First, we learned the Wilcoxon and Mann-Whitney tests. These tests can be considered as nonparametric alternatives for the paired two-sample and independent two-sample T-tests (see the last two pages of classroom notes I.). These tests gave the same conclusion for the questions found in the top of the 3. page of classroom notes I.: the orders of magnitude of day 2 and day 14 cholesterols of patients differ significantly and also the orders of magnitude of the day 14 cholesterols of patients and healthy cholesterol. In case of the Wilcoxon test to decide which variable has the larger order of magnitude, we reran the test with reversing the order of the two variables, and we compared the resulting test statistic with the original one. For the Mann-Whitney test, we wrote a function for the same purpose. Beside the p-value, it outputs the average ranks. We also used boxplots for comparing the order of magnitude of the variables. Finally, we learned the goodness of fit chi-square test (see the second page of classroom notes II., we postponed the first page to next week) and we ran it in R on simulated data.
I remark that instead of the Mann-Whitney test the two-sample Kolmogorov-Smirnov test and the two-sample Wald-Wolfowitz test can also be used to compare the distirbution of variables corresponding to two different groups. Nevertheless, if we are interested in the order of magnitude, then, in my opinion, the Mann-Whitney test is the appropriate nonparametric tool. Of course, if the sample size is large then the t-test can be used without the normality assumptions.