomes and the value placed on those outcomes. But people act on their beliefs about what they can do as well as on their beliefs about the likely outcomes of

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16 performance. The motivating influence of outcome expectancies is thus partly gove rned by efficacy beliefs. There are countless attractive options people do not pursue because they judge they lack the capabilities for them. The predictiveness of expectancy value theory is substantially enhanced by including the influence of perceived self efficacy (Ajzen & Madden, 1986; deVries, Dijkstra, & Kuhlman, 1988; Dzewaltowski, Noble, & Shaw, 1990; Schwarzer, 1992) ( Bandura, 1995, p. 7) Academic and Statistics Self Efficacy Self efficacy can be measured at the global level, the domain level, or the taskspecific level (Bandura, 1997; Finney & Schraw, 2003; Lent, Brown, & Gore, 1997). Measures of academic self efficacy would be considered a global measure. Some researchers have suggested that self efficacy, in general, and different levels o f self efficacy measures, can be hypothesized to exist in a hierarchical relationship where a persons self efficacy beliefs move from the general to the more specific task levels within similar domains (Bandura, 1997; Lent, Brown, & Gore, 1997). As indiv iduals begin to believe that they are capable of completing a specific task at the desired level of performance, it is then possible for them to transfer those personal self efficacy beliefs to more global self eff icacy contexts (Bandura, 1997). Statistics self efficacy measures were reported by Finney and Schraw (2003). Statistics self efficacy is defined as individuals confidence in their ability to complete specific statisticsrelated tasks. Prior to the Finney and Schraw study, the closest self effic acy research related to statistics were measures of ma th self efficacy. Bandura (1997), Pajares (2002), and Schunk and Pajares (2002) state that in order to better predict performance, measures of self efficacy should be task specific and directly related to the domain of interest. Finney and

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17 Schraw (2003) state that measures of math SE (or confidence in ones ability to complete math problems) were found to be better predictors in problem solving performance than confidence to succeed in math related c ourses or to perform math related tasks (2003, p. 162). They also state that: Along the same lines, confidence to receive an A or B in a mathrelated course was the best predictor of mathrelated major. While the particularized measure of self effic acy was the best predictor of the corresponding task, it was also found that each measure of math self efficacy was related to both criterion measures. This implies that domaingeneral self efficacy is somewhat generalizable to specific tasks within that domain; however, the closer the correspondence between the task and self efficacy assessment, the better the predic tion of performance on the task ( Finney & Schraw, 2003, p. 163) Although statistics self efficacy shares some of the same domain characteri stics as math self efficacy, the two are different enough to be considered two separate constructs since they are very different at the task level. Finney and Schraw (2003) state Task specific self efficacy judgments should be better predictors of perfor mance than domain specific judgments, which in turn, should be better predictors than domainrelated judgments (e.g., learning mathematics) (p. 162). Current Research in Self Efficacy Personal self efficacy has been studied in many different domains. Som e of the domains have included mathematics self efficacy, research skills self efficacy, statistics self efficacy, and general academ ic self efficacy to name a few. See Appendix A for a synopsis of the instruments related to self efficacy mentioned throughout this chapter. The data in this chart include the constructs

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18 and the validity and reliability reported by the instrument developers, as well as other explanatory information. Self efficacy research, related to academic or researcher skills, has been st udied by various scholars (Bong, 1998; Finney & Schraw, 2003; Forester, Kahn & Hesson McInnis, 2004; Holden, Barker, Meenaghan, & Rosenbe rg, 1999; Schunk & Pajares 2002; Silver, Smith, & Green e 2001). In the past 10 years, numerous researchers have attempted to identify and define the construct of research self efficacy. According to Forester et al. (2004), research self efficacy may be defined as ones confidence in successfully performing tasks associated with conducting research (e.g., performing a literature review or analyzing data) (p. 4). Forester et al. (2004) conducted confirmatory factor analysis of three measures of research self efficacy: the Res earch Self Efficacy Scale ( originally created by Greeley, Johnson, Seem, Braver, Dias, & Evans i n 1989 ) (Holden, Barker, Meenaghan, & Rosenberg, 1999) and later adapted by Bieschke, Bishop, and Garcia ( 1996) ; the Self Eff icacy in Research Measure by Phillips and Russell ( 1994) ; and the Research Attitudes Measure developed by OBrien, Malone, Schmidt, and Lucas ( 1998) In addition two other scales were also developed. The Research T raining Environment Scale created by Gelso, Mallinckrodt, and Judge (1996) and the Research Self Efficac y scale created by Holden et al. ( 1999 ) Of the many scales created to meas ure research self efficacy, the Research Self Efficac y S cale, the Research Training Environment Scale, and the

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19 Research Attitudes Measure were designed to measure the research self efficacy beliefs of graduate science students. Whereas the Self Ef ficacy in Research Measure and the Research Self Efficacy Scale were designed to measure the research self efficacy beliefs of counseli ng psychology graduate students. N o research studies specifically assessing the statistics self efficacy beliefs of doct oral students enrolled in Colleges of E ducation could be found. Statistics self efficacy measures are few Only two instruments, Current Statistics Self Efficacy (CSSE) and Self Efficacy to Learn Statistics (SELS) have been developed (Finney & Schraw, 2003). The CSSE (current SE measure) and the SELS (future SE measure) instruments measure the relationships between statistics self efficacy and statistics performance and the increase of statistics self efficacy at the end of an introductory statistics course for groups of undergraduate s tudents. In Finney and Schraw, the CSSE (current SE measure) and SELS (future SE measure) instruments were compared to: g eneral test anxiety (Test A nxiety Inventory) statistics test anxiety ( Survey of Attitudes Toward Statistics ) Mathematics Self Efficacy Scale Revised and statistics performance measures. The cons truct of self efficacy is more accurate at predicting outcomes when it is specific in its measurement. It is therefore necessary to differentiate between the m ore global cons truct of academic self efficacy and the more specific constructs such as research self efficacy and statistics self efficacy (Bandura, 1997).

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20 Academic self efficacy was defined by Wood and Locke (1987) as the ability to complete specific tas ks in certain sub domains of functioning. Wood and Locke (1987) classified academic self efficacy into seven task domains, memorization, exam concentration, understanding, class concentration, discriminating concept, expanding concepts, and notetaking (p. 2). Owen and Froman (1988) developed the College Academic Self Efficacy Scale (CASES). According to Choi (2005), the CASES is a self report measure of academic self efficacy designed to measure the degree of confidence of performing typical academic behaviors of college students (p. 200). In the Choi study, academic self efficacy was not found to be as powerful a predictor of term grades as the more specific measure of self efficacy such as the SELS and CSSE scales (Finney & Schraw, 2003). The inst ruments previously discussed tap into several dom ains with similar factors. Appendix A contains the description of the specific instruments and their domains. These domains include research skills, ability to learn statistics, personal self efficacy beli efs to learn statistics, math self efficacy, math competence, and the more global domain of academic self efficacy. Bandura (1997) states that personal self efficacy beliefs can transfer across domains provided that these domains are similar. In the case of the instruments discussed, each shares similarity of tasks and the skills needed to complete research, statistics, and mathrelated work, which is a component of research work.

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21 Goal Orientation Similar to personal self efficacy beliefs which have some influence on motivation and orientation in task outcomes, student motivation and goal orientation combine to influence the outcomes of a learning task. According to Bandalos, Finney, and Giske (2003), the goals of learning can be bivariate. These orienta tions encompass both learning and performance goals. Those with an orientation toward learning goals seek knowledge and are therefore less likely to be affected by an imperfect outcome such as a grade lower than an A. They see their lack of optimal ach ievement outcomes as the result of their choice of study strategies, for example, and will work harder to improve in this area. Those with a performance goal orientation seek to demonstrate their abilities through higher levels of perfor mance such as earning straight As. According to Bell and Kozlowski (2002), students with high levels of learning orientation tend to be able to handle the harmful effects of failure, and therefore, are able to increase or maintain their levels of self efficacy. Those with a performance goal orientation had reduced or negative levels of self efficacy because they believe that effort is not synonymous with ability for task mastery and will not expend the effort needed to succeed in difficult or challenging situations. Bell and Kozlowski (2002) believe: High ability individuals have the capabilities to do well on the difficult aspects of tasks and therefore are expected to experience high levels of self efficacy. Low ability individuals, on the other hand, can be expected t o do very poorly on complex tasks, thereby leading to lower l evels of self efficacy (p. 7)

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22 Motivation of students is dependent on their goal orientation. Students with performance goal orientation may stop or continue their involvement in a particular c ourse based on how they perceive their performance, or how they are viewed by others. They may disengage from a course they find challenging beyond the performance rewards (recognition, high grades, etc.). Those with learning orientation goals will perse vere even when faced with the possibility of lower than expected performance (Bandalos et al., 2003; Bell & Kozlowski, 2002). According to Bandura (1997), a student with high self efficacy beliefs in one domain will persevere in completing a task or reach ing a goal whereas a student with lower self efficacy in a particular domain may quit. A student with a learning orientation goal will act similarly. Researcher Preparation Researcher skills are a component part of graduate study. Most measuremen t and psychology departments offer courses that teach graduate students to interpret the statistics results in research articles and how to design experiments that produce sound research models. Almost all graduate programs require that the graduate student complete a basic set of research and statistics courses in preparation for their dissertation work. Eisenhart and DeHaan (2005), in their article Doctoral Preparation of Scientifically Based Education Researchers s tate that they oppose a narrow definition of scientifically based research as being strictly experimental. Instead they suggest:

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23 a broader conception of scientifically based researchers as professionals who engage in inquiry to identify or develop defensible explanations or interpretations by follow ing six guiding principles: 1. t o pose significant questions that can be investigated empirically; 2. t o link research to relevant theory; 3. t o use methods that permit direct investigation of the question; 4. t o provide an explicit and coherent chain of reasoning; 5. t o replicate and generalize across studies; and 6. t o make research public to encourage pro fessional scrutiny and critique (p. 3) Eisenhart and DeHaan (2005) restate the suggestion of the National Science Foundation and the Institute for Educational Sciences that colleges and universities train graduate students for scientifically based education research ( p. 3). Eisenhart and DeHaan (2005) emphasize the continued importance of developing research skills in graduate education programs. These skills include quantitative inquiry, sampling schemes, data collection methods, and data analysis. Eisenhart and DeHaan state: They [graduate students in education programs] must learn how to pose researchable questions, whether requiring quant itative or qualitative methods and data; they must develop strategies for sampling, data collection, and analysis. They must learn ways of reasoning and arguing from evidence, means of assessing quality, styles of writing for technical reports and publish able articles, and ways of scrutinizing and constructively critiquing others work (p. 7) One major problem when preparing graduate students in education to become researchers is that many of these students have little or no previous research experience. They did not get training as undergraduates, and they may not have had any exposure to training in a masters program a program that was preparing them to teach not conduct research (Eisenhart & DeHaan, 2005).

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24 According to Gelso et al. (1996), the abilit y to create original scholarly work is possible only when educational researchers are given the knowledge and skills necessary to carry out such work. Even the best and brightest of students (these future researchers) struggle with the many concepts and t heories that are a part of any researchers education; and because statistics requires an abundance of various learning strategies called on simultaneously, many students have difficulty utilizing cognitive powers (such as quantitative reasoning) that may not have been their primary mode for learning and processing information (Gelso et al. 1996). In a study of research training environments, Gelso et al. (1996) measured the factors that affect the production of scholarly research. Their research reviewed Ph.D. granting clinical, counseling, and school psychology training programs. They found that the research productivity of doctoral students in applied psychology was very low. Although there were other reasons cited for low research productivity such as financial support and lack of socialization in the culture of research, one of the other reasons cited by Gelso et al. (1996) was that students do not feel competent in their research abilities. Gelso and Lent (2000) in the Handbook of Counseling Psychology state that Personal factors including student ambivalence, anxiety, and under confidence, seem to diminish students enthusiasm for research (pp. 120121). Gelso and Lent (2000) state that the best research training environments are those that reduce or eliminate anxiety and uncertainty, and promote scientific discovery.

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25 Without the requisite research skills, environmental support (both financial support and adequate socialization) graduate students in education will continue to struggle to become c ompetent researchers, possibly reducing the number of qualified researchers in the field of education. One approach that may help counteract this trend is to assess the statistics self efficacy beliefs of graduate students and to apply these findings to t he design of required statistics classes in graduate programs of study. Statistics Anxiety Cruise, Cash, and Bolton (1985) state that statistics anxiety can be defined as the feelings of anxiety experienced by students when taking a statistics course or d oing statistical analysis (p. 92). Onwuegbuzie (2003) defines statistics anxiety as an apprehension that occurs when a student encounters statistics in any form at any level (p. 1023). Onwuegbuzie (2003) explains that the findings that expectation pr edicts statistics achievement suggests that a self fulfilling prophecy prevails, in which students who have low expectations of their statistics ability exhibit behavior that may lead t o underachievement (p. 1033). Bandura (1995) believes that when indivi dual coping efficacy is raised to different levels throug h guided mastery treatment, individuals exhibit little anxiety and autonomic arousal to threats they believe t hey can control. He also writes that after the perceived coping efficacy is raised to t he maximal level by guided mastery experiences, they manage the same threats without experiencing any distress, autonomic arousal, or activation of stress related hormones ( p. 9).

