## Example of a "fishing expedition"

 n <- 25    # sample size; as a rule of thumb, 1/sqrt(n) is a statistically significant correlation
 k <- 100    # variables 

 X <- rnorm(n*k)            # X's are, to begin with, independent Normal(0,1) r.v.'s
 dim(X) <- c(n,k) 

 pairs(X)	                 # "matrix scatterplot" 
 cor(X)                          # correlation matrix

 pval <- matrix(0,k,k)

   for (i in 1:k)
     for (j in 1:k){
       pval[i,j] <- cor.test(X[,i],X[,j])$p.val
     }

  image(1:k, 1:k, 1- (pval < 0.05), main="Significant pairs") 

  # bonferroni correction 
 print(  alpha.star <- 0.05/choose(k,2) )
 image(1:k, 1:k, 1- (pval < alpha.star), main="Significant pairs") 


  (sum(pval < 0.05)-k)/2     # number of "significant" results
 print(familywise <- (sum(pval < 0.05)-k)/2 /choose(k,2))     # estimated familywise error rate