# Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix. Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix. Methods are described in Chapter 5 of Roux (2018) . ```r ApplyFwerCor( data, alpha = NULL, stat_test = "empirical", method = "Sidak", Nboot = 1000, stepdown = TRUE, vect = FALSE, logical = stepdown, arr.ind = FALSE ) ``` ## Arguments - `data`: matrix of observations - `alpha`: level of multiple testing (used if logical=TRUE) - `stat_test`: - **'empirical'**: $\sqrt{n}*abs(corr)$ - **'fisher'**: $\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )$ - **'student'**: $\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)$ - **'2nd.order'**: $\sqrt{n}*mean(Y)/sd(Y)$ with $Y=(X_i-mean(X_i))(X_j-mean(X_j))$ - `method`: choice between 'Bonferroni', 'Sidak', 'BootRW', 'MaxTinfty' - `Nboot`: number of iterations for Monte-Carlo of bootstrap quantile evaluation - `stepdown`: logical, if TRUE a stepdown procedure is applied - `vect`: if TRUE returns a vector of adjusted p-values, corresponding to `vectorize(cor(data))`; if FALSE, returns an array containing the adjusted p-values for each entry of the correlation matrix - `logical`: if TRUE, returns either a vector or a matrix where each element is equal to TRUE if the corresponding null hypothesis is rejected, and to FALSE if it is not rejected if `stepdown=TRUE` and `logical=FALSE`, returns a list of successive p-values. - `arr.ind`: if TRUE, returns the indexes of the significant correlations, with repspect to level alpha ## Returns Returns either * the adjusted p-values, as a vector or a matrix, depending on `vect` * logicals indicating if the corresponding correlation is significant if `logical=TRUE`, as a vector or a matrix depending on `vect`, * an array containing indexes $\lbrace(i,j),\,i\

ApplyFwerCor function