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26 According to Bandura (1995), the stronger a persons sense of efficacy, the more likely they are to take on situations that produce stress and to produce outcomes that are favorable to them. Onwuegbuzies (2003) anxiety expectation mediation Summary (AEM) model demonstrates that social cognitive theory and self efficacy are pertinent t o the processes underlying the learning of statistics because expectation is a manifes tation of self efficacy ( p. 1033). The AEM was first used in studies of library anxiety. The AEM model is based on theories of anxiety and social cognition, which is based on Wines CognitiveAttentional Interference theory. This theory postulates that anxiety produces cognitive interference by causing a shift from taskrelevant thoughts to task irrelevant thoughts (Onwuegbuzie & Jiao, 2004). Personal self effi cacy beliefs are based on Social Cognitive Theory. The foundations of Social Cognitive Theory are behavioral, personal, and environmental factors (Pajares, 2002). Self efficacy influences an individuals persistence and effort when engaged in the complet ion of specific tasks. Personal self efficacy beliefs are influenced by the environment in which the individual find themselves, their previous experience with similar tasks, and vicarious experiences. The number of published studies of the construct of personal self efficacy beliefs has increased greatly in the last decade. The domains being measured include researcher skills and task completion in graduate science and counseling

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27 psychology, and in dissertation completion. While these domains are differ ent than those found in educational research, the tasks and skills required at specific levels of self efficacy bel iefs related to statistics self efficacy are similar. In other words, when the skills are similar across domains they can inform personal self efficacy theory in graduate programs in colleges of education. These domains in other disciplines provide the starting point for statistics self efficacy research within the field of graduate education and educational researcher preparation.

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28 C hapter 3 Methods The purpose of this study was to investigate the relationship between statistics self efficacy, statistics anxiety, and performance in an introductory graduate statistics course. The sections of this chapter include the research design, populat ion and sample, instrumentation, data collection, and data analysis. Research Design A research design was developed to compare personal levels of statistics self efficacy (se lf efficacy to learn statistics and current statistics self efficacy), statistics anxiety, and course performance ( defined as the average of the combined midterm and final exam scores ) in a graduate introductory statistics course. The study design was a correlation analysis comparing the two self efficacy measures with each other and with the statistics anxiety measure and with the course performance measure. A set of demographic questions were included to allow the participants to indicate their age group, gender, and race/ ethnicity It also provided space for the participants to ide ntify prior statistics course experiences as w ell as degrees previously earned and the individuals current degree program This key descriptive data was requested in order to provide an accurate representation of the sample.

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29 Population and Sample The pop ulation of interest was graduate students enrolled in graduate introductory statistics courses in the College of Education at a doctoral degree granting, large metropolitan university with very high research activity in the southeast ern U.S (Carnegie, 2011) According to this Universitys website the median age of students in the College of Education graduate programs was 34 years old; 78% of graduate students were female and 22% were male. At the graduate level, 6.7% of the students were African Americ an, 5.2% we re Hispanic, with a total graduate minority population of 13.8%. The average GRE (Graduate Record Exam) scores (Verbal and Quantitative) were 993. Sample Selection According to the Cohens (1988) power tables on sample size estimation, a sample size sufficient to determine a difference between the sample and the population of interest is best satisfied when estimates of effect size and power are set and tested so that the sample size is not too small to determine an effect or so large that the researcher wastes time and resources unnecessarily. Cohen (1988) suggested that effect size can be set at the small, medium, and large levels. The size chosen by the researcher depends on how much Type 1 or Type 2 error risk is acceptable. Type 1 and 2 errors are balanced against the desired goals of the researcher and the research design (Cohen, 1988, 1992). Based on Cohens (1988) power tables the chance of correctly rejecting the null hypothesis in a twotailed test is improved when the significance of a product moment r with a .05 (alpha) significance criterion and a medium effect

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30 size of .30 and a power of 82 can be established with a minimum sample size of 88. Although 108 instrument packages were distributed, the actual number of participants re maining was 88, which coincidentally wa s the minimum number of respondents required. The difference of 20 consisted of 8 students who dropped the course before the final exam 2 students who did not sign the informed consent and 10 students who submitted incomplete surveys. These last 12 students were classified as non usable participants The sample inclu ded graduate students (both masters degreeseeking and doctoral degreeseeking) enrolled in graduate introductory statistics courses during two semes ters In this study data collection began in the fall semester of 2009 and cont inued through the spring semester of 2010 The sample participants were obtained from College of Education graduate students enrolled in EDF 6407 Statistical Analysis for Edu cational Research I Four sections were offered during this time period. Three sections during fall 2009 included two traditional classroom courses and one online course. During spring 2010, one traditional classroom course was offered. Instrumentation The instrumentation for this research study consisted of a demographic questionnaire, two self efficacy measures, one anxiety measure, and course performance measures T o collect the information needed for this study four of the instruments were combined into one package (instrument packet) fo r administration to students

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31 The four instruments that were combined for ease of administration in gathering data are : a demographic questionnaire; t he Computational Self Concept Subscale of the STARS ; t he Current Statistics Self Efficacy (CSSE) scale ; and t he Self Efficacy to Learn Statistics (SELS) scale. Each of these instruments is discussed below. Demographic Q uestionnaire The demographic questionnaire was developed by the researcher to gather informatio n about individual student s involved in this study. Items were chosen to obtain a demographic characteristics profile of the participants as a means of describing the sample The questions included information related to age group, gender, race/ethnicity degree program, and prior statistics experience. See A ppendix B for a copy of the demographic q uestionnaire. Statistical Anxiety Rating Scale (STARS). The Statistics Anxiety Rating Scale (STARS) was developed by Cruise and Wilkins (1980). The STARS wa s developed to assess students levels of statistics anxiety. It consisted of an initial set of 89 items and was given to 1,150 statistics students. The final form of the instrument consisted of 51 items and six factors, which were Worth of Statistics, I nterpretation Anxiety, Test and Class Anxiety, Computation Self Concept, Fear of Asking for Help, and Fear of Statistics Teachers. See Appendix C for a copy of the complete STARS instrument.

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32 The first factor, Worth of Statistics is described by the authors as the individual students perceptions of the worth of statistics The second factor, Interpretation Anxiety is described as the anxiety experienced by a student when they are required to interpret data or make a decision based on the data. The third factor, Test and Class Anxiety is described as the anxiety experienced when taking a statistics course or test. The fourth factor, Computational Self Concept is described as anxiety experienced when solving mathematics problems and the students perceptions of their ability to understand and calculate statistics. The fifth factor, Fear of Asking for Help is described as the anxiety experienced when asking for help from a professor or student. The sixth factor Fear of Statistics Teachers The instrument consists of two parts. The first part includes 23 items (or situations) related to statistics anxiety. Item responses are scored on a Likert type scale from 1 to 5. A score of 1 indicates no anxiety and a score of 5 indicates high anxiety. The second part includes 28 items dealing with or related to statistics (p. 92). Items are scored on a Likert type scale from 1 to 5. A score of 1 indicates strong disagreement with the statement and a score of 5 indicates strong agreemen t with the statement. is describe d as the students perception of their statistics teacher. A high score on any one of the factors is interpreted as a high anxiety level within that construct (Cruise, Cash, & Bolton, 1985). Computation Self Concept Subscale of the STARS. The fourth factor, Computational Self Concept has been used by various researchers to assess statistics anxiety ( Cruise & Wilkins, 1980; Onwuegbuzie, 2003). According to

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33 Onwuegbuzie (2003) a high score on this [computational self concept] subscale represent s high anxiety associated with poor computation self concept (p. 1027). Singular use of the computation self concept subscale was justified because many introductory statistics courses require that students calculate statistics by hand in order to develop a better understanding of the underlying theory before they move on to using a statistical software package to solve statistical problems. See Appendix D for a copy of the specific items contained in the C omputation Self C onc ept Subscale of the STARS (s tatistics anxiety measure) Onwuegbuzie (2003) justifies the use of this subscale as appropriate to assess anxiety by explaining that scores on this subscale were found by Onwuegbuzie, Slate, et al. (2000), alongside students levels of achievement expectation, to be the best predictor of overall success in research methodology courses explaining 12.2% of the variance in achievement ( p. 1027) Onwuegbuzie (2003) reported the alpha reliability for the sample data of 130 graduate students on the computation sel f concept subscale at .86. The C SCS (statistics anxiety measure) consists of seven items. Scores on the scale range from a low of 7 to a maximum of 35 on this scale. According to the authors, the subscale measures the level of anxiety experienced [by students] when doing mathematical problems, as well as the students self perception of his/her ability to understand and calculate statistics. It doesnt reflect so much the students ability to do mathematics, but rather measures the students attitude toward mathematics. A person scoring high on this factor might not mind statistics per se, but experiences anxiety because it involves mathematical calculations, and he/she feels inadequate to comprehend statistics (Cruise, Cash, & Bolton, 1985, p. 93)

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34 Validity. The Statistical Anxiety Rating Scale (STARS) instrument was validated in the following ways. The reviewers consisted of five statistics professors and five doctoral students. Each reviewer was presented with a description of the six factors an d a list of possible items for each factor. A coefficient of agreement was determined for each item under each factor. Factor analysis was also conducted to establish construct validity. The original 89item inst rument was given to a sample of 1,265 gra duate students of whom 1,150 participants completed the instrument. Principal component analysis was completed and the extracted components were rotated using varimax procedures. The initial factor analysis determined that a total of 14 possible factors e xisted; however, the factors were further tested using a new combination of factors and variables because the researchers considered the initial factor structure to be weak. The ideal combination was to have each item load only on one factor and items wit h similar characteristics load on the same factor. The results of the analysis determined that the best solution consisted of six factors and 51 items. Reliability Reliability measures for the STARS (Cruise & Wilkins, 1980) consisted of coefficient alph a, point multi serial correlations, and test retest estimates. Coefficient alpha estimates ranged between .678 and .940. Point multiserial correlations were between .589 and .906. The test retest estimates fell between .671 and .833. Specifically related to the CSCS Onwuegbuzie (2003) found an alpha reliability of .86 for the CSCS of the STARS in his study

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35 Administration. Cruise and Wilkins (1980) explained that there are no special qualifications needed to administer the instrument. The instrument can be given individually or in groups. The authors suggest that even though the directions are self explanatory, the instructions for taking the instrument should be read aloud and any students questions answered at that time. The authors also recommend that students not take too much time on any one question since no grade will be assigned to this particular activity The entire STARS is a self diagnosis instrument and should take an average of 15 minutes to complete. The CSCS (statistics anxiety me asure) should take no more than 5 minutes to complete. Current Statistics Self Efficacy (CSSE) and Self Efficacy to Learn Statistics (SELS). The CSSE (current SE measure)and the SELS (future SE measure) were developed in 2003 to assess the growth in stati stics self efficacy beliefs of undergraduates enrolled in a semester long introductory statistics course. A copy of the CSSE (current SE measure) is provided in A ppendix E, while a copy of the SELS (future SE measure) is provided in Appe ndix F These ins truments are statistics specific (domain and task specific) and were chosen to assess the changes in statistics self efficacy for graduate students i n an introductory graduate statistics course. These were the only two statistics specific self efficacy sc ales available in the literature. According to Finney and Schraw (2003), items for the SELS (future SE measure) and CSSE (current SE measure) scales were developed by reviewing various introductory statistics textbooks and course syllabi. The items were t hen

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36 reviewed by 13 introductory statistics instructors. The instructors were asked to review an initial set of 10 items to see if the items should be modified or deleted and also to determine seven common goals students are required to achieve at the end of an introductory statistics course. After agreement on the common goals by all the instructors, additional items were written to represent the common goals identified by the instructors. The original 10 items along with 4 new items comprised the final v ersions of CSSE (current SE measure) and SELS (future SE measure) The primary diffe rence between the two scales is in the instructions for completing the scales. The SELS (future SE measure) asks students to rate their current self efficacy belief in th eir ability to learn statistics, whereas the CSSE (current SE measure) asks students to rate their confidence in their current ability to comp lete specific statistics tasks. The SELS (future SE measure) and CSSE (current SE measure) use a 6point scale fro m 1 (no confidence at all) to 6 (complete confidence). All items were designed to represent particular statistical concepts introductory statistics students would experience. The choice to use both these instruments was directly influenced by the smaller number of items per instrument to help prevent participant fatigue (Finney & Schraw, 2003) Validity Factor analysis was conducted separately for the first and second administrations of the CSSE (current SE measure) and SELS (future SE measure) A sing le factor solution was determined for both the CSSE (current SE measure) and SELS (future SE measure) The CSSE (current SE measure)

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37 onefactor solution accounted for 44.53% of the variance ( N = 138). Other identified CSSE (current SE measure) factors ac counted for less than 10% of the variance and had eigenvalues less than 1.00. The SELS (future SE measure) onefactor solution accounted for 73.71% of the variance ( N = 140). The CSSE (current SE measure) and SELS (future SE measure) were reported by Fi nney and Schraw (2003) as demonstrating preliminary evidence of validity. According to the authors both measures had predictable relationships with performance (p. 179). Finney and Schraw discussed self efficacy and achievement. Specifically, current statistics self efficacy at the end of the course had relationships in the r = .40 .50 range with achievement as predicted based on previous findings (Bandura, 1997; Pajares, 1996b, 1997; Zimmerman & Bandura, 1994). While the SELS did have positive relat ionships with achievement, the relationships were lower than predicted. Schunk (1989, 1991) found that self efficacy to learn tended to have relationships in the range of r = .33 .42 with achievement. The correlations found in the current study are weake r than the lower bound. Further study of the relationship between achievement and the SELS is needed in order to establish its predictive utility. Findings that current statistics self efficacy at the end of the semester had moderate (.441 and .496) relationships with the performance task score and course percentage is extremely important given that two recent studies examining self efficacy for statistics failed to report a significant positive relationship between self efficacy and achievement (Bandalo s et al., 1995; Benson, 1989) (Finney & Schraw, 2003, pp. 179 180) Reliability Cronbachs (1951) coefficient alpha for the CSSE (current SE measure) for the first administration was .907 ( N = 138), and .935 ( N = 130) for the second administration, and item total correlations for all 14 items were above .53. The coefficient alpha for the SELS (future SE measure) was equal to .975 ( N = 140) and item total correlations were above .77 for all 14 items

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38 Administration. The only difference between the two self efficacy instruments is in the directions for completing each instrument. The instructions for administering the CSSE (current SE measure) assessed the participants confidence in their current ability to successfully complete the identified tasks. The item scale has six possible responses: 1 equals no confidence at all, 2 equals a little confidence, 3 equals a fair amount of confidence, 4 equals much confidence, 5 equals very much confidence, and 6 equals complete confidence. On the other hand, the instructions for administering the SELS (future SE measure) assessed the participants confidence in learning the skills necessary while they we re in the class to successfully complete the tasks that follow ed. The item response scale was identical to th at used in the CSSE (current SE measure) as described above. Instrument Development Process. According to Finney and Schraw (2003) the CSSE (current SE measure) and SELS (future SE measure) items were initially developed by reading several introductory s tatistics textbooks. Thirteen instructors who taught introductory statistics were contacted and asked to review a first set of 10 items written by the researcher (Finney). Each instructor reviewed the items and was asked to add or remove items that they felt were missing or were not appropriate. Each instructor was also asked to identify seven fundamental course goals. Goals were combined to incorporate similarity among instructors. New items were written to represent all goals. The first 10 items and the newly written items were combined. The final number of items was 14 for the statistics self efficacy instruments.

