# Re: [Rd] same test statistic for t-test with and without equal variance assumption

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Fri 01 Oct 2004 - 21:15:06 EST

> 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
 0.5989774
> sp <- ( (n1-1)*v1 + (n2-1)*v2 )/(n1 + n2 - 2)
> denom2 <- sp * sqrt( 1/n1 + 1/n2 )
> num / denom2 # gives 0.5913777
 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

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Received on Fri Oct 01 21:21:32 2004

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