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#### perfroms the non-selective MC test
#### assumes that y is a MATRIX, one column per replication
#### test.index is the index into x for which we test the nullity of the regression coefficient
#### x is assumed to have at most one column from each of the original groups
#### sigma is assumed known -- so a normal reference distribution
nonselective.mc.test <-
function(x, y, test.index, mu, sigma){
n = nrow (y)
### are we estimating mu?
X = x
if (is.null(mu)){
X = cbind (1, x)
test.index = test.index+ifelse(is.null(mu), 1, 0) # move the index over one to account for the intercept
}else{
y = y - mu
}
M = ncol(X)
### coefficient and standard error
XX = t(X)%*%X
Xy = t(X)%*%y
beta.hat = solve(XX, Xy)[test.index,]
std.error = sqrt(solve (XX, sigma^2*diag(M))[test.index, test.index])
### test stat and p.val
ts = beta.hat/std.error
p.val = 2*pnorm(abs(ts), 0, 1, lower.tail=FALSE)
list (ts=ts, p.val=p.val)
}
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