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39 Course Performance Measures. The dependent variable, class performance measure, was calculat ed by combining the midterm and final exam scores and dividing by two to obtain an average. A performance measurement score was calculated for each student in each class section. Validity Validity of the midterm and final exam s was verified by the instructor s of each section. All of the faculty teaching the statistics courses stated that a stud ent could attend one instructor s class and take the exam in a different instructor s class and pass either instructor s exam The instructor s stated that the test items and the course content were very s imilar even though the instructor s wrote their own exams and no two exams were identical. Also the scoring of the exams and the percentage of each exam as part of the final grade were identical. Therefore combining the exam scor es from the three instruc tors was appropriate. Exam scores for both the midterm and final test could range from 0100 points. In the context of the course grading, each exam counted for 30% of the final course grade. In addition, there were two collectible individual projects, one research group project, and various weekly activities included in determining the final course grade that were not part of the performance measure used in this study Reliability The reliability measures for each course section were as follows. For S ection s 1 and 2 the midterm and final scores correlated to .65, and when the midterm and final were treated as two items going into a score, the internal consistency based on these two items was .77 (course instructor,

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40 personal communication, January 11, 2010) Section 3 (online) was .68 for the midterm and .79 for the final exam (course instructor, personal communication, December 16, 2009). Section 4 demonstrated a reliability of .76 for the midterm and .80 for the final exam (course instructor, person al communication, May 22, 2010) Administration. Whether participants were in the traditional classroom sections or the online section, the exam procedures for both the midterm and the final test were similar. The midterm and final exam procedures f or e ach exam included two parts. One part utilized a take home computational set of test items and the second was an inseat multiple choice exam The takehome test required each student to complete computational problems using a statistics software package such as SAS or SPSS. This part of t he exam counted as 50 points, or half of the overall score. Th e in seat portion of the exam required students to complete multiple choi ce items This part of the exam also counted for half of the overall score and was administered during class time for the traditional classes and in a statistics computer lab for the on line class Each individual students score for the takehome and in seat exams were combined which resulted in a total exam score for midterm and final exam The scores used to compute the performance measures for this study were drawn from the addition of the midterm and final exam scores. These two scores were then divided by two to get the average which was the performance measure for each student.

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41 C ourse Section Comparison. There were four introductory graduatelevel statistics class sections in this study. Sections 1, 2, and 4 were traditional classroom courses and Section 3 was an online course. One instructor taught two sections (Sections 1 and 2) in the traditional classroom format in the fall semester of 2009. A third section (Section 3) was taught online in the fall semester of 2009 and was faci litated by a different instructor T he fou rth section (Section 4) was taught in traditional class room format and was taught in the spr ing of 2010 by a third instructor The data for Sections 1, 2 and 3 were collected in the fall semester of 2009. The data for Section 4 were collected in the spring semester of 2010. Data Collection The data for this study were collected in several phases depending on whether the class was a traditional classroom course or an online course The first phase consisted of distribution of data collection and research items to students in each class. The second phase co nsisted of obtaining the midterm and final exams from each of the instructors. In the traditional classroom courses (S ections 1, 2, and 4), t he combined instruments were given to each introductory statistics course during the first week of the semester. Participants were given the informed consent form requesting their participation in the study which included requesting their permission to obtain their midterm and final exam scores from their instructors They were informed that their scores would be ke pt confidential and that no personal information including name would be published in the research study thus ensuring anonymity

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42 Each student received an instrument packet inserted into an envelope which included the informed consent, the CSCS (statistic s anxiety measure) the CSSE (current SE measure) the SELS (future SE measure) the demographic questionnaire, and a threeby five index card with a unique ID number The unique ID number was used so that th e instrument packet could be matched to each participant using the number as the common link to ensure anonymity in data reporting These packets were distributed at the beginning of the class during the first week of the semester. Prior to distribution of the packets to students the instructor intr oduced the researcher to the students Subsequently the researcher read the instructions for completing the instruments and stated the importance of the research study. The words current ability and learning were emphasized so that participants were able to distinguish between the CSSE (current SE measure) and SELS (future SE measure) respectively. Students were informed that they did not have to participate and that they would not be penalized for non participation. Completion rates by section were: S1 = 100%, S2 = 100%, S3 = 42%, and S4 = 100%. The students were given the instruments just prior to the class break and completed them during the class break. All packets were returned in closed envelopes and were collec ted by the researcher for analys is. The researcher did not know who participated and who did not until after the data were collected, the instruments were checked for completion and the informed consent was verified as signed.

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43 Section 3 was also taught in the fall of 2009 ; however, Sec tion 3 was unique in that it was the online statistics course. The instruments and the informed consent form were uploaded to the course Blackboard site for distribution to the students. The researcher did not have control over when the instruments were completed and did not have the opportunity to distribute the instruments in person. The administration was handled by the course instructor. The instruments and informed consent forms of those students who participated were returned to the researcher by the course instructor. Because no unique ID was assigned to this group of online students the researcher assigned these ID numbers after the instruments were returned. Time Line for Data Collection. The time line involved in collecting data for this s tudy extended over two semesters. Data collection began in the fall of 2009 and concluded in the spring of 2010. For all traditional classroom sections the researcher distributed the instrument packets at the beginning of the class during the first week of the semester The on line class received the instruments, consent form demographic questionnaire, and a letter of explanation of the study purpose from the information posted online on the Blackboard site. Data Analysis After all the data from the st udents and the instructors were obtained, the researcher analyzed the results. T he researcher then matched and verified all pieces of information and data for each persons unique ID. To allow for accurate and reliable judgments of significance given a se t sample size, a power analysis was conducted to detect the possibility of Type I

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44 and T ype II error. High (2000) suggests that a power analysis is the ability of a test to detect an effect, given that the effect actually exists (p. 1). According to Hig h (2000), in an exploratory study, a significance level of .10 is considered adequate probability of detecting a T ype 1 error. Th e power to detect an effect or T ype 2 error is commonly set at .80. In some studies, these numbers have been set lower and st ill were considered significant. For this study to reduce the probability of Type 1 and T ype 2 error, power was set at the .05 level of significance. Effect size measures w ere set at .30, a medium effect siz e. Means and standard deviations were also calc ulated. Based on Cohens (1988) power tables the chance of correctly rejecting the null hypothesis in a twotailed test is improved when the significance of a product moment r with a .05 (alpha) significance criterion and a medium effect size of .30 and a power ( 1 beta) of 82 can be determined with a minimum sample size of 88. The resultant final sample size of 88 which matches the minimal sample size suggested by Cohens (1988) power tables is strictly coincidental Score Reliability Hatcher (1994) and Nunnally (1978) defined the reliability coefficient as the proportion of variance in the observed variable accounted for by true scores on the underlying cons truct. Nunnally (1978) suggested that instruments used in basic research have a reliability of .70 or greater. A Coefficient Alpha of .70 or greater is considered adequate reliability consistency in social science research and was used as the benchmark in this study. Reliability estimates were calculated for the three instruments (CSCS, CSSE, and SELS)

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45 Analysis by Research Question Th e research questions were analyzed in the following ways. 1. What is the relationship between statistics self efficacy and statistics anxiety? Correlation analysis was conducted to compare the relationships among in strument results and any trends in the data. A correlation analysis was conducted between the SELS (future SE measure) and statistics anxiety. A correlation analysis was c onducted between the CSSE (current SE measure) and C omputational Self Concept subsc ale (CSCS) of the STARS. Mea n s and standard deviations were calculated to determine the representative score on the SELS (future SE measure) and CSSE (current SE measure) and the CSCS of the STARS (statistics anxiety measure) in the group of scores. 2. Wh at is the relationship between the two statistics self efficacy instruments and performance in a graduate introductory statistics course? M ultiple regression correlation analysis was conducted to compare the relationships among instrument results and any t rends in the data. Correlation analysis was conducted between the SELS (future SE measure) and performance ( average combined midterm and final exam scores ) and between the CSSE (current SE measure) and performance ( average combined midterm and final exam scores) Means and standard deviations were calculated to determine the representative scores on the SELS (future SE measure) and performance (average of combined midterm and final exam scores ) and the

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46 CSSE (current SE measure) and performance (average o f combined midterm and final exam scores ) Analysis of variance (ANOVA) was conducted to test for differences in mean scores and percent age of variation accounted for by each section on the CSSE (current SE measure) and SELS (future SE measure) 3. What i s the relationship between statistics anxiety and performance in a graduate introductory statistics course? Multiple regression correlation analysis was conducted to compare the relationships among instrument results and any trends in the data. A correlat ion analysis was conducted between the Computational Self Concept (CSCS) subscale of the STARS and performance ( average combined midterm and final exam scores ) Means and standard deviation s were calculated to determine the representative scores on the CS CS (statistics anxiety measure) a nd performance ( average combined midterm and final exam scores ) Analysis of variance was conducted to test for differences in mean scores and percent age of variation accounted for by each section on the CSCS (statistics a nxiety measure) 4. What is the relationship between statistics self efficacy, statistics anxiety, and performance? Multiple regression correlation analysis was conducted to compare relationships among instrument results and any trends in the data. A corr elation analysis was conducted between the CSSE (current SE measure) and C omputational Self Concept subscale (CSCS) of the STARS. Correlation analysis was conducted between the SELS (future SE measure) a nd performance (average of combined midterm and final exam scores ) and CSSE

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47 (current SE measure) a nd performance (average of combined midterm and final exam scores ) A correlation analysis was conducted between the C omputational Self Concept subscale (CSCS) of the STARS and performance (average of combined midterm and final exam scores ) Means and standard deviations were calculated to determine the representative score on the SELS (future SE measure) and CSSE (current SE measure) and the Computational Self Concept subscale (CSCS) of the STARS in the group of scores.

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48 Chapter 4 R esults The purpose of this study was to investigate the relationship between statistics self efficacy, statistics anxiety, and performance in an introductory graduate statistics course. T he parts of this chapter include response rates for participants demog raphic characteristics, screening methods, ANOVA results, findings and results of research questions, observations and summary Response Rates for Participants The total number of students in this study was 108 After removin g students who dropped the class or who provided incomplete responses to the instruments, there were 88 participants left for inclusion in the analysis. These participants came from four class sections as enumerated below Section 1 was taught in the fall of 2009 and had 29 students enrolled with a completion rate in this study of 100% Of the or iginal 29 who completed the instruments one student dropped the cour se, one unusable set of data was removed by the researcher prior to analysis and another four sets of incomp lete data were eliminated during the analysis leaving 23 participants as part of the study Section 2 was taught in the fall of 2009 and had 41 stude nts enrolled with a completion rate in this study of 100% Of the original 41, three stud ents

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49 dropped the course and two sets of incomplete data were eliminated during the analysis, leaving 36 participants in the study S ection 3, taught during fall 2009, was the only online course Although it had 26 students enrolled, only 11 (42%) volunteered to participate in the study From this number three unusable sets of data were removed by the researcher prior to analysis and another two sets of incomplete data were subsequently eliminated during the analysis, leaving 6 participants included in t he study S ection 4 was taught in the spring of 2010 and had 27 students enrolled with a completion rate in this study of 100%. Of the original 27 two students dropped the course, one unusable set of data was removed by the researcher prior to analysis and one set of incom plete data was eliminated during the analysis, leaving 23 participants as part of the study The t otal number of participants from these four sections was 88. This number was the minimum sample size identified by Cohen for a medium eff ect size as shown in Cohens power tables (Cohen, 1988) The information from these participants was analyzed by the SAS program (SAS Institute, 2005). Demographic Characteristics of Participants Analysis was conducted on 88 master s level and doctor al le vel students enrolled in four introductory graduate statistics classes in a College of Education at a doctoral granting, large metropolitan university with very high research activity in the southeast ern U.S. during the fall 2009 semester and spring 2010. Three sections of the course were taught in a traditional classroom and one section was offered as an online version. Sixtynine out of a total of 88 students

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50 completed all or part of the demographic questionnaire found in Appendix B. The ages of the participants ranged from 22 to 59 years of age and were classified as shown in Figure 2. The two largest percentages were the 2630 year olds (20%) and the 3135 years of age (18%). The smallest categories were the 2225 year olds (8%) and the 4149 year olds (9%). About 22% of the participants did not specify their age group. Fifty one percent of the participants in this study were between the ages of 26 to 40 years. 26-30 years old 20% 31-35 years old 18% 36-40 years old 13% 50-59 years old 10% 41-49 years old 9% 22-25 years old 8% Age group not specified 22% Figure 2. Pie chart of percentages of age groups as reported by participants.

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51 Figur e 3 depicts the current degree enrollment of the participants at the time of the study. Eight students (9%) were enrolled as masters degree seeking students, 59 were enrolled as doctoral degree seeking students (67%), two others were identified as other , and 19 did not specify an answer. Enrolled in masters 9% Enrolled in doctorate 67% Current degree not specified 22% Enrolled in other or none 2% Figure 3 Pie chart of percentages of degree programs in which participants were currently enrolled. The earned academic degrees of participants are shown in Figure 4. Prior to enrolling in the graduate introductory statistics classes, 10 participants had received a bachelors degree, 58 had received a masters degree, and 1 reported

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52 receiving a doctoral or professional degree. There were an additional 19 who did not specify their degree program. Bachelors 11% Prior degree not specified 22% Masters 66% Doctorate or Professional 1% Figure 4. Pie chart of percentage of earned degrees as reported by participants. Forty five participants reported that they had previously taken a statistics course in college. An additional four students were not sure if they had taken a previous course in statistic s. Based on the written responses to when they had taken a statistics course, 22 students reported having taken a statistics class within the last five years. Nineteen students reported taking a statistics course more than 10 years ago.

