Welch versus Satterthwaith (PR#2111)

maechler@stat.math.ethz.ch maechler@stat.math.ethz.ch
Wed, 13 Nov 2002 14:31:56 +0100 (MET)

>>>>> "TL" == Thomas Lumley <tlumley@u.washington.edu>
>>>>>     on Sun, 6 Oct 2002 09:19:27 -0700 (PDT) writes:

    TL> 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.

    TL> 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?

    TL> It's the same method.

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

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

I've added "Satterthwaite" to the help page now.

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