i have a 3-way mixed anova design: 2 IVs that are within-subject and 1 IV's that is a between-subject variable. the assumption of equality of variance (Leven's Test) was violated, as the test came out significant. the reason for that is that one group has slightly smaller SD compare to the rest. how should i treat it? do i have to use a different procedure?
Fisrtly,use another homogenity of variance test such as hartley Fmax to see results also true. In some analysis small variance differences may be result a significant levene result. Levene uses difference scores in each group and perform a ANOVA, So Levene results may be significant If groups size drastically differ or ıf some groups in your data extreme scores. According to Howell (2013, page 234) the results of variance analysis more likely to be valid when the ratio of largest variance to smallest variance was four or below among the groups.
Secondly, continue your analysis and use post hoc Games-Howell. and report homogenity of variance violated so I used games-howell
Third, perform a bootsrap analysis, ıt is no requirement for assumptions.
Fourth, you can also perform a Bayesian mixed anova design
Howell, D. C. (2013).Statistical Methods for Psychology. Belmont, CA: Wadsworth Cengage Learning.
Best.
If you have a total sample size greater than 30 and equal sub-sample sizes, ANOVA is robust to violations of homogeneity of variance. Noa Magal
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