1) Test for normality: Kolmogorov-Smirnov one-sample test
2) Comparing two related samples: Wilcoxon Signed Ranks Test
3) Comparing two unrelated samples: Mann-Whitney U-Test (both variables are categorical, ranksum2 in Stata)
4) Comparing more than two related samples: The Friedman Test
5) Comparing more than two unrelated samples: the Kruska-Wallis H-Test (kwallis2 in Stata)
6) Comparing variables of ordinal or dichotomous scales: Spearman Rank-Order (both variables are ordinal, spearman in Stata), Point-Biserial (pbis in Stata), Biserial (if one is ordinal, one is continuous) Correlations
7) Tests for nominal scale data: Chi-square and Fisher Exact Tests