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denom
2004 Oct 01
3
same test statistic for t-test with and without equal variance assumption
...$statistic # 0.5989774 ???
Here are my own calculations that shows that perhaps the result when
var.equal=TRUE is wrong.
n1 <- length(x1); n2 <- length(x2)
m1 <- mean(x1) ; m2 <- mean(x2) ; num <- (m1 - m2)
v1 <- var(x1) ; v2 <- var(x2)
# t-test with UNequal variance
denom1 <- sqrt( v1/n1 + v2/n2 )
num / denom1 # gives 0.5989774
# t-test with equal variance
sp <- ( (n1-1)*v1 + (n2-1)*v2 )/(n1 + n2 - 2)
denom2 <- sp * sqrt( 1/n1 + 1/n2 )
num / denom2 # gives 0.5913777
I tested this using R-1.9.1 (21/06/2004) on Redhat Fedora Core 2 and
Windows 2000 Pro...