Statistics notes: Multiple significance tests: the Bonferroni method

Multiple significance tests: the Bonferroni method.

Statistics from the inside. 2. 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...

Some Notes on Parametric Significance Tests for Geographically Weighted Regression

The technique of geographically weighted regression (GWR) is used to model spatial ‘drift’ in linear model coefficients. In this paper we extend the ideas of GWR in a number of ways. First, we introduce a set of analytically derived significance tests allowing a null hypothesis of no spatial parameter drift to be investigated. Second, we discuss ‘mixed’ GWR models where some parameters are fixe...

Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests

The confirmatory analysis of pre-specified multiple hypotheses has become common in pivotal clinical trials. In the recent past multiple test procedures have been developed that reflect the relative importance of different study objectives, such as fixed sequence, fallback, and gatekeeping procedures. In addition, graphical approaches have been proposed that facilitate the visualization and com...