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

Year 2019, Volume: 10 Issue: 3, 302 - 314, 04.09.2019

Lokman Akbay , Tuncer Akbay , Osman Erol , Mustafa Kılınç

https://doi.org/10.21031/epod.524511

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

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