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53 There were 37 (42%) females and 31 (35%) males who participated in the study. Another 20 students did not specify their gender. These numbers are presented in Figure 5. Male 35% Female 42% Gender not specified 23% Figure 5. Pie chart of percentages of males and females as reported by participants. Race/ethnici ty categories were self selected. The results of this item are shown in the pie chart in Fi gure 6. Participants were instructed to write in their own race/ethnicity as the demographic questionnaire did not provide preidentified categories for them to se lect. Thirty seven participants identified themselves as White/Caucasian, 9 as Black/AfricanAmerican, 4 identified as

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54 Asian/Southeast As ian American, 2 as Hispanic, 1 as Black/West Indian, 1 as Black/Caribbean, 1 as Multiracial, and 33 did not specify their race. White & Caucasian 42% Race/ethnicity not specified 38% Asian & SE Asian American 5% Black & African American 10% Hispanic 2% Multi-racial 1% Black W. Indian & Black Caribbean 2% Figure 6. Pie chart of percentages of race/ethnicity as self reported by participants. Data Screening Methods Student data from the four sections of the introductory statistics classes were entered into a Microsoft Excel spreadsheet after being reviewed for the informed consent form with authorizing signature, verification of completion of each instrument (CSCS, CSSE, and SELS), and verification of completion of the

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55 demographic questionnaire. Any participants who failed to sign the informed consent or who dropped the course were excluded from the analysis. A scatter plot analysis of the data was conducted to test for outliers that could affect the outcome of results of the multiple regression correlation analysis. Outliers were detected in all three scatter plots: the CSCS (statistics anxiety measure) with performance, CSSE (current SE measure) with performance, and SELS (future SE measure) with performance. Six outliers were dropped from the scatter plot analysis to produce a more relevant view of the data. The scatter plots for each of the instrument s are included to illustrate the relationship between each instrument and the performance measure. The CSCS with performance The scatter plot for the CSCS (statistics anxiety measure) data is presented in Figure 7. There are some data points stacked up on the left side of the graph and there is a loose D pattern of data. There did n ot appear to be any correlation between the measures. The CSSE with performance. The scatter plot for the CS SE (current SE measure) data is presented in Figure 8. There is no discernible pattern. There is some clustering of data at the lower end of the CSSE scale; however, overall there did not appear to be any correlation between the measures The SELS with performance. The scatter plot for the SELS (future SE measure) data is presented in Figure 9. There is a group of data points vertically aligned near the middle and the right of the graph. Ov erall there did not appear to be any correlation betw een the SE LS (future SE measure) and performance (average combined midterm and final exam scores)

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5 6 Performance 60 70 80 90 100 CSCSTotal 0 10 20 30 40 Figure 7 Scatter plot of the relationship between Performance (average combined midterm and final exam scores) and the Computation Self Concept Subscale (statistic s anxiety measure) total s core.

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57 Performance 60 70 80 90 100 CSSETotal 10 20 30 40 50 60 70 80 Figure 8. Scatter plot of relationship between Performance (average combined midterm and final exam scores) and Current Statistics Self Efficacy (current SE measure) total s core.

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58 Performance 60 70 80 90 100 SELSTotal 30 40 50 60 70 80 90 Figure 9. Scatter plot of relationship between Performance (average combined midterm and final exam scores) and Self Efficacy to Learn Statistics (future SE measure) total s core.

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59 ANOVA results. Results were analyzed using onefactor ANOVA testing the differences in means between the four course sections and by each instrument (CSCS, CSSE and SELS). Differences in mean scores and percentage of variation accounted for by each section on the CSCS (statistics anxiety measure) CSSE (current SE measure) and SELS (future SE measure) are displ ayed in Tables 1, 2, and 3. Table 1 ANOVA and Coefficient of Determination Values for Course Section and Computational Self Concept Subscale Source df SS MS F p R 2 Section 3 259.88 86.63 2.59 .058 .0846 Within Groups 84 2811.21 33.47 Tot al 87 3071.09 Note N = 88. p Table 2 <.05 ANOVA and Coefficient of Determination Values for Course Section and Current Statistics Self Efficacy Source df SS MS F p R 2 Section 3 493.74 164.58 .57 .635 .0200 Within Groups 84 24179.24 287.85 Total 87 24672.99 Note. N = 88. p <.05

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60 Table 3 ANOVA and Coefficient of Determination Values for Course Section and Self Efficacy to Learn Statistics Source df SS MS F p R 2 Section 3 1743.87 581.29 2.7 .051 .0881 Within Groups 8 4 18059.40 214.99 Total 87 19803.27 Not e. N = 88. p There was no significant effect between instruments (CSCS, CSSE, and SELS) and course sections and there was no differ ence in course sections and the p values for each were greater than .05. The amount of variation on each instruments (CSCS, CSSE and SELS) mean score was approximately 8% for the CSCS (statistics anxiety measure) and SELS (future SE measure) and 2% for the CSSE (current SE measure). There were no main or simple effects dem onstrated in the data. <.05 Means and least square means. The means, standard deviation s, and range of scores for the performance measure for each course section were as follows: Section 1 had a mean of 85.83 ( SD = 10.91) with a range from 62 to 100 points Se ction 2 had a mean of 82.76 ( SD = 9.10) with a range from 64 to 99 points Section 3 had a mean of 87.67 ( SD = 7.45) wit h a range f rom 77 to 98 points, and Section 4 had a mean of 84.91 ( SD = 9.11) with a range from 72 to 97 points These means are based on the number of students who were used in

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61 the analysis in each course section. The highest means were reported in Section 3 ( n = 6). The lowest means were reported in Section 2 ( n The least square (LS) means procedure in SAS was used to analyze t he means for each instrument for each secti on This procedure is appropriate because each course section had a different number of participants thus creating an unbalanced design. The least square means for each instrument with each course section is de picted in Figure 10. = 36). The graph shows the least square mean score s for each instrument. Secti on 1 had the highest mean score s f or the SELS (future SE measure) and CSSE (current SE measure) and the lowest mean score s for the CSCS (statistics anxiety measur e) compared to the other three course sections. Sections 2, 3, and 4 are almost identical in their mean scores The means for all sections were comparable and the differences were not significant. Legend LS Means Graph 0 10 20 30 40 50 60 70 80 1 2 3 4 Class Section Mean SELS CSSE CSCS Figure 10. A comparison of least square means for each of the instruments by course section.

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62 Cronbachs Alpha for eac h instrument Alpha reliability measures for each instrument are as shown in Table 4. Alphas for each instrument were as follows: the CSCS (statistics anxiety measure) had an alpha coefficient of .90, the CSSE (current SE measure) had an alpha coefficient of .95, and the SELS (future SE measure) h ad an alpha coefficient of .98. These were consistent with the results of the Finney and Sc hraw (2003) study. Table 4 Coefficient Alpha Estimates, Means, Standard Deviations, and Correlations, of Study Measures Variable Coef. Alpha Est. Mean/ Total Possible SD CSCS r CSSE* r SELS* r Perf* r CSCS 0.90 13.68/ 35 5.94 --CSSE 0.95 39.01/ 84 16.84 .35 --a SELS 0.98 68.90/ 84 15.08 .52 .26a --a Performance --84.63/ 100 9.09 .18 .04 .13 --Note. CSCS = Computational Self Concept Subscal e (statistics anxiety measure) CSSE = Current Statistics Self Efficacy (current SE measure) SELS = Self Eff icacy to Learn Statistics (future SE measure) Perf = Performance ( average of combined midterm a nd final exams ) ap <.05 N = 88. These correlations are statistically significant.

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63 Findings and Results by Research Question Question 1 What is the relationship between statistics self efficacy and statistics anxiety? Multiple regression correlation analysis was conducted to compare the relationships among instrument results and any trends in the data. Means and standard deviations were calculated to determine the representative score on the CSCS of the STARS (statistics anxiety measure) the CSSE (c urrent SE measure), and the SELS (future SE measure) in the group of scores. The means, standard deviations, and correlations for the CSCS (statistics anxiety measure) CSSE (current SE measure), and SELS (future SE measure) were presented in Table 4. A c orrelation analysis was conducted between the SELS (future SE measure) scale and statistics anxiety as measured by the CSCS of the STARS (statistics anxiety measure) See Table 4 for the correlations for the study measures. The correlation between the SELS and CSCS was .52 ( p <.0001). This is consistent with the findings of Finney and Schraw (2003) who found a negative correlation of .471 between the SELS (future SE measure) and Spielbergers 1980 Statistics Test Anxiety (STA) instrument during the first administration of the instruments. The correlation between the CSCS (statistics anxiety measure) and SELS (future SE measure) in this study may be the result of the fact that the CSCS (statistics anxiety measure) assessed participants level of anxiety as it related to

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64 specific statistics test items on that day; whereas the SELS (future SE measure) assessed their personal beliefs in their ability to learn specific statistics tasks over a semester. This difference in the perception of time available to learn statistics may give students a feeling of confidence over and above what they would experience if they were given less time to learn statistics or were tested on their statistical problem solving on that day. A correlation analysis was conducted between the CSSE (curre nt SE measure) and CSCS of the STARS (statistics anxiety measure) The correlation between the CSSE and CSCS was .35 ( p = .0007). The resulting correlation between the CSCS (statistics anxiety measure) and CSSE (current SE measure) in th is study may be partly a result of the fact that the CSCS (statistics anxiety measure) assessed participants level of anxiety as it related to specific statistics test items, whereas the CSSE (current SE measure) assessed their personal beliefs in their c urrent ability to complete specific statistics tasks. The higher negative correlation between the CSCS (statistics anxiety measure) and SELS (future SE measure) compared to the CSCS (statistics anxiety measure) and CSSE (current SE measure) may be the result of the fact that th e SELS (future SE measure) assessed participants beliefs in their ability to learn, which, because of this future skill requirement, makes individuals more confident, whi ch is dissimilar enough to the statistics anxiety construct rep resented by the CSCS (statistics anxiety measure) The CSSE (current SE measure) is closer in construct to the CSCS (statistics anxiety measure) since the CSSE (current SE measure) assessed about participants current ability to

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65 complete specific statisti cs tasks and this construct is similar to the CSCS (statistics anxiety measure) which also assessed participants feelings about completing specific statistics tasks. A student with low current statistics self efficacy could have higher statistics anxiety This study demonstrated that the CSSE (current SE measure) and CSCS (statistics anxiety measure) data have a weaker relationship than the relationship between the CSCS (statistics anxiety measure) and SELS (future SE measure) data. All correlations wer e significant at the .05 level. Question 2. What is the relationship between the two statistics self efficacy instruments and performance in a graduate introductory statistics course? Performance measures for this study are defined as the average of the combined midterm and final exam scores in the introductory statistics course that account for part of the final course grade. The average of the combined scores on the midterm and final exam scores in an introductory statistics class were correlated with t he CSSE (current SE measure) and SELS (future SE measure). The relationship between the two predictor variables (CSSE and SELS) and performance is presented in Table 4. Performance (average combined midterm and final exam scores) was negatively correlated to a slight degree with the CSSE (current SE measure), but not significant at the .05 level of significance The SELS (future SE measure) and Performance (average combined midterm and final exam scores) were positively correlated to a slight degree, but also not significant at the .05 level

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66 Question 3. What is the relationship between statistics anxiety and performance in a graduate introductory statistics course? Multiple regression correlation analysis was conducted between the CSCS of the STARS (sta tistics anxiety measure) and performance (average combined midterm and final exam scores) The results of the multiple regression correlation analysis show a small negative correlation between the CSCS (statistics anxiety measure) and performance (average combined midterm and final exam scores) ( .18) ( p = .0931). The relati onship is not significant as p value > .05. Question 4. What is the relationship between statistics self efficacy, statistics anxiety, and performance? Multiple regression correlation analysis was conducted to compare relationships among instrument results and any trends in the data. A multiple regression correlation analysis was conducted between the CSSE (current SE measure) scale, CSCS of the STARS (statistics anxiety measure) the SELS (future SE measure) scale, and the performance measure (average combined scores for the midterm and final exams ) T he data in the multiple regression correlation analysis indicated that when the three predictor variables (CSCS, CSSE, and SELS) were added, the R2 value was .0475 explaining 4 .7 % of the variance in performance (average combined scores for the midterm and final exams) as shown in Table 5, which includes the beta weights and uniqueness indices by instrument

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67 Table 5 Beta Weights and Uniqueness Indices Obtained in Multiple Regression Analysis Predicting Performance Predictor B SE B t Uniqueness Index CSCS 0.3037 0.2046 .1983 1.48 .0255 CSSE 0.0708 0.0630 .1310 1.12 .0146 SELS 0.0462 0.0777 .0766 0.59 .0041 Note R 2 = .0475 ( F [6,81] = .93). The multiple regression R 2 = .047. CSCS = Computational Self Concept Su bscal e, CSSE = Current Statistics Self Efficacy, SELS = Self Efficacy to Learn Statistics p >.05 for predictor variables. The correlation between performance (average combined midterm and final exam scores) CSCS (statistics anxiety measure) CSSE (cur rent SE measure), and SELS (future SE measure) measures are listed in Table 4. In reviewing the data, there were moderate and significant relationships. These are the relationships between the CSCS and the SELS .52 ( p <.0001), the CSCS and the CSSE .35 ( p = .0007), and the CSSE and SELS .26 ( p As discussed earlier, the results between the CSCS and SELS ( = .0143). r = .52) ( p The relationship between the CSCS and the CSSE .35 ( <.0001) show a moderate negative correlation. As an individuals score on the CSCS (statistics anxiety measure) decreases, his sco re on the SELS (future SE measure) increases and vice versa. So an individual with low CSCS (statistics anxiety measure) scores would inversely have high self efficacy to learn statistics SELS (future SE measure) scores. p = .0007) is negative and significant. There was a slight correlation between the CSCS

