Multiple significance tests

Significance levels for multiple tests

Let X 1 . . . . . X, be n random variables, with cumulative distribution functions F1, . . . , F,. Define ¢i := Fi(Xi) for all i, and let ~(1) ~< ... ~< ~(,) be the order statistics of the (~)~. Let cq ~< ... ~< ~. be n numbers in the interval [0, 1]. We show that the probability of the event R := {(") ~< ct~ for all 1 ~< i ~< n} is at most min~n~Ji }. Moreover, this bound is exact: for any giv...

Multiple significance tests: the Bonferroni method.

Some Remarks on Simes Type Multiple Tests of Significance

Simes' theorem, posed in a multiple testing setup, has its genesis in the classical ballot theorem in uniform order statistics. The purpose of this note is to comment on this rediscovery of the Ballot theorem in multiple testing theory, and with a view to enhance scope of applications, to stress its ramifications in the same context. This privides sharper error rates. AMS Subject Classification...

Permutation versus Bootstrap Significance Tests in Multiple Regression and Anova

Kempthorne's (1952) formulation of the randomization test is extended to yield a permutational analog of the bootstrap significance test. In the new test, residuals of a multiple regression are permuted instead of being bootstrapped. The test is an attractive alternative for Oja's test that permutes predictors (Austr. J.

Tests of Significance

1. Introduction In applied investigations, one is often interested in comparing some characteristic (such as the mean, the variance or a measure of association between two characters) of a group with a specified value, or in comparing two or more groups with regard to the characteristic. For instance, one may wish to compare two varieties of wheat with regard to the mean yield per hectare or to...