The purpose of the experiment is to determine whether a particular drug (the treatment T) has a greater effect in genetically modified mice (Mut) than in normal mice (Wild-Type). Four independent groups of mice are selected: normal untreated (WT_C), normal with drug (WT_T), mutants untreated (Mut_C), and mutants with drug (Mut_T). The variable under study is a particular parameter of cardiac function we will label 'X'. It is well-known from the literature that T decreases X in WT mice. There is less evidence for this mutant strain, but here too T appears to decrease X. When X is (more or less) normally distributed and sample sizes are adequate, we would use a two-way ANOVA treatment no yes wild-type WT_C WT_T genome mutant Mut_C Mut_T and test the interaction term: genome x treatment. But the experiment is long and difficult and costly, and our entire sample size is only 14. So we have no choice but to use an exact nonparametric test, and I thought of npar1way with apriori contrasts of the form 1 -1 -1 1 but I can find no way to set this up, basically (WT_C - WT_T) - (Mut_C - Mut_T). The short sas program below produces two exact Mann-Whitney tests, WT_C versus WT_T and Mut_C versus Mut_T; without the 'by' statement, one gets the exact Kruskal-Wallis test for all 4 groups. The number of cases in each group is correct (3,5,2,4) but I have not used the original X values. ODS RTF File ="/folders/myshortcuts/Norman/Ahmad/test-4.rtf" bodytitle; data ahmad; input G$ X W; cards; WT_C 25 1 WT_C 24 1 WT_C 23 1 WT_T 22 1 WT_T 21 1 WT_T 20 1 WT_T 19 1 WT_T 18 1 Mut_C 23 2 Mut_C 22 2 Mut_T 15 2 Mut_T 14 2 Mut_T 13 2 Mut_T 12 2 ; run; proc npar1way data=ahmad plots=none wilcoxon; class G; by W; exact wilcoxon; var X; run; ODS RTF close;
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