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68 (statistics anxiety measure) and CSSE (current SE measure) and this may be because the CSSE (current SE measure) is closer in construct to the CSCS (statistics anxiety measure) The CSSE (current SE measure) assessed participant s current ability to complete specific statistics tasks and this construct was similar to the CSCS (statistics anxiety measure) which also assessed participants feelings about completing specific statistics tasks. A student with low current statistics self efficacy would also have higher statistics anxiety and thus the CSSE (current SE measure) and CSCS (statistics anxiety measure) would have a lower negative correlation com pared to the CSCS (statistics anxiety measure) with the SELS (future SE measure). The association between the SELS and CSSE was weak, but significant .26 ( p = .0143). As was discussed in Chapter 2, the CSSE (current SE measure) and SELS (future SE measure) consist of the same 14 items and the only difference between them is in the instructions given to the participants prior to completing the instruments. Specifically, the CSSE (current SE measure) assessed participants confidence in their current abilit y to complete statistics related tasks and th e SELS (future SE measure) assessed their confidence in their ability to learn statistics related tasks. The main difference was in their rating their current ability and their ability to learn. Finally, a mult iple regression correlation was conducted between the CSCS (statistics anxiety measure) SELS (future SE measure) CSSE (current SE measure), and performance as measured by the average of the combined midterm and final exam scores. The data from the CSCS ( .18) ( p = .0931), the

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69 CSSE ( .04) ( p = .7299), and the SELS (.13) ( p The beta weights and uniqueness indices for the six predictors are presented in Table 5. Using multiple regression, performance scores (average combined midterm and final exam scores) were regressed on the linear combination of CSCS (statistics anxiety measure) SELS (future SE measure), and CSSE (current SE measure). The equation c ontaining these three variables accounted for approximately 4% of the observed variance in performance, = .2131) showed only slight correlations with performance and none of the correlations were significant. F (6, 81) = .93, p Beta weights (standardized multiple regression coefficients) and uniqueness indices were reviewed to assess the relative importance of the three variables in the prediction of performance. The uniqueness index for a given predictor is the percentage of variance in the criterion accounted for by that predictor, beyond the variance accounted for by the other predictor variables. Beta weights and uniqueness indices are presented in Table 5. >.05. None of the predictors displayed significant beta weights as presented in Table 5. The CSCS has the largest beta weight at .1983 ( p >.05). The uniqueness index for the CSCS was .0255. The C SCS accounted for 2% of the variance in performance beyond the variance accounted for by the other two predictors, F (6, 81) = .93, p Summary >.05. This chapter described the results of one measure of computational self concept as measured by the CSCS (stati stics anxiety measure) and two

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70 measures of self efficacy; specifically current statistics self efficacy (CSSE) and self efficacy to learn statistics (SELS) with performance (average combined midterm and final exam scores) in an introductory graduate stati stics course. Students enrolled in four sections in the fall of 2009 and the spring of 2010 were assessed to determine whether computational self concept and statistics self efficacy influence performance as measured by the average of the midterm and fina l exam scores. Internal consistency among items for each instrument was high (CSCS = .90, CSSE = .95, and SELS = .99). This was consistent with the findings of Finney and Schraw (2003). The results of the statistical data analysis were presented to answer four research questions. Means and standard deviations were presented and the results of each instrument and the correlation and intercorrelation of each instrument with performance were also reported. In addition, multipl e regression and correlation were conducted on the data to determine the amount of variance accounted for by the scores of each participant for each instrument and course section with performance. The results of the multiple regression correlation indicate that when all course sections we re added to the regression equation along with the three instruments; th e amount of variance explained was approximately 6%. Th e SELS (future SE measure) and performance (average combined midterm and final exam scores) were positively correlated to a sli ght degree but not significant at the .05 level. Bandura (1997) suggested that when self efficacy

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71 measures are assessed in close proximity to performance measures, the results of the self efficacy measures is more valid and reliable. Therefore the lack of significance may be the result of the fact that the SELS (future SE measure) was measured during the first week of the semester but the performance measures (midterm and final exams) were not assessed until the middle and end of the semester. Another possibility is that the sample was different from the sample in the Finney and Schraw (2003) study. The sample in the Finney and Schraw study was undergraduates. The sample in this study was primarily doctoral students and they may have seen themselves as more confidant as most have already earned a degree beyond the bachelors. A multiple regression correlation was conducted between the CSCS (statistics anxiety measure) CSSE (current SE measure), SELS (future SE measure), and performance as measured by midterm and final exam scores. The CSCS ( .18) ( p = .0931), the CSSE (.04) ( p = .7299), and the SELS (.13) ( p = .2131) showed only slight correlations with performance and were not significant. As previously stated these results may be because the self effi cacy measures and performance were assessed at different times and beyond what is recommended by Bandura (1997). The results of the multiple regression correlation analysis show a small negative correlation between the CSCS and performance (average combined scores for the midterm and final exams) ( .18) ( p = .0931). The relationship is not significant as the p value is greater than (.05).

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72 The correlation between the SELS (future SE measure) and the CSCS was ( .52) ( p The resulting correlation between the CS CS (statistics anxiety measure) and SELS (future SE measure) in this study may be the result of the fact that the CSCS (statistics anxiety measure) is asking participants to identify their level of anxiety as it relates to specific statistics test items at the present moment; whereas the SELS (future SE measure) is asking about their personal beliefs in their ability to learn specific statistics tasks at a later date. The difference of personal perception of time available to learn statistics could give st udents a feeling of over confidence. <.0001). This is consistent with Finney and Schraw (2003) who found a negative correlation of ( .471) between the SELS (future SE measure) and Spielbergers 1980 Statistics Test Anxiety (STA) instrument during the first administration of the instruments. The correlation between the Current Statistics Self Efficacy (CSSE) and Computational Self Concept (CSCS) subscale of the STARS was ( .35) ( p The stronger inverse correlation between the CSCS (statistics anxiety measure) and SELS (future SE measure) compared to the CSCS (statistics = .0007). As previously stated the resulting correlation between the CSCS (s tatistics anxiety measure) and CSSE (current SE measure) in this study could be because the CSCS (statistics anxiety measure) assessed participants level of anxiety as it related to completing specific statistics test items whereas the CSSE (current SE me asure) assessed participants personal beliefs in their current ability to complete specific statistics tasks.

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73 anxi ety measure) and CSSE (current SE measure) may be the result of the fact that the SELS (future SE measure) is asking about participants beliefs in their ability to learn statistics which because the SELS (future SE measure) asks participants to access their own level of confidence in acquiring future skills makes them more confident which is dissimilar to the Statistics Anxiety construct represented by the CSCS (statistics anxiety measure) which asks them to access their statistics problem solving skills in the present. The CSSE (current SE measure) is closer in construct to the CSCS (statistics anxiety measure) as the CSSE (current SE measure) asks about participants current ability to complete specific statistics tasks which is similar to the CSCS (stat istics anxiety measure) The CSCS (statistics anxiety measure) also asks participants to rate their feelings about completing specific statistics tasks. A student with low current statistics self efficacy would also have higher statistics anxiety. The r elationship between the CSSE (current SE measure), SELS (future SE measure) and CSCS (statistics anxiety measure) were significant at the .05 level. Observations Several observations occurred during the conduct of the study which were not a direct part of the research, but which were noteworthy. The Section 3 statistics course was unique compared to the other course sections in that it was offered online and that administration of the instrument packet did not exactly follow the process of the three tradit ional classroom courses. However, there was not difference in the four course sections The instruments were not provided to the course participants until after the first week of classes and the

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74 researcher did not have the opportunity to state the nature of the study. The instruments were uploaded to the course Blackboard web site and the students downloaded the instruments and informed consent forms. Study participants returned the informed consent forms and the completed instruments to the course inst ructor who then gave them to the researcher. The Section 4 traditional classroom statistics course was taught by a different instructor than the Section 1 and Section 2 instructor led statistics courses. Prior to administration of the instrument packet the course instructor introduced the researcher to the students but did not state the importance of the research study as had the instructor of Sections 1 and 2. This omission may have impacted the level of participation of the students. Two of the professors who typically teach the introductory graduate statistics class expected different outcomes in relation to the effect that statistics anxiety and statistics self efficacy would have on student exam performance. One of the professors who taught course se ctions used in this study stated that he was not surprised that there was no relationship between the statistics anxiety measure, statistics self efficacy, and performance He commented: Anecdotally I have seen students that appear anxious do well in my course and other students that appear anxious do not so well in my course. Similarly, I have seen students that dont appear anxious at all do both well and not so well in my course. ( statistics course professor personal communication, March 24, 2011) Th e other s tatistics professor stated that he was surprised that the results of the study showed no relation between statistics anxiety, statistics self efficacy, and performance.

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75 Chapter 5 Summary C onclusions I mplications and R ecommendations The purpose of this study was to investigate the relationship between statistics self efficacy, statistics anxiety, and performance in an introduct ory graduate statistics course. The sections of this chapter are a summary of the st udy, conclusions impli cations, and recommendation for further research Summary Little research had been conducted on the relationship between statistics self efficacy, statistics anxi ety, and performance in introductor y graduate statistics courses. The perception was that many graduate st udents struggle with statistics courses, because they do not have the necessary level of personal self efficacy t o achieve at the required level. The purpose of this study was to determine if there was a relationship between self efficacy, statistics anxie ty, and performance in introductory graduate statistics courses. Specifically, if a students statistics anxiety was high would their statistics self efficacy be low demonstrating a negative relationship? Also would lower levels of self efficacy and higher levels of statistics anxiety have an influence on performance in statistics classes? The research questions identified for this study included: 1. What is the relationship between statistics self efficacy and statistics anxiety?

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76 2. What is the relationship be tween the two statistics self efficacy instruments and performance in a graduate introductory statistics course? 3. What is the relationship between statistics anxiety and performance in a graduate introductory statistics course? 4. What is the relationship betw een statistics self efficacy, statistics anxiety, and performance? The research design compared the relationship between personal levels of statistics self efficacy ( future self efficacy to learn statistic s and current statistics self efficacy), statistics anxiety, and performance. Performance was defined as the average of the combined midterm and final exam scores in a graduate introductory statistics course. During the fall of 2009 and the spring of 2010 the instruments were distributed to 108 graduate s tudents from four different sections o f an introductory graduate statistics course in a College of Education at a doctoral degree granting, large metropolitan university with very high research activity in the southeastern U.S After removing the students who did not complete all the instruments or informed consent or who dropped the course prior to taking the final exam, the study was left with 88 graduate students The study design compared two statistics self efficacy measures (current stati stics self e fficacy and self efficacy to learn statistics), with each other and with statistics anxi ety and course performance (average combined midterm and final exam scores ). The two statistics self efficacy mea sures used the same 14

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77 items; however, the difference between the two instruments was in the instructions to the students. To view the items from different perspectives, t he Self Efficacy to Learn Statistics ( SELS ) instrument assessed the student to rate their confidence in their ability to learn statistics, whereas the Current Statistics Self Efficacy ( CSSE) assessed the students confidence in their ability to complete those tasks at the current point in time. In other words the SELS (future SE measure) assessed their confidence in learning tasks in the f uture, without requiring them to demonstrate their current ability; while the CSSE (current SE measure) assessed their ability to compl ete those tasks in the present. A demographic questionnaire was i ncluded to assess the sample from this doctoral degree g ranting, large metropolitan university with very high research activity in the southeastern U.S by age group, gender, and race/ ethnicity and to identify prior statistics course ex periences as well as the degree being sought. The three instruments plus th e demographic questionnaire were combined into one package for administration to participants. The dependent variable, class performance, was measured by averaging the comb ined midterm and final exam scores for each student in each class section. There w ere f our class sections with the following characteristics. Sections 1 and 2 were traditional classroom courses that were taught in the fall semester of 2009 by one instructor Section 3 was conducted as an online c lass that was taught in the fall semes ter of 2009 by a second instructor Section 4 was a traditional classroom course that was taught in the spring semester of 2010 by a third instructor

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78 All instrument s were distributed in the first week of classes except in the online class section. The four instruments used to gather data were: A demographic questionnaire; t he Computational Self Concept Subscale of the STARS an anxiety measure; t he Current Statistics Self Efficacy (CSSE) scale a current SE measure; and t he Self Efficacy to Learn Statistics (SELS) scale a future SE measure. Both of the statistics self efficacy measures (CSSE and SELS) demonstrated a low to moderate relationship with statistics anxiety (CSCS). The relationship between the CSSE (current SE measure) and SELS (future S E measure) was small positive and significant The relationship between statistics anxiety and performance (average combined midterm and final exam scores) was small and negative, but not significant. The relationship between the statistics self effica cy measures and performance (average combined midterm and final exam scores) was weak but positive for the SELS (future SE measure) and weak but negative for the CSSE (current SE measure) Neither stati stics self efficacy measure was significant in relat ion to performance. Conclusions There was an inverse relationship between s tatistics self efficacy and statistics anxiety. As student s level of statistics anxiety increased, their level of statistics self efficacy decreased. So student s experiencing moderate to high l evels of statistics anxiety would display low to moderate levels of personal statistics self efficacy.

