Structural Equation Modelling applied to proposed Statistics Attitudes-Outcomes Model: A case of a University in South Africa
Abstract
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.Downloads
References
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. DOI: https://doi.org/10.1037/0033-2909.103.3.411
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. DOI: https://doi.org/10.1177/0049124192020003002
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.
BaloÄŸlu, M. (2003). Individual differences in statistics anxiety among college students. Personality and Individual Differences, 34(5), 855-865. DOI: https://doi.org/10.1016/S0191-8869(02)00076-4
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. DOI: https://doi.org/10.1037/0033-2909.107.2.238
Bentler, P. M. & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological bulletin, 88(3), 588. DOI: https://doi.org/10.1037/0033-2909.88.3.588
Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological Methods & Research, 17(3), 303-316. DOI: https://doi.org/10.1177/0049124189017003004
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. DOI: https://doi.org/10.1080/10691898.2008.11889551
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. DOI: https://doi.org/10.1016/j.lindif.2008.10.008
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. DOI: https://doi.org/10.1177/0734282911404985
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. DOI: https://doi.org/10.2307/249690
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. DOI: https://doi.org/10.1177/0013164404266386
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. DOI: https://doi.org/10.1080/10705519709540066
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. DOI: https://doi.org/10.1080/10691898.2009.11889515
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. DOI: https://doi.org/10.1177/0146167295213003
Eccles, J. S. & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual review of psychology, 53(1), 109-132. DOI: https://doi.org/10.1146/annurev.psych.53.100901.135153
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. DOI: https://doi.org/10.1007/0-387-23823-9_15
EmmioÄŸlu, 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.
EmmioÄŸlu, 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. DOI: https://doi.org/10.1016/S0361-476X(02)00015-2
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. DOI: https://doi.org/10.1207/S15328007SEM1101_7
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. DOI: https://doi.org/10.1177/1088868310361240
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. DOI: https://doi.org/10.1016/j.ejca.2012.04.008
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. DOI: https://doi.org/10.1080/10705519909540118
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. DOI: https://doi.org/10.1037/a0014694
Jöreskog, K. G. (1966). Testing a simple structure hypothesis in factor analysis. Psychometrika, 31(2), 165-178. DOI: https://doi.org/10.1007/BF02289505
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. DOI: https://doi.org/10.1037/h0078792
Lehmann, E. L. (1999). Elements of large-sample theory: Springer Science & Business Media, New York. DOI: https://doi.org/10.1007/b98855
Lesser, L. M. & Pearl, D. K. (2008). Functional fun in statistics teaching: Resources, research and recommendations. Journal of Statistics Education, 16(3), 1-11. DOI: https://doi.org/10.1080/10691898.2008.11889572
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. DOI: https://doi.org/10.1109/TPC.2014.2312452
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. DOI: https://doi.org/10.1207/s15328007sem1103_2
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. DOI: https://doi.org/10.1037/0033-2909.97.3.562
McDonald, R. P. & Ho, M. H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological methods, 7(1), 64-82. DOI: https://doi.org/10.1037/1082-989X.7.1.64
Miles, J. & Shevlin, M. (2007). A time and a place for incremental fit indices. Personality and Individual Differences, 42(5), 869-874. DOI: https://doi.org/10.1016/j.paid.2006.09.022
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. DOI: https://doi.org/10.1037/0033-2909.105.3.430
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. DOI: https://doi.org/10.1080/10691898.2003.11910726
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. DOI: https://doi.org/10.1080/10691898.2004.11910717
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. DOI: https://doi.org/10.1080/00220670009598724
Onwuegbuzie, A. J. (2003). Modelling statistics achievement among graduate students. Educational and Psychological measurement, 63(6), 1020-1038. DOI: https://doi.org/10.1177/0013164402250989
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. DOI: https://doi.org/10.1080/1356251032000052447
Onwuegbuzie, A. J. (2004). Academic procrastination and statistics anxiety. Assessment & Evaluation in Higher Education, 29(1), 3-19. DOI: https://doi.org/10.1080/0260293042000160384
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. & EmmioÄŸlu, 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. DOI: https://doi.org/10.1080/10705510903203433
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. DOI: https://doi.org/10.1177/0013164495055005022
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. DOI: https://doi.org/10.1207/s15327906mbr2502_4
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. DOI: https://doi.org/10.1111/j.2044-8317.1985.tb00834.x
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. DOI: https://doi.org/10.1037/h0087099
Ullman, J. B. (2006). Structural equation modelling: Reviewing the basics and moving forward. Journal of personality assessment, 87(1), 35-50. DOI: https://doi.org/10.1207/s15327752jpa8701_03
Wiberg, M. (2009). Teaching statistics in integration with psychology. Journal of Statistics Education, 17(1), 1-16. DOI: https://doi.org/10.1080/10691898.2009.11889509
Wigfield, A. & Eccles, J. S. (2000). Expectancy–value theory of achievement motivation. Contemporary educational psychology, 25(1), 68-81. DOI: https://doi.org/10.1006/ceps.1999.1015
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. DOI: https://doi.org/10.1016/B978-012750053-9/50006-1
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.
Copyright (c) 2016 Journal of Economics and Behavioral Studies
This work is licensed under a Creative Commons Attribution 4.0 International License.
Author (s) should affirm that the material has not been published previously. It has not been submitted and it is not under consideration by any other journal. At the same time author (s) need to execute a publication permission agreement to assume the responsibility of the submitted content and any omissions and errors therein. After submission of a revised paper in the light of suggestions of the reviewers, editorial team edits and formats manuscripts to bring uniformity and standardization in published material.
This work will be licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) and under condition of the license, users are free to read, copy, remix, transform, redistribute, download, print, search or link to the full texts of articles and even build upon their work as long as they credit the author for the original work. Moreover, as per journal policy author (s) hold and retain copyrights without any restrictions.
