From: Adaikalavan Ramasamy <ramasamy_at_cancer.org.uk>

Date: Fri 01 Oct 2004 - 23:17:25 EST

R-devel@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Fri Oct 01 23:29:17 2004

Date: Fri 01 Oct 2004 - 23:17:25 EST

Apologies, I made an incorrect statement. The statistics from t-test with difference variance assumptions are the same if both groups have the same length. Sorry for troubling everyone again.

On Fri, 2004-10-01 at 13:56, Adaikalavan Ramasamy wrote:

> Peter, thank you! I forgot the to square root in calculating sp.

*>
**> sp <- sqrt( ( (n1-1)*v1 + (n2-1)*v2 )/(n1 + n2 - 2) )
**>
**> For several simulation runs, the test statistics from both tests are
**> remarkably similar (difference is less than 10e-16). I naively assumed
**> that the statistics value should be slightly but visibly different too.
**>
**> It appear that the effects of equal and unequal variance assumptions are
**> only felt through the degrees of freedom calculation.
**>
**> Regards, Adai
**>
**>
**> On Fri, 2004-10-01 at 12:15, Peter Dalgaard wrote:
**> > 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
**> >
**>
**> ______________________________________________
**> R-devel@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-devel
*

>

R-devel@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Fri Oct 01 23:29:17 2004

*
This archive was generated by hypermail 2.1.8
: Wed 03 Nov 2004 - 22:45:19 EST
*