We start with a brief review of Bonferroni-based test procedures and subsequently describe parametric graphical approaches that account for the correlation between the test statistics as well as graphical approaches using the Simes test.
One general disadvantage of Bonferroni-based approaches is a perceived power loss, motivating the use of weighted parametric tests that account for the correlation between the test statistics or the use of weighted Simes tests.
In this section we give details on different test procedures that could be employed to test the intersection hypotheses, including weighted Bonferroni tests, weighted min- p tests accounting for the correlation between the test statistics, and weighted Simes' tests.
The Pearson coefficient for the correlation between the test and retest Actionable scores, that we obtained with one week interval, was 0.85, which indicates a good test-retest reliability.
This allows one to first derive suitable weighting strategies that reflect the given study objectives and subsequently apply appropriate test procedures, such as weighted Bonferroni tests, weighted parametric tests accounting for the correlation between the test statistics, or weighted Simes tests.
A weighted multiple test can then be applied to each intersection hypothesis H J, such as a weighted Bonferroni test, a weighted min- p test accounting for the correlation between the test statistics, or a weighted Simes test; see Section 3 for details.
Such gene set testing methods must specifically account for the correlation between gene-level test statistics.
Pearson's correlation test was used for the correlations between the expressions of all three genes, which show normal distribution.
Correlation between the tests was moderate.
Pearson's correlation coefficient was used for testing the correlation between morning and evening cortisol.
The modified t test presented by Dutilleul [1993. Modifying the t test for assessing the correlation between two spatial processes.
