I have a data set with population information for 6 age groups. In theory, I wish to know if a specific two of these age groups are different from each other.
My first question is: Can I subset the data so that I only test one population against the other and completely ignore the other age groups? I am only interested in the difference between the specific two age groups. The data comes from one sample, and I created the age groups.
My second question is: In testing for significant differences in populations through different variables in the data set, I have conducted Kolmogorov-Smirnov and Wilcoxon rank sum tests on the variables that are obviously not normally distributed. There are some variables which are highly right-skewed, and a log transformation, confirmed by a Q-Q plot makes the data approximately normal. These tests have come out as significant, but I wish to know if there is a way to conduct an analysis on how much of a difference there is in each variable. Performing a t-test on the log transformed data doesn't seem to make sense because the geometric mean does not really carry the same meaning. Is it appropriate to conduct a regression with a continuous variable as the response and the categorical age variable as the predictor? In this case, I am not testing prediction power, but just wish to know the value of the coefficients. Is this method appropriate and how do I justify it if it is?