I'm pretty new in statistical testing and I'd like some help in what I'm doing. I have two groups of scores from 0-100. Group A has 10 values and group B has 70 values. Initially I'm testing normality using Shapiro-Wilk separately for each group. Is this correct or should I treat my data as one group with 80 values?
Assuming that is correct the separate testing, I found that Group A is not normal and group B is normal. Therefore I'm using the Mann-Whitney-Wilcoxon test for non-parametric testing as one of the groups is not normal. Is this correct or not?
After this I split Group B in 4 sub-groups with different sample sizes (11,20,24,15). Now I have 5 groups, Group A (same as initially) which is not normal and 4 sub-groups from the initial Group B which are normal again using Shapiro-Wilk.
Then I'm testing all 5 groups using Kruskal-Wallis for significant difference (non-parametric test, as I have one non-normal sample). From this I get significant difference among the five groups.
Finally using t-Test (when both samples are normal) and Mann-Whitney-Wilcoxon (when one of the two samples are not normal) I test all combinations of groups two by two in order to find which groups have and which don't have significant differences. Is this correct?
Could you help me with this? Any references to books or papers would be really helpful for me. I hope I used terminology correctly and explained my case well enough.