Sensitivity of a 2 x 3 ANOVA on Normality and Homogeneity of Variances Assumptions

This study explored the differential results of parametric test and nonparametric test as applied to a 2 x 3 ANOVA. The data used in this study were those of NEU’s 2018 Science Fair Satisfaction Survey with the mean satisfactory rating (AVG) as the dependent variable for the original or untransformed data. The AVG for the six cells of the factorial design exhibited varying degree of negative skewness (-0.562 to -1.293). Five data transformation techniques (second to sixth power) were tried to satisfy assumptions of normality (skewness close to zero) and variance homogeneity (by Levene’s test). The fourth power transformation produced the data set that was closest to normality and simultaneously satisfied homogeneity of variances. Alternatively, nonparametric test was employed. The 2 x 3 ANOVA of untransformed and transformed data had the same output as Kruskal Wallis test in terms of the significance of main effect. ANOVA of untransformed and transformed data had the same result in the test of significance of interaction effect but there were differences in the result of post hoc tests brought by the effect of transformation on the homogeneity of variances. Transformation also had effect on power and effect size. Power and effect size tend to decrease as the power of transformation increased.