Structural Equation Modelling applied to proposed Statistics Attitudes-Outcomes Model: A case of a University in South Africa

  • Bokang Ncube North West University DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)
  • Ntebogang Dinah Moroke North West University


The purpose of the study is to investigate the structural relationships among constructs of the statistics attitudes-outcomes model (SA-OM) using exploratory structural equation modelling (ESEM) methodology. The sample consists of 583 first-year undergraduate students enrolled for statistics courses at the university in South Africa. ESEM reveal that all but two of the nine constructs have well to excellent reliability. To enhance the model, we deleted the eight variables. All other indicators have a significant loading into a construct. Congruency of the SA-OM and expectancy value model (EVM) is noted. The SRMR for all modified models are less than 0.10 suggesting that all these models have acceptable fit. Moreover, all the modified models have RMSE values within the ranges of adequate fit. On the contrary, all the models have unacceptable fit according to PCF, CFI, AGFI and PGFI statistics, i.e. according to all parsimony fit indices except the RMSE. The results also reveal that all incremental fit indices but the BBNFI approve the modified models as acceptable since most of these indices are almost equal to a cut-off point of 0.9. However, BBNNI disapprove the ML3 and ML5 models as being acceptable. A host of inconsistencies in fit indices are noted.


Download data is not yet available.


Ajzen, I. (2005). Attitudes, personality, and behavior. McGraw-Hill Education, United Kingdom.
Anderson, J. C. & Gerbing, D. W. (1988). Structural equation modelling in practice: A review and recommended two-step approach. Psychological bulletin, 103(3), 411.
Anderson, J. C. & Gerbing, D. W. (1992). Assumptions and comparative strengths of the two-step approach comment on Fornell and Yi. Sociological Methods & Research, 20(3), 321-333.
Arumugam, R. N. (2014). Student's Attitude towards Introductory Statistics Course at public universities using partial least square analysis. Interdisciplinary Journal of Contemporary Research in Business, 6(4), 94 -123.
Bagozzi, R. P. (1980). Causal models in marketing. New York: Wiley.
Baloğlu, M. (2003). Individual differences in statistics anxiety among college students. Personality and Individual Differences, 34(5), 855-865.
Bandura, A. (1996). Social cognitive theory of human development. International encyclopaedia of education, 2, 5513-5518.
Bentler, P.M. (1989). EQS, Structural Equations, Program Manual, Program Version 3.0, Los Angeles: BMDP Statistical Software, Inc.
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological bulletin, 107(2), 238-246.
Bentler, P. M. & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological bulletin, 88(3), 588.
Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological Methods & Research, 17(3), 303-316.
Browne, M. W. & Cudeck, R. (1993). Alternative ways of assessing model fit. Sage focus editions, 154, 136.
Byrne, B. M. (1998). Structural Equation Modelling with LISREL, PRELIS and SIMPLIS: Basic concepts, applications and programming. Mahwah, New Jersey: Lawrence Erlbaum Associates.
Carnell, L. J. (2008). The effect of a student-designed data collection project on attitudes towards statistics. Journal of Statistics Education, 16(1), 1-15.
Cherney, I. D. & Cooney, R. R. (2005). Predicting student performance in a statistics course using the mathematics and statistics perception scale (MPSP).
Chiesi, F. & Primi, C. (2009). Assessing statistics attitudes among college students: Psychometric properties of the Italian version of the Survey of Attitudes toward Statistics (SATS). Learning and Individual Differences, 19(2), 309-313.
Chiesi, F. & Primi, C. (2010). Cognitive and non-cognitive factors related to students’ statistics achievement. Statistics Education Research Journal, 9(1), 6-26.
Chiesi, F., Primi, C. & Carmona, J. (2011). Measuring statistics anxiety cross-country validity of the Statistical Anxiety Scale (SAS). Journal of psychoeducational assessment, 29(6), 559-569.
Chin, W. W. & Todd, P. A. (1995). On the use, usefulness, and ease of use of structural equation modelling in MIS research: a note of caution. MIS quarterly, 2, 237-246.
