BHCor: Benjamini & Hochberg (1995)'s procedure for correlation testing.

Description

Benjamini & Hochberg (1995)'s procedure on the correlation matrix entries (no theoretical proof of control).

Usage

BHCor(
  data,
  alpha = 0.05,
  stat_test = "2nd.order",
  vect = FALSE,
  arr.ind = FALSE
)

Arguments

data

matrix of observations

alpha

level of multiple testing

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 \(Y=(X_i-mean(X_i))(X_j-mean(X_j))\)

vect

if TRUE returns a vector of TRUE/FALSE values, corresponding to vectorize(cor(data)) if FALSE, returns an array containing TRUE/FALSE values for each entry of the correlation matrix

arr.ind

if TRUE, returns the indexes of the significant correlations, with respect to level alpha

Value

Returns

an array containing indexes \(\lbrace(i,j),\,i<j\rbrace\) for which correlation between variables \(i\) and \(j\) is significant, if arr.ind=TRUE.

References

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society. Series B (Methodological), 289-300.

Examples

Run this code

# NOT RUN {
 
n <- 100
p <- 10
corr_theo <- diag(1,p)
corr_theo[1,3] <- 0.5
corr_theo[3,1] <- 0.5
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
alpha <- 0.05
# significant correlations:
BHCor(data,alpha,stat_test='empirical',arr.ind=TRUE)
# }