There appear to be some problems in Table 2.

For instance, Bonferroni is categorized here as specifically for "parametric situations." But in fact, Bonferroni is well known to be valid for any tests, parametric or not. Indeed, the Bonferroni inequalities are simply basic facts of probability. Consider for example the case of 2 events, each with a .025 probability. Certainly the probability that at least one of those events will occur cannot exceed the sum of the two individual probabilities: .025 + .025 = .05. That principle holds regardless of whether the 2 events are test results at all, let alone whether they are parametric test results. Thus, using the Bonferroni procedure provides valid experimentwise Type I error control regardless of whether the tests are parametric. The same is true of Holm's (1979) sequential modification of the Bonferroni procedure.

Similarly, the Šidák procedure's validity does not depend on the tests being parametric. By basic principles of probability, the Šidák procedure is valid for any nonnegatively dependent events (e.g., two-sided significance tests).

Of course, if the tests themselves are parametric (such as t-tests) and the parametric testing assumptions are not met, then the assumptions will remain unmet when Bonferroni (or Holm or Śidák) is applied. But those assumptions are inherent to the parametric tests themselves and have nothing to do with Bonferroni. If valid nonparametric tests are used, those tests will remain valid when Bonferroni-adjusted.

The Mann–Whitney–Wilcoxon U test is not a multiple comparison test at all. It's simply a type of comparison (like a t-test is a type of comparison). If one is performing multiple Mann–Whitney–Wilcoxon U tests, then one could apply a multiple comparison procedure (such as Bonferroni or Holm or Šidák) to those tests. But the Mann–Whitney–Wilcoxon U test itself is not a method of accounting for multiple testing, just like the t-test itself is not a method of accounting for multiple testing.