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79 Neither statistics self efficacy nor statistics anxiety had an influence on course performance. Measures of statistics self efficacy (CSS E) and statistics anxiety (CSCS) displayed a negative relationship with performance. The relationship was weak and not significant. The CSSE (current SE measure) had a slightly larger negative relationship to performance (average combined midterm and final exam scores) than did the CSCS (statistics anxiety measure) The SELS (future SE measure) displayed a weak but positive relationship with performance (average combined midterm and final exam scores) However none of the instruments were significant i n relation to performance. The CSCS (statistics anxiety measure) showed a moderate but negative relationship with the SELS (future SE measure) and the relationship was significant. The correlation between the CSCS (statistics anxiety measure) and the SELS (future SE measure) in this study may be partly a result of the fact that the CSCS (statistics anxiety measure) is assessing participants level of anxiety as it related to spec ific statistics test items on that day ; whereas the SELS (future SE measure) i s assessing their personal beliefs in their ability to learn specific statistics tasks over a semester. This difference in the perception of time available to learn statistics may give students a feeling of confidence over and above what they would experi ence if they were given less time to learn statistics, or were tested on their s tatistical problem solving on that day The CSCS (statistics anxiety measure) showed a weak but negative relationship with the CSSE (current SE measure) and the relationship w as significant. The resulting correlation between the CSCS (statistics anxiety

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80 measure) and CSSE (current SE measure) in this study may be partly a result of the fact that the CSCS (statistics anxiety measure) is asking participants to identify their level of anxiety as it relates to specific statistics test items whereas the CSSE (current SE measure) is asking about their personal beliefs in their current ability to complete specific statistics tasks. The higher negative relationship between the CSCS (sta tistics anxiety measure) and SELS (future SE measure) compared to the CSCS (statistics anxiety measure) and CSSE (current SE measure) may be the result of the fact that the SELS (future SE measure) is asking about participants beliefs in their ability to learn; which because of this future skill requirement, makes them more confident, which is dissimilar enough to the Statistics Anxiety construct represented by the CSCS (statistics anxiety measure) The CSSE (current SE measure) is closer in construct to the CSCS (statistics anxiety measure) as the CSSE (current SE measure) relates to a participants current ability to complete specific statistics tasks and this construct is similar to the CSCS (statistics anxiety measure) which also asks participants to rate their feelings about completing specific statistics tasks. A student with low current statistics self efficacy could have higher statistics anxiety. This study demonstrates that the CSSE (current SE measure) and CSCS (statistics anxiety measure) dat a have a weaker relationship than the relationship between the CSCS (statistics anxiety measure) and SELS (future SE measure) data. There was no relationship between the two self efficacy instruments (SELS and CSSE) and course performance. However the dir ection of the

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81 relationship indicated students had more confidence in their future ability than in their current ability. This may be a product of the age and experience level of the graduate students. Course performance did not appear to be affected by statisti cs self efficacy in the graduate students. There was no relationship between the statistics anxiety instrument (CSCS) and course performance (average combined midterm and final exam scores) However the direction indicated an inverse relationship. S tudents demonstrated that as their statistics anxiety decreased their performance increased This may be a product of the prior statistics experience level of the graduate students. Those students with prior statistics knowledge could have lower stati stics anxiety than those students who had no prior statistics experience. Course performance did not appear to be affected by statistics anxiety in the students. As discussed earli er, the results between the CSCS (statistics anxiety measure) and the SELS (future SE measure) show ed a moderate negative relationship. As an individuals score on the CSCS (statistics anxiety measure) decreased, his score on the SELS (future SE measure) increased and vice versa. A n individual with low statistics anxiety would inversely have high self efficacy to learn. The inverse relationship between the CSCS (statistics anxiety measure) and the CSSE (current SE measure) was weaker than the inverse relationship between the CSCS (statistics anxiety measure) and SELS (future SE measure) This weaker relationship between the CSCS (statistics anxiety measure) and

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82 CSSE (current SE measure) may be because the CSSE (current SE measure) appears to be closer in construct to the CSCS (statistics anxiety measure) compared to the relationship between the CSCS (statistics anxiety measure) and SELS (future SE measure) The CSSE (current SE measure) assessed a participants current ability to complete specific statis tics tasks and this construct was similar to the CSCS (statistics anxiety me asure) which also assessed participants feelings about completing specif ic statistics tasks. The CSSE (current SE measure) w ith the CSCS (statistics anxiety measure) had a lower negative relationship compared to the CSCS (statistics anxiety measure) with the SELS (future SE measure) in this study. The association between the SELS (future SE measure) and CSSE (current SE measure) w as weak but significant. As discussed in Chapter 2, the CSSE (current SE measure) a nd SELS (future SE measure) consist ed of th e same 14 items ; and th e only difference between them was in the instructions given to the participants prior to completing the instruments. Specifically, the CSSE (current SE measure) assessed participants confidence in their current ability to complete statisticsrelated tasks and the SELS (future SE measure) assessed their confidence in their ability to learn statistics related tasks. The main difference was the emphasis that participant s were rating their current ability to learn in one instance and the other was their ability to learn in the future. Implications The implications arising from the research relate to faculty, students, researchers, and programs

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83 Faculty. The three instruments the CSCS (statistics anxiety measure) the CSSE (current SE measure), and the SELS (future SE measure) may not be appropriate with graduate students because their age and/or experiences may impact their self efficacy or anxiety levels and there were no significant differences between the instruments and performance The setting for this study was in a College of Education at a doctoral degree granting, large metropolitan university with very high research activity in the southeastern U.S The sample was primarily doctoral students from four different sections of a graduate statistics course. These students were primarily enrolled in educationrelated doctoral programs. Finney and Schraw (2003) in their research study found lower mean scores on the first administration of the CSSE (current SE measure) for their sample than the mean scores of the sample in this study. Their sample included undergraduate students enrolled in a statistics course offered through the Educational Psychology department. The sample for their study was made up of sophom ores (32.1%), juniors (32.1%) and seniors (19.3%). This difference in th e characteristics between Finney and Schraw s study and this study was mainly that this study included graduate students many who had already taken and completed statistics courses in the past and had e arned a bachelors or master s degree prior to enrollment, which may have contributed to a higher level of statistics self efficacy at the beginning of a statistics course. The mean score in the Finney and Schraw (2003) study was 29.33 ( SD = 11.33). In this study the mean score for the CSSE was 39.01 ( SD = 16.84). This 10 point variance between the two studies may be a result of this difference.

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84 Of note to the researcher was the fact that the SELS (future SE measure) mean score for the Finney and Schraw (2003) study was higher 71.55 ( SD = 11.77) than in this study 68.90 ( SD = The statistics anxiety in struments used in each study were different but the c onstruct was similar For this study the total possible score on the CSCS (statistics anxiety measure) was 35 points indi cating high statistics anxiety. In the Finney and Schraw (2003) study the total possible number of points was 80. The mean score i n this stud y for the CSCS (statistics anxiety measure) was 13.88 ( 15.08). However in this study the SELS (future SE measure) did not appear to influence course performance (average combined midterm and final exam scores) It appears that gradu ate students who may have had a low sense of self efficacy to learn at the beginning of the semester did not let that influence their performance on the midterm or final exams. SD = 5.94) and in the Finney and Schraw (2003) study the mean score was 37.56 ( SD Und erstanding where student s rank in relation to their statistics anxiety level and statistics sel f efficacy level can help to identify those students who may need extra attention at the beginning of a semester. Faculty can target students demonstrating low self efficacy in statistics and offer them assistance in developing statistics study skills. H elping students develop these skills could reduce their statistics anxiety and increase their self efficacy to learn statistics, which may in turn give them a psychological boost to their self worth and reduce the struggle associated with learning statisti cs. = 13.01).

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85 Determining a graduate students level of statistics self efficacy early in the semester is important in creating a st ress free and supportive learning environment allowing graduate students to approach other classes with more confidence. Faculty can use the SELS (future SE measure) and the CSSE (current SE measure) instruments during a graduate/ doctoral retreat or in the first statistics class, along with the class schedule list of assignments, etc. as a way to identify students who may require some additional support during the semester and during their programs of study. Neither the statistics self efficacy measures nor the statistics anxiety measure were significant in this study. The data indicate d that performance (average of combined midterm and final exam scores) wa s not affected by either statistics self efficacy level or statistics anxiety level. Two of the professors who typically teach the statistics courses expressed two different opinions One professor stated that he was surprised that there were no significant relationships between the statistics anxiety measure and performance. His expectation was that statistics anxiety would affect performance. The other professor stated that he was not surprised at the results and he expected there to be no significant relationship between statistics anxiety and performance. The instructor s who taught the courses used in this study provide a su pportive learning environment and t hey are available to meet with their students as needed. There is als o a lab staffed with tutors avail able to students who seek extra help. This support could be another factor that influenced course outcomes in this study.

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86 Faculty at other institutions in a different learning environment may not be as supportive. They may believe in a sink or swim approach to learning statistics and therefore, may have higher levels of statistics anxiety related to their statistics classes. Student s Students preparing to take statistics courses can assess their own levels of statisti cs self efficacy and statistics anxiety to see how ready they believe themselves to be when beginning a statistics course. Those students who score high on statistics self efficacy measures can begin a statistics plan of study with confidence. Those stud ents who score lower on statistics self efficacy measures can request extra help, utilize extra resource materials, and visit the lab to increase their statistics self efficacy and decrease their statistics anxiety. Students at other institutions can also assess their levels of statistics self efficacy and statistics anxiety prior to or at the beginning of a statistics course. In this way they can develop an assessment of their abilities and seek out extra resource s and assistance as needed. Researcher s This study did not find a relationship between statistics anxiety, statistics self efficacy and performance in a graduate statistics course. The Finney and Schraw (2003) study did find a relationship. One of the main differences between the two studies was that the CSSE (current SE measure) was given a second time before the final exam in th e Finney and Schraw (2003) research. Finney and Schraw were able to show an increase in current statistics self efficacy over the course of a semester and as a resu lt conclude that statistics anxiety affected performance.

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87 Finney and Schraw (2003) used a series of performance measures to define course performance. These included a students performance on 14 statistics problems that corresponded to each item on the C SSE (current SE measure) and the SELS (future SE measure) and the total percentage of points earned in the class. In this study the average of the combined midterm and final exam scores were used as the definition of performance. The 14 statistics problems u sed by Finney and Schraw (2003) were given to students at the same time that the CSSE (current SE measure) was distributed. Bandura (1997) suggested that the closer the criterion measure is to the performance outcome, the more accurate are the resul ts. In this study the performance m easure was not obtained until the mid point of the semester and again at the end of the semester. Increase in statistics self efficacy and reduction of statistics anxiety are goals in themselves. CSSE (current SE measur e) would be useful when developing different teaching methods and assessing if they affect personal self beliefs about statistics. The SELS (future SE measure) instrument would be helpful when administered prior to beginning a course to identify students who have low self efficacy beliefs to learn the skills necessary to finish statistical tasks. Researchers can use the statistics self efficacy measures and statistics anxiety measures as part of a set of diagnostic tools to identify statistics anxiety in a sample of students By doing so they may be able to create better ways of reducing statistics anxiety to a level where it is manageable for students.

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88 This study contributes to the body of research by confirming that items in the three instruments had hi gh int ernal reliability and measured graduate student s level of statistics self efficacy and statistics anxiety for the sample. Even though the results of the instruments did not show a significant relationship with performance the results did show that these measures of statistics anxiety and statistics self efficacy existed in a sample of graduate students. Recommendations for Further Research Further research could be conducted with a larger sample size from the same population using the same instruments, but offering the CSSE (current SE measure) ins trument a second time, the week pr ior to final exams. In this way a comparison bet ween CSSE (current SE measure) at time 1 and time 2 could be compared to performance at the end of the semester. Questions that could be raised might include the following Specifically, does current statistics self efficacy increase by the end of the semester? D oes level of current statistics self efficacy influence performance? As previously stated no relationship was found in this study between the statistics anxiety, statistics self e fficacy and pe rformance measures However, other studies have found a relationship between, statistics anxiety statistics self efficacy, and performance measures Therefore, more research could be conducted in the area of statistics anxiety, statistics self efficacy, and performance measures as discussed below. Additional research could be conducted to c ompare the statistics self efficacy and statistics anxiety of graduate and under graduate populations.

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89 Statistics se lf efficacy measures can investigate whether there is a difference in the statistics anxiety and statistics self efficacy of undergraduates compared to graduate students. Specifically, do graduate students possess higher levels of statistics self efficacy and lower levels of statistics anxiety than undergraduates? A nother possibility for future research might be to conduct a longitudinal r esearch study to measure the change in statistics self efficacy and statistics anxi ety of students as they advance through their college career. It could begin as they enter college as undergraduates and continue to the point where they enter and complete an advanced graduate or doctoral degree. Specifically, does statistics self effic acy increase and statistics anxiety decrease as a student progresse s through undergraduate studies and advances through doctoral studies? Another study could be conducted to compare differences between female and male graduate student s levels of statistic s self efficacy and statistics anxiety. Specifically, do female graduate students possess different levels of statistics self efficacy or statistic s anxiety than their male counterparts ? A follow on research study could include a set of interviews with those participants who scored high or low on the statistics self efficacy and statistics anxiety measures. These interviews would focus on the thoughts and feelings of participants as they relate to statistics. Ideally these interviews could be conducted once a w eek prior to class attendance. In this way the scope of the thoughts, feelings and actions of students as they relate to statistics self efficacy

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90 and statistics anxiety and their relationship to class performance could be better defined. Other r esearch could include a sample of graduate or doctoral dropouts or non starters to help determine what factors influenced their decision to leave a doctoral program of study or not pursue the doctorate. Specifically, a set of diagnostic instruments (including statistics self efficacy measures and statistics anxiety measures) and interviews could be used to assess common issues, program characteristics and student profiles. Determining these factors could help doctoral programs to minimize or alleviate th ese factors so that doctoral students have fewer roadblocks to the attainment of the degree. A comparison of graduate students studied in this research and students at other similarly classified i nstitutions could be conducted. Finally a research study co uld be develop ed to determine if there is a difference between levels of statistics anxiety and statistics self efficacy in graduate students who attend public universities compared to those who attend private universities

