[R] Does the t.test in R uses Welch procedure or ordinary student t-test?

Tim Hesterberg timh at insightful.com
Wed Feb 20 00:23:03 CET 2008

First, a clarification.  The subject line suggests that the
Welch procedure is not an ordinary student t-test.
That is incorrect.

There are two common two-sample t-tests:
	non-pooled variance (Welch version)
	pooled variance

I would refer to the non-pooled version just as a "two-sample t-test";
if you want to be definite, you could refer to Welch or non-pooled.

The other common t-test is the pooled-variance t-test.  In the old
days, the pooled-variance t-test was considered standard, but
statistics has shifted in favor of the non-pooled test being the
standard; someone using the pooled-variance version should note the
choice, and justify the choice (at least to him or her-self).

Also note that an F-test is often a poor way to justify pooling,
because it F-test is not robust against non-normality.  "To make a
preliminary test on variances is rather like putting to sea in a
rowing boat to find out whether conditions are sufficiently calm for
an ocean liner to leave port."  (G.E.P. Box, "Non-normality and tests
on variances", Biometrika, 40 (1953), pp 318-335, quote on page 333;
via from Moore & McCabe.

Tim Hesterberg

>Dear all
>I have run t.test(), and get a output similar to this:
>t.test(extra ~ group, data = sleep)
>        Welch Two Sample t-test
>data:  extra by group
>t = -1.8608, df = 17.776, p-value = 0.0794
>alternative hypothesis: true difference in means is not equal to 0
>95 percent confidence interval:
>-3.3654832  0.2054832
>sample estimates:
>mean in group 1 mean in group 2
>           0.75            2.33
>Should this be refered as a Welch procedure or ordinary student t-test?
>Regards Kes

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