From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>

Date: Fri 01 Oct 2004 - 21:15:06 EST

Date: Fri 01 Oct 2004 - 21:15:06 EST

Adaikalavan Ramasamy <ramasamy@cancer.org.uk> writes:

> 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.
*

Your calculation is wrong. Try increasing the variance of x1 and x2...

*> set.seed(1066)
**> x1 <- rnorm(50,,100)
**> x2 <- rnorm(50,,100)
*

> m1 <- mean(x1) ; m2 <- mean(x2) ; num <- (m1 - m2)

*> v1 <- var(x1) ; v2 <- var(x2)
**> denom1 <- sqrt( v1/n1 + v2/n2 )
**> num / denom1 # gives 0.5989774
*

[1] 0.5989774

> sp <- ( (n1-1)*v1 + (n2-1)*v2 )/(n1 + n2 - 2)

*> denom2 <- sp * sqrt( 1/n1 + 1/n2 )
**> num / denom2 # gives 0.5913777
*

[1] 0.005913777

-- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907 ______________________________________________ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-develReceived on Fri Oct 01 21:21:32 2004

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