Inadvertent Use of ANOVA in Educational Research: ANOVA is not A Surrogate for MANOVA

Abstract

ANOVA and MANOVA address different research questions and decision on conducting one or the other of these tests relies on the research purpose. One prominent illegitimate analysis of multivariate data is developed out of conducting multiple ANOVAs rather than conducting a MANOVA. Another common mistake about MANOVA applications is the use of improper post hoc procedure. Post hoc procedures are needed to determine why the null hypothesis was rejected. Although the correct post hoc procedure for MANOVA is descriptive discriminant analysis (DDA), many researchers fail to conduct DDA to interpret their MANOVA results. The purpose of this study is two-fold; (1) we aim to emphasize the theory behind the MANOVA and its appropriate post hoc procedure and make clear distinction between surrogate statistical procedures such as ANOVA; and (2) this study also investigates the extent of incorrect analysis of multivariate dependent variables in educational research in Turkey. First, we provided a small simulation study to demonstrate the extent to which multiple ANOVAs yields contradictory results when they are inadvertently used to test group mean differences on multiple dependent variables. Results of the simulations indicated that MANOVA and multiple ANOVAs had severe disagreements under many conditions. Disagreement rate is elevated under the conditions where MANOVA retains the null hypothesis. Then, we systematically reviewed the archives of three education journals, which are classified as higher-, medium, and lower quality journals. Results indicated that correct use of MANOVA with its proper post hoc procedure is not common practice across educational researchers who publish in Turkish education journals.

Keywords

• Multivariate data analysis,multivariate dependent variable,ANOVA,MANOVA

References

1. Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. London; Routledge.
2. Fish, L. J. (1988). Why multivariate methods are usually vital. Measurement and Evaluation in Counseling and Development, 21, 130-137.
3. Glenn A. Bowen. (2009). Document Analysis as a Qualitative Research Method. Qualitative Research Journal, 9 (2), 27-40.
4. Huberty, C. J., & Morris, J. D. (1989). Multivariate analysis versus multiple univariate analysis. Psychological Bulletin, 105, 302-308.
5. Hummel, T. J., & Sligo, J. R. (1971). Empirical comparison of univariate and multivariate analysis of variance procedures. Psychological Bulletin, 76, 49-57.
6. Kieffer, K. M., Reese, R. J., & Thompson, B. (2001). Statistical techniques employed in AERJ and JCP articles from 1988 to 1997: A methodological review. Journal of Experimental Education, 69, 280-309.
7. R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http:www.R-project.org/.
8. Sherry, A. (2006). Discriminant analysis in counseling psychology research. The Counseling Psychologist, 34, 661-683.

9. Stevens, J. P. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaum Associates.
10. Tonidandel, S., & LeBreton, J. M. (2013). Beyond step-down analysis: A new test for decomposing the importance of dependent variables in MANOVA. Journal of Applied Psychology, 98, 469-477.
11. Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0
12. Warne, R. T. (2014). A primer on multivariate analysis of variance (MANOVA) for behavioral scientists. Practical Assessment, Research & Evaluation, 19(17), 1-10.
13. Warne, R. T., Lazo, M., Ramos, T., & Ritter, N. (2012). Statistical methods used in gifted education journals, 2006-2010. Gifted Child Quarterly, 56, 134-149.
14. Zientek, L. R., & Thompson, B. (2009). Matrix summaries improve research reports: Secondary analyses using published literature. Educational Researcher, 38, 343-352.