Chin, W. W. (1998). The partial least squares approach to structural equation modelling. Modern methods for business research, 295(2), 295-336.
Cronbach, L. J. & Shavelson, R. J. (2004). My current thoughts on coefficient alpha and successor procedures. Educational and psychological measurement, 64(3), 391-418.
Dauphinee, T. L., Schau, C. & Stevens, J. J. (1997). Survey of attitudes toward statistics: Factor structure and factorial invariance for women and men. Structural Equation Modelling: a multidisciplinary journal, 4(2), 129-141.
Deci, E. L. & Ryan, R. M. (2002). Handbook of self-determination research. University Rochester press, 2002.
Dempster, M. & McCorry, N. K. (2009). The role of previous experience and attitudes toward statistics in statistics assessment outcomes among undergraduate psychology students. Journal of Statistics Education, 17(2), 1-7.
Dykeman, B. F. (2011). Statistics anxiety: Antecedents and instructional interventions. Education, 132(2), 441.
Eccles, J. S. & Wigfield, A. (1995). In the mind of the actor: The structure of adolescents' achievement task values and expectancy-related beliefs. Personality and Social Psychology Bulletin, 21, 215-225.
Eccles, J. S. & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual review of psychology, 53(1), 109-132.
Eccles, J. S., O'Neill, S. A. & Wigfield, A. (2005). Ability self-perceptions and subjective task values in adolescents and children. In What Do Children Need to Flourish? (237-249). Springer, United States.
Emmioğlu, E. (2011). The relationship between mathematics achievement, attitudes toward statistics, and statistics outcomes: A structural equation model analysis. Unpublished doctoral dissertation. Middle East Technical University, Ankara, Turkey.
Emmioğlu, E. & Çapa-Aydın, Y. (2011). A meta-analysis on students' attitudes toward statistics. A paper presented at the 58th world statistics congress of International Statistical Institute, Dublin, Ireland.
Emmioğlu, E. S. M. A. & Capa-Aydin, Y. E. S. I. M. (2012). Attitudes and achievement in statistics: A meta-analysis study. Statistics Education Research Journal, 11(2), 95-102.
Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage publishers.
Finney, S. J. & Schraw, G. (2003). Self-efficacy beliefs in college statistics courses. Contemporary Educational Psychology, 28(2), 161-186.
Galli, S., Chiesi, F. & Primi, C. (2010). Assessing Mathematics Competence in Introductory Statistics Courses: An Application of the Item Response Theory: ICOTS8.
Gefen, D., Straub, D. & Boudreau, M. C. (2000). Structural equation modelling and regression: Guidelines for research practice. Communications of the association for information systems, 4(1), 1-79.
Ghulami, H. R., Ab Hamid, M. R. & Zakaria, R. (2014). Partial least squares modelling of attitudes of students towards learning statistics. Journal of Quality Measurement and Analysis, 10(1), 1-16.
Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E. & Tatham, R. L. (2006). Multivariate data analysis (Vol. 6).
Hair, J. F., Black, W. C., Babin, B. & Anderson, R. (2010). Multirative Data Analysis: A Global Perspective: Pearson Prentice Hall, New Jersey.
Hamid, H. S. A. & Sulaiman, M. K. (2014). Statistics anxiety and achievement in a statistics course among psychology students. International Journal of Behavioral Science, 9(1), 55-66.
Hilton, S. C., Schau, C. & Olsen. J. A. (2004). Survey of attitudes toward statistics: Factor structure invariance and by administration time. Structural Equation Modelling, 11(1), 92-109.
Hopwood, C. J. & Donnellan, M. B. (2010). How should the internal structure of personality inventories be evaluated? Personality and Social Psychology Review, 14, 332-346.
Howell, D., Husain, A., Seow, H., Liu, Y., Kustra, R., Atzema, C. & Barbera, L. (2012). Symptom clusters in a population-based ambulatory cancer cohort validated using bootstrap methods. European Journal of Cancer, 48(16), 3073-3081.
Hu, L. T. & Bentler, P. M. (1995). Evaluating model fit. In R. H. Hoyle (Ed.), Structural Equation Modelling. Concepts, Issues, and Applications, Sage, London.
