Omnibus permutation tests of the overall null hypothesis in datasets with many covariates.

Tests of the overall null hypothesis in datasets with one outcome variable and many covariates can be based on various methods to combine the p-values for univariate tests of association of each covariate with the outcome. The overall p-value is computed by permuting the outcome variable. We discuss the situations in which this approach is useful and provide several examples. We use simulations to investigate seven omnibus test statistics and find that the Anderson-Darling and Fisher's statistics are superior to the others.