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91 References Bair, C., & Haworth, J. ( November, 1999). Doctoral student attrition and persistence: A meta synthesis of research. Paper presented at the annual meeting of the Association for the Study of Higher Education, San Antonio, TX. Bandalos, D. L., Finney, S. J., & Geske, J. A. (2003). A model of statistics performance based on achievement goal theory. Journal of Educational Psychology, 95 (3), 604 607. doi:10.1037/00220663.95.3.604 Bandura, A. (1989). Regulation of cognitive processes through perceived self efficacy. Developmental Psychology 25 (5), 729. doi:10.1037//00121649.25.5.729 Bandura, A. (1995). Exercise of personal and collective efficacy in changing societies. In A. Bandura (Ed). Sel f efficacy in changing societies (pp. 1 45) Cambridge UK : Cambridge University Press Bandura, A. (1997). Self efficacy: The exercise of control. New York, NY: W. H. Freeman. Bell, B. S., & Kozlowski, S. W. 1. (2002). Goal orientation and ability: Interactive effects on self efficacy, performance, and knowledge. Journal of Applied Psychol ogy, 87 (3), 497 505. doi:10.1037//00219010.87.3.497 Bieschke, K., Bishop, R., & Garcia, V. (1996). The utility of the research self efficacy scale. Journal of Career Assessment, 4 (1), 5975. doi:10.1177/106907279600 400104 Bishop, R., & Bieschke, K. (1998). Applying social cognitive theory to interest in research among counseling psychology doctoral students: A path analysis Journal of Counseling Psychology, 45 (2), 182 188. doi:10.1037 //0022 0167. 45.2.182 Bong, M. (1998). Tests of the internal/external frames of reference model with subject specific academic self efficacy and framespecific academic self concepts. Journal of Educational Psychology, 90 (1), 102110. doi:10.1037 //0022 0663.90.1.102

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92 The Carnegie Foundation for the Advancement of Teaching. (2011). The Carnegie Classification of Institutions of Higher Education. Retrieved from www.carnegiefoundation.org/classifications Choi, N. (2005). Self efficacy and self concept as predictors of college students academic performance. Psychology in th e Schools 42 (2), 197205. doi:10.1002/pits.20048 Cohen, J. (1988). Statistical power analysis for the behavioral sciences Hillsdale, NJ: Lawrence Erlbaum. Cohen, J. (1992). A power primer. Quantitative Methods in Psychology, 112 (1), 155159 doi:10.10 37// 00332909.112.1.155 Cronbach, L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16 (3), 297334. doi:10.1007/BF02310555 Cruise, R. J., Cash, R. W., & Bolton, D. L. (1985). The development and validation of an instrument to measure statistical anxiety Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL. Cruise, R. J., & Wilkins, E. M. (198 0). STARS: Statistical Anxiety Rating Scale Unpublished manuscript, Andrews Universit y, Berrien Springs, MI. Eisenhart, M., & DeHaan, R. (2005). Doctoral preparation of scientifically based education researchers. Educational Researcher 34 (4), 3 13. doi:10.3102/0013189X034004003 Finney, S., & Schraw, G. (2003). Self efficacy beliefs in c ollege statistics courses. Contemporary Educational Psychology 28 161 186. doi:10.1016/ S0361476X(02)000152 Forester, M., Kahn, J., & HessonMcInnis, M. (2004). Factor structure of three measures of research self efficacy. Journal of Career Assessment 12 (1), 3 16. doi:10.1177/1069072703257719 Gelso C. J., & Lent, R. W. (2000). Scientific training and scholarly productivity: The person, the training environment, and their interaction. In S. D. Brown & R. W. Lent (Eds.), Handbook of counseling psychol ogy (3rd ed. pp. 109139). New York, NY: Wiley. Gelso, C. J., Mallinckrodt, B., & Judge, A. B. (1996). Research training environments, attitudes toward research, and research self efficacy: The revised research training environment scale. The Counseling Psychologist 24 (2), 304 322. doi:10. 177/0011000096242010

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93 Greeley, A., Johnson, E., Seem, S., Braver, M., Dias, L., & Evans, K. (1989). Research self efficacy scale Unpublished scale presented at the Conference of the Association for Women in Psychology Bethesda, MD. Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education 20 261273 doi:10.2307/749515 Hatcher, L. (1994). A step by step approach to using SAS for factor analysis and structural equation modeling Cary, NC: SAS Institute. Haynes, V. D. (2004). High rate of doctoral dropouts draws concern, research of its own Dixie Sun Online Edition 34 (20), 1 3. High, R. (2000). Important factors in designing statistical power analysis studies: The size of your study sample is critical to producing meaningful results. Computing News S ummer 20 00. Retrieved from http://cc.uoregon.edu /cnews /summer2000/index.html Holden, G., Bark er, K., Me enaghan, T., & Rosenberg, G. (1999). Research self efficacy: A new possibility for educational outcomes assessment Journal of Social Work Education, 35 (3), 463476. Lent, R. W., Brown, S. D., & Gore, P. A. (1997). Discriminant and predictive validity of academic self concept, academic self efficacy, and mathematics specific self efficacy. Journal of Counseling Psychology 44 (3), 307315. doi:10.1037/00220167.44.3.307 Lent, R. W., Lopez, F. G., & Bieschke, K. J. (1991). Mathematics self efficacy: Source s and relation to sciencebased career choice. Journal of Counseling Psychology 38 (4), 424 430. Nunnally, J. C. (1978). Psychometric theory (2nd ed.). New York, NY: McGraw Hill. OBrien, K., Malone, M., Schmidt, C., & Lucas, M. (19 98). Research self efficacy: Improvements in instrumentation. Poster session presented at the annual conference of the America Psychological Association, San Francisco, CA. Onwuegbuzie, A. J. (2003). Modeling statistics achievement among graduate students. Educational and Psy chological Measurement, 63 (6), 10201038. doi:10.1177/0013164402250989 Onwuegbuzie, A. J & Jiao, Q. G. (2004). Information search performance and research achievement: An empirical test of the Anxiety Expectation

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94 Mediation model of library anxiety. Jour nal of the American Society for Information Science and Technology 55 41 54. doi:10.1002/asi.10342 Owen, S., & Froman, R. (1988). Development of a college academic self efficacy scale (Report No. 012 263). East Lansing, MI: National Center for Research on Teacher Learning. (ERIC Document Reproduction Service No. ED298158) Pajares, F. (2002). Overview of social cognitive theory and of self effic acy Retrieved from http://www.emory.edu/EDUCATION/ mfp/eff.html Phillips, J., & Russell, R. (1994). Researc h self efficacy, the research training environment, and research productivity among graduate students in counseling psychology. Counseling Psychologist, 22 (4), 628641. doi:10.1177/0011000094224008 Roberts, D. M. & Bilderback, E. W. (1980). Reliability and validity of a statistics attitude survey. Educational and Psychological Measurement, 40 235 doi: 10.1177/00131644 8004000138 SAS Institute. (2005). SAS 9.1.2 Cary, NC: SAS Institute. Schau, C., Stevens, J., Dauphinee, T. L., & Del Vecchio, A. ( 1995). The development and validation of the survey of attitudes toward statistics. Educational and Psychological Measurement 5 5 868 doi: 10.1177 /0013164495055005022 Scholl, R. W. (2002). Affective motivation and emotional competency Retrieved from http://www.uri.edu/research/lrc/scholl/webnotes /Motivation_ Affective.htm Scholl, R. W. (2002). Expectancy theory. Retrieved from http://www.uri.edu / research /lrc/ scholl/ webnotes/ Motivation_Expectancy.html Schunk, D., & Pajares, F. (2002). The development of academic self efficacy. In A. Wigfield & J. Eccles (Eds.), Development of achievement motivation doi:10.1016/B9780127500539/500036 (pp. 1531). San Diego, CA: Academic Press. Sherer M. et al. (1982). The Self efficacy Scale: Construction and validation. Psychological Reports, 51 (2 ), 663671. Shivy, V., Worthington, E., Wallis, A., & Hogan, C. (2003). Doctoral research training environments (RTEs): Implications for the teaching of psychology. Teaching of Psychology 30 oi:10.1207/S15328023 TOP3004_03 (4), 297 302. d

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95 Silver, B., Smith, E., & Greene, B. (2001). A study strategies self efficacy instrument for use with community college students. Educational and Psychological Measurement, 61 (5), 849 865. doi:10.1177/001316 40121971563 Smallwood, S. (2004). Doctor dropout. The Chronicle of Higher Education, 50 (19), p. A10 Unrau, Y., & Beck, A. (2004). Increasing research sel f efficacy among students in professional academic programs. Innovative Higher Education, 28 187204. Varney, J. (2005). A study of the relationships among doctoral program components and dissertation self efficacy on dissertation progress Dissertation Abstracts International: Section A. Humanities and Social Sciences, 66 (04), 1239. Wei, P., & Tang, M. (2005). Students' perceptions on factors of statistics anxiety and instr uctional strategies Journal of Instructional Psychology 3 (32) Retrieved from http://findarticles.com/p/articles /mi_m0FCG /is_3_32 /ai_n15882749/ Wise, S. (1985). The development and validation of a scale measuring attitudes toward statistics Educational and Psychological Measurement 45 (2), 401405. Wood, R., & Locke, E. (1987). The relation of self efficacy and grade goals to academic performance. Educational and Psychological Measurement, 47 (4), 10131024. doi:10.1177/0013164487474017

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96 Appendices

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 97 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Bieschke, Bishop & Garcia, (1996) Research Self Efficacy Scale (RSES) 177 51 items 0 to 100 point scale Research SE with four dimensions: research conceptualiz ation, research implementati on, early tasks, and presenting results. An instrument to measure self efficacy related to the research process. Graduate students in the Sci ences and Humanities NI 0.98 Finney & Schraw (2003) Current Statistics Self -Efficacy (CSSE) 154 14 items 1 -6 Likert type scale Statistics SE An instrument to assess student's confidence in their ability to solve specific statistics related tasks. (current ability) Undergradu ate students enrolled in an introductory statistics methods course Parallel Analysis (PA) was used to extract a 1 factor solution explaining 74% of the variance in the responses W eek 1/ .90, W eek 2/ .93 Appendix A Comparative Matrix for Self Efficacy Instruments

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 98 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Finney & Schraw (2003) Self -Effi cacy to Learn Statistics (SELS) 154 14 items 1 -6 Likert type scale Statistics SE An instrument to assess student's confidence in their ability to learn to solve specific statistics related tasks. Undergradu ate students enrolled in an introductory statisti cs methods course Parallel Analysis (PA) was used to extract a 1 factor solution explaining 45% of the variance in the responses. 0.97 Gelso, et al. (1996) Revised Research Training Environment Scale (RTES-R) 173 54 items 5 point scale Research SE NI 173 doctoral students enrolled in six different universities NI 0.9 Hackett & Betz(1989) Mathematics Course Self Efficacy (SECourse) 205 18 items 10 point scale Math SE Ability to complete a series of math intensive college courses with a grade of B or better Undergradu ate students in an introductory psychology course Parallel Analysis (PA) was used to extract a 1factor solution explaining 51% of the variance in the responses. 0.94

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 99 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Hackett & Betz (1989) Mathematics Problem Self Efficacy (SEProblem) 2 05 19 items 11 point scale Math SE An instrument asking students to estimate their ability to solve 18 math problems. Undergradu ate students in an introductory psychology course NI 0.88 Holden, Barker, Meenaghan & Rosenberg (1999) Research Self Efficacy (RSE) Scale 135 9 research tasks 11 point scale Social Work (SW) and SpeechLanguage Pathology (SLP) A self -report survey instrument to assess student's confidence in their ability to perform specific research tasks. Social Work (SW) and SpeechLanguage Pa thology (SLP) graduate students NI 0.94 Adapted from Lent, Brown and Larkin (1986)/Lent, Brown & Gore (1997) Self -efficacy for Broad Academic Milestones Scale (SE-Broad) 205 12 items 10 point scale Academic SE Confidence in performing 12 generic academic behaviors Undergradu ate students in an introductory psychology course NI 0.88

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 100 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Lent, Lopez & Bieschke (1991) Mathematics Self Efficacy #1 295 #2 481 40 5 point scale Math SE Four "rationally developed" scales measuring the four sources of efficacy as desc ribed by Albert Bandura Freshmen and sophomores enrolled in an introductory psychology class (study #1), and high school students enrolled in math courses (study #2). Four factor model (NNFI=.989, CFI=. 992, =(51), 63.70 .56 to .90 (Study 1), .59 to .90 (Study 2) Lent, Lopez & Bieschke (1991) Perceived Sources of Mathematics Self -Efficacy #1 296 #2 481 40 6 point scale Math SE Four "rationally developed" scales measuring the four sources of efficacy as described by Albert Bandura. Freshmen and sophomores enrolled in an introductory psychology class (study #1), and high school students enrolled in math courses (study #2). Four factor model (NNFI=.989, CFI=.992, =(51), 63.71 .56 to .90 (Study 1), .59 to .90 (Study 2) O'Brien, Malone, Schmidt & Lucas, (1998) Research Attitudes Measure (RAM) 150 23 items 0 to 4 Research SE A different measure of research self efficacy. Graduate students in Counseling Psychology NI 0.89

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 101 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Owen & Froman (1988) College Academi c Self -Efficacy Scale (CASES) 230 33 items 5 point scale Academic SE A self -report measure of academic SE designed to measure the degree of confidence of performing typical academic behaviors of college students. Undergradu ate students enrolled in four general education classes NI 0.92 Phillips & Russell, (1994) Self -Efficacy in Research Measure (SERM) NI 33 items 0 to 9 Research SE A measure of graduate student self efficacy in research design, practical, writing, and quantitative skills. Graduate student s NI 0.96 Roberts and Bilderback (1980) Statistics Attitude Survey (SAS) NI 33 items 1 -5 Likert type scale (1)statistics usefulness (2) personal competence (3) affective responses An instrument designed to improve the prediction of success in statistics courses NI NI 0.93 in three samples

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 102 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Schau et al. (1995) Survey of Attitudes Toward Statistics Scale (SATS) NI 28 items 7 point Likert -type scale (1) attitudes about intellectual knowledge and skills when applied to statistics, (2) positive and negative feelings concerning statistics, (3) usefulness, relevance, and worth of statistics, and, (4) statistics difficulty. Four subscales measuring positive and negative feelings toward statistics NI NI .81 to .85 for Affect subscal e, .77 to .8 3 for the Cognitiv e subscal e, and .64 to .77 for the Difficult y subscal e. Sherer et al., (1982) General Self Efficacy Subscale of the Self Efficacy Scale 230 23 items 5 point scale General SE A general SE measure with two subscales (general and social) Undergradu ate students enrolled in four general education classes NI 0.86