Hu, L. T. & Bentler, P. M. (1999). Cutoff criteria for fit indexes iin covariance structure analysis: Conventional criteria versus new alternatives. Structural eqquation modelling. A Multidisciplinary Journal, 6(1), 1-55.
Hulsizer, M. R. & Woolf, L. M. (2009). A guide to teaching statistics: Innovations and best practices (Vol. 10): John Wiley & Sons.
Jackson, D. L., Gillaspy Jr, J. A. & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: an overview and some recommendations. Psychological methods, 14(1), 6-23.
Jöreskog, K. G. (1966). Testing a simple structure hypothesis in factor analysis. Psychometrika, 31(2), 165-178.
Jöreskog, K. G. & Sorbom, D. (1984). LISREL VI: Analysis of linear structural relationships by the method of maximum likelihood. Mooresville, IN: Scientific Software.
Keeley, J., Zayac, R. & Correia, C. (2008). Curvilinear relationships between statistics anxiety and performance among undergraduate students: Evidence for optimal anxiety. Statistics Education Research Journal, 7(1), 4-15.
Kline, R. B. (2011). Convergence of structural equation modelling and multilevel modelling. na.
Lalonde, R. N. & Gardner, R. C. (1993). Statistics as a second language? A model for predicting performance in psychology students. Canadian Journal of Behavioural Science, 25(1), 108.
Lehmann, E. L. (1999). Elements of large-sample theory: Springer Science & Business Media, New York.
Lesser, L. M. & Pearl, D. K. (2008). Functional fun in statistics teaching: Resources, research and recommendations. Journal of Statistics Education, 16(3), 1-11.
Lowry, P. B. & Gaskin, J. (2014). Partial least squares (PLS) structural equation modelling (SEM) for building and testing behavioural causal theory: When to choose it and how to use it. IEEE Transactions on Professional Communication, 57(2), 123-146.
Marsh, H. W., Hau, K. T. & Wen, Z. (2004). In research of golden rules: Comment on hypothesis testing approaches to setting cutoff values fit indexes and dangers in over generalizing Hu & and Bentler's (1999) findings. Structural equation modelling, 11(3), 320-341.
Marsh, H. W. & Hocevar, D. (1985). Application of confirmatory factor analysis to the study of self-concept: First-and higher order factor models and their invariance across groups. Psychological bulletin, 97(3), 562.
McDonald, R. P. & Ho, M. H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological methods, 7(1), 64-82.
Miles, J. & Shevlin, M. (2007). A time and a place for incremental fit indices. Personality and Individual Differences, 42(5), 869-874.
Mueller, R. O. & Hancock, G. R. (2008). Best practices in structural equation modelling. In J.W Osborne (Ed). Best practices in quantitative methods (488-508) Thousand Oaks, CA Sage.
Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S. & Stilwell, C. D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105(3), 430.
Mvududu, N. (2003). A cross-cultural study of the connection between students' attitudes toward statistics and use of constructivist strategies in the course. Journal of Statistics Education, 11(3), 1-17.
Nasser, F. M. (2004). Structural model of the effects of cognitive and affective factors on the achievement of Arabic-speaking pre-service teachers in introductory statistics. Journal of Statistics Education, 12(1), 1-28.
O'Rourke, N. & Hatcher, L. (2013). A step-by-step approach to using SAS for factor analysis and structural equation modelling. SAS Institute.
Onwuegbuzie, A. J. (2000). Statistics anxiety and the role of self-perceptions. The Journal of Educational Research, 93(5), 323-330.
Onwuegbuzie, A. J. (2003). Modelling statistics achievement among graduate students. Educational and Psychological measurement, 63(6), 1020-1038.
Onwuegbuzie, A. J. & Wilson, V. A. (2003). Statistics Anxiety: Nature, etiology, antecedents, effects, and treatments-a comprehensive review of the literature. Teaching in Higher Education, 8(2), 195-209.
Onwuegbuzie, A. J. (2004). Academic procrastination and statistics anxiety. Assessment & Evaluation in Higher Education, 29(1), 3-19.
