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apval_Cai2014_diffcov <- function(sam1, sam2){
n1 <- dim(sam1)[1]
n2 <- dim(sam2)[1]
p <- dim(sam1)[2]
b <- 2*log(p) - log(log(p))
diff <- colMeans(sam1) - colMeans(sam2)
sam.cov1 <- cov(sam1)
sam.cov2 <- cov(sam2)
sam.diag1 <- diag(sam.cov1)
sam.diag1[sam.diag1 <= 10^(-10)] <- 10^(-10)
sam.diag2 <- diag(sam.cov2)
sam.diag2[sam.diag2 <= 10^(-10)] <- 10^(-10)
test.stat <- max(diff^2/(sam.diag1/n1 + sam.diag2/n2))
test.stat <- as.numeric(test.stat)
stan.stat <- test.stat - b
pval <- 1 - exp(-exp(-stan.stat/2)/sqrt(3.14159))
out <- NULL
out$sam.info <- c("n1" = n1, "n2" = n2, "p" = p)
out$cov.assumption <- "the two groups have different covariances"
out$method <- "asymptotic distribution"
out$pval <- pval
return(out)
}
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