From ramasamy at cancer.org.uk  Fri Oct  1 12:48:53 2004
From: ramasamy at cancer.org.uk (Adaikalavan Ramasamy)
Date: Fri Oct  1 12:47:51 2004
Subject: [Rd] same test statistic for t-test with and without equal variance
	assumption
Message-ID: <1096627733.3352.10.camel@ndmpc126.ihs.ox.ac.uk>

Could some kindly tell me if I am supposed to be getting the same test
statistic value with var.equal=TRUE and var.equal=FALSE in t.test ?

set.seed(1066)
x1 <- rnorm(50)
x2 <- rnorm(50)

t.test(x1, x2, var.equal=FALSE)$statistic # 0.5989774
t.test(x1, x2, var.equal=TRUE)$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 Professional with the same results.

Any suggestions would be kindly appreciated.

Regards,
-- 
Adaikalavan Ramasamy                    ramasamy@cancer.org.uk
Centre for Statistics in Medicine       http://www.ihs.ox.ac.uk/csm/
Cancer Research UK                      Tel : 01865 226 677
Old Road Campus, Headington, Oxford     Fax : 01865 226 962


[Rd] same test statistic for t-test with and without equal variance assumption
Adaikalavan Ramasamy