First, I am not great with stats, it was definitely my weakest class in undergrad/honours, so please be patient (and gentle!)
I have a data set with responses to a 4 point survey item, gathered from 12 groups (which differ in size). My goal is to determine whether the groups are sufficiently similar so as to suggest that they belong to the same population (i.e. are a representative sample).
My first step was to run an ANOVA, which tells me that the means are significantly different between groups, but I'd like to see how their distributions compare too before ruling out the hypothesis that the groups' responses are similar between groups, not just the mean. I figured that although the means may vary, if the distributions of each group overlapped sufficiently, I could argue that they were similar.
I've looked at the coefficient of variation, which "[normalizes] the standard deviation so that it can be compared across various mean scales", I got the SD of the means of each group, CV = .47, which, it is suggested, indicates relatively low variation between group means.
I've also looked at KS test (which I am very vague on), but that appears to be suited only to 2 groups?
I'd love some guidance (handholding). I've always been afraid of stats since I first struggled, and now really regret not learning more.