# Welch versus Satterthwaith (PR#2111)

Thomas Lumley tlumley@u.washington.edu
Sun, 6 Oct 2002 09:19:27 -0700 (PDT)

```On Sat, 5 Oct 2002 roxburg@kih.net wrote:

> This is not a bug report but didn't see another way to ask a question.

Well, you could try the r-help or r-devel mailing lists

> For the approximate t-test assuming unequal variances, the R docs cite
> Welch's method for the df of the approximating distribution.
> I have several methods books, and they all uses Satterthwaite's method.
> Why does R use Welch's method where can I learn about Welch's method?
>

It's the same method.

The t-statistic is the difference in means divided by a more-or-less
unbiased estimate of its standard deviation. There's only one natural way
to do this and in sufficiently large samples that's all you need.

The more difficult part is the sampling distribution, which is
approximated by a t-distribution with degrees of freedom from some
complicated formula involving the two sample sizes and variances.  It was
indepedently derived by Welch and Satterthwaite.

-thomas

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```