4 Matching Annotations
 May 2019

stats.stackexchange.com stats.stackexchange.com

Multiple comparisons: It is not good practice to test for significant differences among pairs of group means unless the ANOVA suggests some such differences exist. Nevertheless, I admit it is tempting to take another look at the comparison of G1 with G3 (ignoring the existence of G2 and perhaps assuming normality), but then you should use a Welch t test to account for the differences in sample variances, and you should not make claims about the result unless the Pvalue is as low as .01 or .02. Looking at that difference more carefully might prompt a subsequent experiment.
Test for significance among pairs when the overall f test is not significant.

 Apr 2019

statistics.laerd.com statistics.laerd.com

statistics.laerd.com statistics.laerd.com

There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test. Alternatively, you could run a KruskalWallis H Test. For most situations it has been shown that the Welch test is best. Both the Welch and Brown and Forsythe tests are available in SPSS Statistics (see our Oneway ANOVA using SPSS Statistics guide).
ANOVA is robust against violation of the assumption of equal variances, but...

However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed or (2) choose the nonparametric KruskalWallis H Test which does not require the assumption of normality.
ANOVA is robust against violation of normality, but...
