SidakCor: Sidak multiple testing procedure for correlations.

Description

Sidak multiple testing procedure for correlations.

Usage

SidakCor(
  data,
  alpha = 0.05,
  stat_test = "empirical",
  vect = FALSE,
  logical = FALSE,
  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 \(Y=(X_i-mean(X_i))(X_j-mean(X_j))\)

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

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

Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Universit<U+00E9> Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

<U+0160>id<U+00E1>k, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626-633.

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)
# adjusted p-values
res <- SidakCor(data,stat_test='empirical')
round(res,2)
# significant correlations with level alpha:
alpha <- 0.05
whichCor(res<alpha)
# directly
SidakCor(data,alpha,stat_test='empirical',arr.ind=TRUE)
# }