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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?

Thanks!

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Regarding your first question, it depends whether or not you came to the data set with an a priori intention to focus on those two age sets (e.g. if the hypothesis you came in with was to compare differences between kids before and after they enter high school - or something like that). If you did have that kind of a priori hypothesis, then I don't see why focusing your analysis on those two groupings is a problem. However, if you split the data set into six yourself and then noticed after the fact that the comparison between two of them was interesting while the other pair-wise comparisons weren't, then no, you can't do that: that would be data dredging (aka data mining aka a fishing expedition...).

In this case, if you created the groups yourself and you were only interested in 2 of them, why did you create 6 groups in the first place?

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  • $\begingroup$ The research question is very broad, so I came to the data set with the hypothesis already constructed; however, not all the data fits into the two groups that are of interest to me. Rather than eliminating the rest of the data, I just split the data into six groups in case I wanted to do any further analysis. The narrow hypothesis I have come up with here certainly is not the only hypothesis testing I will be doing. I was just wondering if estimation would be possible for this data, as well. $\endgroup$ – dc3 Oct 28 '15 at 21:18

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