Pan, W. & Tang, M. (2004). Examining the effectiveness of innovative instructional methods on reducing statistics anxiety for graduate students in the social sciences. Journal of Instructional Psychology, 31(2), 149.
Pan, W. & Tang, M. (2005). Students' perceptions on factors of statistics anxiety and instructional strategies. Journal of Instructional Psychology, 32(3), 205.
Pett, M. A., Lackey, N. R. & Sullivan, J. J. (2003). Makiing sense of factor analysis for instrument development in health care research. Sage.
Ramirez, C., Emmioğlu, E., & Schau, C. (2010). Understanding students’ attitudes toward statistics: New perspectives using an Expectancy-Value Model of motivation and the Survey of Attitudes toward Statistics. Paper presented at the Joint Statistical Meetings, Vancouver.
Ramirez, C., Schau, C. & Emmioğlu, E. (2012). The importance of attitudes in statistics education. Statistics Education Research Journal, 11(2), 57-71.
Saris, W. E., Satorra, A. & Van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications. Structural Equation Modelling, 16(4), 561-582.
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, 55(5), 868-875.
Schau, C. (2003a). Students’ attitudes: The other important outcome in statistics education. Paper presented at the Proceedings of the Joint Statistical Meetings.
Sorge, C. & Schau, C. (2002). Impact of engineering students’ attitudes on achievement in statistics: A structural model. Paper presented at the annual meeting of the American Educational Research Association. New Orleans.
Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate behavioural research, 25(2), 173-180.
Steiger, J. H. & Lind, J. M. (1980). Statistically based tests for the number of common factors. Paper presented at the annual meeting for the Psychometric society, Iowa City, IA.
Suhr, D. D. (2006). Exploratory or confirmatory factor analysis? Cary: SAS Institute.
Suhr, D. D. & Shay, M., (2009). September. Guidelines for reliability, confirmatory and exploratory factor analysis. In Procedure of 2009 Western Users of SAS Conference, San Jose, CA.
Tanaka, J. S. & Huba, G. J. (1985). A fit index for covariance structure models under arbitrary GLS estimation. British Journal of Mathematical and Statistical Psychology, 38(2), 197-201.
Tanaka, J. S. (1993). Multifaceted conceptions of fit in structural equation models. Sage focuses editions, 154, 10.
Tempelaar, D. T., Schim van der Loeff, S. & Gijselaers, W. H. (2007). A structural equation model analysing the relationship of students’ attitudes toward statistics, prior reasoning abilities and course performance. Statistics Education Research Journal, 6(2), 78-102.
Tremblay, P. F., Gardner, R. & Heipel, G. (2000). A model of the relationships among measures of affect, aptitude, and performance in introductory statistics. Canadian Journal of Behavioral Science, 32(1), 40.
Ullman, J. B. (2006). Structural equation modelling: Reviewing the basics and moving forward. Journal of personality assessment, 87(1), 35-50.
Wiberg, M. (2009). Teaching statistics in integration with psychology. Journal of Statistics Education, 17(1), 1-16.
Wigfield, A. & Eccles, J. S. (2000). Expectancy–value theory of achievement motivation. Contemporary educational psychology, 25(1), 68-81.
Wigfield A. & Eccles J. S. (2002). The development of competence beliefs and values from childhood through adolescence. In A. Wigfield and J.S. Eccles (Eds.), Development of Achievement Motivation (pp. 92-120). Academic Press, San Diego, CA.
Wigfield, A., Eccles, J. S., Schiefele, U. R. R. & Davis-Keane, P. E. (2006). Development of achievement motivation. Handbook of child psychology, 933-1002.
Wright, S. (1918). On the nature of size factors. Genetics, 3(4), 367.
How to Cite
NCUBE, Bokang; MOROKE, Ntebogang Dinah. Structural Equation Modelling applied to proposed Statistics Attitudes-Outcomes Model: A case of a University in South Africa. Journal of Economics and Behavioral Studies, [S.l.], v. 8, n. 5, p. 222-239, oct. 2016. ISSN 2220-6140. Available at: <>. Date accessed: 28 feb. 2017.
Research Paper