# How to test differences of means of 3 independent groups

I'm new to statistics and the only software i know how to use is SPSS. I need help....

I have 3 independent groups with sizes: 24, 27, 37. I wanted to test the difference between the means of their ages using ANOVA.

                                *mean age ± SD*
*Group1:   40.7297 ± 6.01225
*Group2:   31.5926 ± 4.93231
*Group3:   32.125  ± 4.4557

I have no problem with variances because Levene's test says they have equal. When I tested the NORMALITY of each group (with Shapiro-Wilk), one of them is NOT (p=0.022). I tried transforming my data using natural log and checked for normality of each.This time the other group gave p=0.031. Is it correct if i still use ANOVA? or is there any other test I can use with this situation?

Any help would be much appreciated.

• The Kruskal-Wallis test does not assume similar distribution shapes, and is therefore widely applicable. In it's most general sense it is a test for stochastic dominance among $k$ groups. The question of similarity of distributions only arises when one wants to interpret the results of the Kruskal-Wallis test (and say, post hoc multiple comparisons' i.e. using Dunn's test) in terms of median difference. – Alexis Aug 5 '14 at 18:54