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Appendix A Comparative Matrix for SelfEfficacy Instruments (Continued) 103 Developer Instrumentation N No. of Items Response Scale Domains Instrument Description Population Description Validity Varney (2005) Dissertation Appraisal Inventory 51 16 0 to 100 Dissertation writing tasks and statistics methods tasks A 16 item instrument assessing students ability to write the dissertation, select appropriate statistical tests, to seek help from leaders in the field, and dissertation committee. Doctoral students in the dissertation stage NI .90 -.97 Wise (1985) Attitudes Toward Statistics Scale (ATS) NI 9 ite m course subscale a nd a 20 item field sub scale 1 -5 Likert type scale (1) attitudes toward current statistics course, and (2) usefulness of statistics in chosen field of study Two subscales based on the SAS which measure students attitudes toward statistics NI NI 0.9 Wood a nd Locke (1987) Specific Self Efficacy 230 7 items none re-ported Course Specific SE SE specific to a course in seven major academic areas Undergradu ate students enrolled in four general education classes NI 0.92 Note. NI = No Information

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104 Appendix B De mographic Questionnaire ID# Please write in the unique ID number assigned to you. Gender: Male __ Female __ What r ace/ethnic group? _______________ ___ To What Age Group do you belong: Under 21 2225 2630 3135 3640 4149 5059 Over 60 What i s the highest college degree you have received? Bachelors Masters Doctorate/Professional Please indicate if you are degree seeking and in which program you are currently enrolled: Non degree seeking Degree seeking Enrolled in Masters degree program Enrolled in Doctoral degree program Enrolled in other degree program, please specify Please indicate if you have taken a Bachelors or Masters level statistics course prior to this one: Yes, please indicate date completed ____________________ No

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105 Appendi x C Statistical Anxiety Rating Scale ( STARS ) Part I The items below refer to experiences that may cause anxiety. Circle the number indicating the amount of anxiety you would experience in each of the following situations. No Anxiety Very Much Anxiety 1 2 3 4 5 __________________________ ___________________________________________________ 1. Studying for an examination in a st atistics course 1 2 3 4 5 2. Interpret ing the meaning of a table in a journal article 1 2 3 4 5 3. Going to ask my statistics teacher for individual help with material I am h aving difficulty under standing 1 2 3 4 5 4. Doi ng the homework for a statistics course 1 2 3 4 5 5. Making an objective decision based on empirical data 1 2 3 4 5 6. Reading a j ournal article that includes some statistical analyses 1 2 3 4 5 7. Trying to decide which analysis is appropriate for your research project 1 2 3 4 5 8. Doing the final examination in a statistics course 1 2 3 4 5 9. Reading an advertisement for an automobile which includes figures on gas mileage, compliance wit h population regulations, etc. 1 2 3 4 5 10. Walki ng into the classroom to take a statistics test 1 2 3 4 5 11. Interpreting the meaning of a probability value once I have found it. 1 2 3 4 5 12. Arranging to have a body of data put into t he computer 1 2 3 4 5 13. Finding that another student in class got a different answer than you did to a stati stical problem 1 2 3 4 5 14. Figuring out whether to r eject or retain the null hypothesis 1 2 3 4 5 15. Waking up in the morning on the day of a statistics test 1 2 3 4 5 16. Asking one of your professors for help in understanding a printout 1 2 3 4 5 17. Trying to understand the odds in a lottery 1 2 3 4 5

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106 Appendix C Statistical Anxiety Rating Scale (STARS) (Continued) No Anxiety Very Much Anxiety 1 2 3 4 5 _____________________________________________________________________________ 18. Seeing a student poring over the computer printouts related to his/her researc h 1 2 3 4 5 19. Asking som eone in the computer center for h elp in understanding a printout 1 2 3 4 5 20. Trying to understand the statistical analyses described in the abstract of a journal article 1 2 3 4 5 21. Enro lling in a statistics course 1 2 3 4 5 22. Going over a final examination in statistics aft er it has been graded 1 2 3 4 5 23. Asking a fellow student for help in under standing a printout 1 2 3 4 5 24. Since I am by nature a subjective person, the objectivity of statistics is inappropriate for me. 1 2 3 4 5 25. I haven't had math for a long time. I know I'll have problems get ting through statistics 1 2 3 4 5 26. I wonder why I have to do all these things in statistics when in actual life I'll never use them. 1 2 3 4 5 27. Statistics is worthless to me since it's empirical and my area of specialization is philosophical. 1 2 3 4 5 28. Statistics takes more time than it's worth. 1 2 3 4 5 29. I feel statistics is a waste. 1 2 3 4 5 30. Statistics teachers are so abstract they seem inhuman. 1 2 3 4 5 31. I can't even understand seventhand eighthgrade math; how can I possibly do statistics. 1 2 3 4 5 32. Most statistics teachers are not human. 1 2 3 4 5 33. I lived this long without knowing statistics, why should I learn it now? 1 2 3 4 5 34. Since I've never enjoyed math, I don't see how I can enjoy statistics. 1 2 3 4 5 35. I don't want to learn to like statistics. 1 2 3 4 5

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107 Appendix C Statistical Anxiety Rating Scale (STARS) (Continued) No Anxiety Very Much Anxiety 1 2 3 4 5 _____________________________________________________________________________ 36. Statistics is for people, who have a natural leaning toward math. 1 2 3 4 5 37. Statistics is a grind, a pain I could do without. 1 2 3 4 5 38. I don't have enough brains to get through statistics. 1 2 3 4 5 39. I could enjoy statistics if it weren't so mathematical 1 2 3 4 5 40. I wish the statistics requirement would be removed from my academic program. 1 2 3 4 5 41. I don't understand why someone in my field needs statistics. 1 2 3 4 5 42. I don't see why I have to clutter up my head with statistics. It has no significance to my life work. 1 2 3 4 5 43. Statisti cs teachers talk a different language. 1 2 3 4 5 44. Statisticians are more number oriented than they are people oriented. 1 2 3 4 5 45. I can't tell you why, but I just don't like st atistics. 1 2 3 4 5 46. Statistics teachers talk so fast you cannot logically follow them. 1 2 3 4 5 47. Statistical figures are not fit for human consumption. 1 2 3 4 5 48. Statistics isn't really bad. It's just too mathematical. 1 2 3 4 5 49. Affective skills are so important in my profession that I don't want to clutter my thinking with something as cognitive as statistics. 1 2 3 4 5 50. I'm never going to use statistics so why should I have to take it? 1 2 3 4 5 51. I'm too slow in my thinking to get t hrough statistics. 1 2 3 4 5

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108 Appendix D Computational Self Concept Subscale (CSCS) This is an inventory of your feelings toward statistics. There are no right or wrong responses only different ones. You can ind icate whether or not a statement describes your feelings by circling the appropriate response below. Please respond to all of the items. A score of 5 indicates that you strongly agree. A score of 1 indicates that you strongly disagree. Strongly Strongly Disagree Agree 1 2 3 4 5 (Item 25) I haven't had math for a long time. I know I'll have problems getting through statisti cs 1 2 3 4 5 (Item 31) I can't even understand seventhand eighthgrade math; how can I possibly do statistics. 1 2 3 4 5 (Item 34) Since I've never enjoyed math, I don't see how I can enjoy statistics 1 2 3 4 5 (Item 38) I don't have enough brains to get through statistics 1 2 3 4 5 (Item 39) I could enjoy statistics if it weren't so mathematical. 1 2 3 4 5 (Item 48) Statistics isn't really bad. It's just too mathematical. 1 2 3 4 5 (Item 51) I'm too slow in my thinking to get through statistics. 1 2 3 4 5

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109 Appendix E Current Statistics Self Efficacy (CSSE) Please rate your confidence in your current ability to successfully complete the following tasks. The item scale has 6 possible responses: (1) = no confidence at all, (2) = a little confidence, (3) = a fair amount of confidence, (4) = much confidence, (5) = very much confidence, (6) = complete confidence. For each task, please mark the one response that represents your confidence in your current ability to successfully complete each task. 1 2 3 4 5 6 No confidence Complete confidence 1. Identify the scale of measurement for a variable. 1 2 3 4 5 6 2. Interpret the probability value ( p value) from a statistical procedure. 1 2 3 4 5 6 3. Ident ify if a distribution is skewed when given the values of three measures of central tendency. 1 2 3 4 5 6 4. Select the correct statistical procedure to be used to answer a research question. 1 2 3 4 5 6 5. Interpret the results of a statistical procedure in terms of the research question. 1 2 3 4 5 6 6. Identify the factors that influence power. 1 2 3 4 5 6 7. Explain what the value of the standard deviation means in terms of the variable being measured. 1 2 3 4 5 6 8. Distinguish between a Type I error and a Type II error in hypothesis testing. 1 2 3 4 5 6 9. Explain what the numeric value of t he standard error is measuring. 1 2 3 4 5 6 10. Distinguish between the objectives of descriptive versus inferential statistical procedures. 1 2 3 4 5 6 11. Distinguish between the information given by the three measures of central tendency. 1 2 3 4 5 6 12. Distinguish between a population par ameter and a sample statistic. 1 2 3 4 5 6 13. Identify when the mean, median and mode should be used as a measure of central tendency. 1 2 3 4 5 6 14. Explain the difference between a sampling distribution and a population distribution. 1 2 3 4 5 6 Permission to use granted by Finney and Schraw (personal communication, 2004).

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110 Appendix F Self effica cy to Learn Statistics (SELS) Please rate your confidence in learning the skills necessary while you're in this class to successfully complete the following tasks. The item scale has 6 possible responses: (1) = no confidence at all, (2) = a little confide nce, (3) = a fair amount of confidence, (4) = much confidence, (5) = very much confidence, (6) = complete confidence. For each task, please mark the one response that represents your confidence in learning the skills necessary in this course to successfull y complete the task. 1 2 3 4 5 6 No confidence Complete confidence 1. Identify the scale of measurement for a variable. 1 2 3 4 5 6 2. Interpret the probability value ( p value) from 1 2 3 4 5 6 a statistical procedure. 3. Identify if a distribut ion is skewed when given the 1 2 3 4 5 6 values of three measures of central tendency. 4. Select the correct st atistical procedure to be used 1 2 3 4 5 6 to answer a research question. 5. Interpret the results of a statistical 1 2 3 4 5 6 procedure in terms of the research question. 6. Identify the factors that influence power. 1 2 3 4 5 6 7. Exp lain what the value of the standard deviation 1 2 3 4 5 6 means in terms of the variable being measured. 8. Distinguish between a Ty pe I error and a Type II error 1 2 3 4 5 6 in hypothesis testing. 9. Explain what the numeric value of the standard 1 2 3 4 5 6 error is measuring. 10. Distinguish between t he objectives of descriptive 1 2 3 4 5 6 versus inferential statistical procedures 11. D istinguish bet ween the information given by 1 2 3 4 5 6 the three measures of central tendency. 12. Distinguish betwee n a population parameter and 1 2 3 4 5 6 a sample statistic. 13. Identify when the mean, median and mode 1 2 3 4 5 6 should be used as a measure of central tendency. 14. Explain the di fference between a sampling 1 2 3 4 5 6 distribution and a population distribution. Permission to use granted by Finney and Schraw (personal communication, 2004).

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111 Appendix G Letter to Graduate S tudents Dear Graduate Student, I am conducting a research study to measure the personal self efficacy beliefs of graduate students as they relate to completing statistic s related tasks. My research study involves the completion of an instrument and a demographic questionnaire that needs to be completed during the second week of the semester. Participation in this study will help you to have a better understanding of your personal self efficacy beliefs as they relate to statistics tasks. Self efficacy beliefs are those beliefs you have about your confidence in your ability to complete specific tasks. For example: I am confident that I can select the appropriate statistic al procedure when estimating validity I hope that you will help me further my research by completing the survey and demographic questionnaire. Your responses are critical to my research. Thank you. William Ray Schneider Doctoral C andidate

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About the Au thor William (Ray) Schneider was honorably discharged from the United States Marine Corps in 1985 and began working in various industries over the next few years. He began attending community college in 1989 at the age of 25. After earning an associate s degree in 1992, he attend ed the University of South Florida (USF) in St. Petersburg, Florida earning a bachelors degree in English and American Literature in 1994. For the next few years he worked in the construction trades until enrolling in a master s degree program in 1998 at U SF in Tampa. After earning his masters degree in Adult Education, he began working as an instructional designer and performance consultant. His Doctor of Philosophy degree is in Curriculum and Instruction with a specializatio n in Adult Education and a cognate in Measurement and Research. He currently lives in North Caroli na with his wife and four dogs.


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The relationship between statistics self-efficacy, statistics anxiety, and performance in an introductory graduate statistics course
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ABSTRACT: The purpose of this study was to determine the relationship between statistics self-efficacy, statistics anxiety, and performance in introductory graduate statistics courses. The study design compared two statistics self-efficacy measures developed by Finney and Schraw (2003), a statistics anxiety measure developed by Cruise and Wilkins (1980), and a course performance measure. To view self-efficacy from two perspectives, the Current Statistics Self-Efficacy (CSSE) assessed student confidence in their ability to complete specific statistics tasks in the present, whereas Self-Efficacy to Learn Statistics (SELS) assessed student confidence in their ability to learn statistics in the future. The performance measure was the combined average of the midterm and final exam scores only, excluding grades from other course activities. The instruments were distributed to four sections of an introductory graduate statistics course (N=88) in a College of Education at a large metropolitan university during the first week of the semester during Fall 2009 and Spring 2010. Both of the statistics self-efficacy measures revealed a low to moderate inverse relationship with statistics anxiety and a low to moderate direct relationship with each other. In this study there was no correlation between statistics anxiety (CSCS), statistics self-efficacy (CSSE and SELS), and course performance. There was high internal reliability for each instrument's items making the instruments suitable for use with graduate students. However, none of the instruments' results were significant in relation to course performance with graduate students in this sample. Unlike prior research involving undergraduate-level statistic students that has reported a relationship between the CSSE and SELS, the present study, involving graduate students, did not find any significant correlation with performance. Additional research is suggested to investigate the reasons for the differences between the studies.
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