SidakCor_SD: Sidak multiple testing method for correlations with stepdown...
In TestCor: FWER and FDR Controlling Procedures for Multiple Correlation Tests

Description Usage Arguments Value References See Also Examples

Sidak multiple testing method for correlations with stepdown procedure.

SidakCor_SD(
  data,
  alpha = 0.05,
  stat_test = "empirical",
  vect = FALSE,
  logical = TRUE,
  arr.ind = FALSE
)

`data`	matrix of observations
`alpha`	level of multiple testing
`stat_test`	4 test statistics are available: 'empirical' √{n}abs(corr)* 'fisher' √{n-3}1/2\log( (1+corr)/(1-corr) ) 'student' √{n-2}abs(corr)/√(1-corr^2)* '2nd.order' √{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
`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 FALSE, returns a list of successive p-values : element [[i+1]] of the list giving the p-values evaluated on the non-rejected hypothesis at step [[i]]; p-values are either as a vector or a list depending on `vect`
`arr.ind`	if TRUE, returns the indexes of the significant correlations, with respect to level alpha

Returns

logicals, equal to TRUE if the corresponding element of the statistic vector is rejected, as a vector or a matrix depending of the value of vect,
an array containing indexes \lbrace(i,j),\,i<j\rbrace for which correlation between variables i and j is significant, if arr.ind=TRUE.

Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Université Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626-633.

ApplyFwerCor, SidakCor

  
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:
SidakCor_SD(data,alpha,stat_test='empirical', arr.ind=TRUE)
# successive p-values
res <- SidakCor_SD(data,stat_test='empirical', logical=FALSE)
lapply(res,FUN=function(x){round(x,2)})
# succesive rejections
lapply(res,FUN=function(x){whichCor(x<alpha)})