[R] type III Sum Sq in ANOVA table - Howto?
Felipe
dbcfmp at unileon.es
Fri Mar 7 11:29:35 CET 2003
Hi! I have found your comments very interesting, but I feel I am one of
these people that do not understand what the hell they are really
testing :D
Could you (or anybody) suggest me a good web site to gather this kind
of information? Sometimes I cannot fully understand the messages of the
list because I lack some knowledge background.
Thank you.
Felipe
El Viernes, 7 marzo, 2003, a las 01:31 AM, Rolf Turner escribió:
>
> Andy Liaw wrote:
>
>> The long(er) answer: think harder about what question(s) you want
>> answered
>> (i.e., what hypotheses you really want to test, and test only
>> those). The
>> model hierarchy says that a model should not have an interaction term
>> involving a factor whose main effect is not present in the model.
>> Seen in
>> this light, the hypothesis you're trying to test involves a
>> non-sensical
>> model.
>
> Not really. The hypothesis being tested by Type III sums of square
> may be suspected of not being of ``central interest'', but it is NOT
> (as is commonly believed) ``non-sensical''.
>
> Let us think about the 2-way ANOVA case, where one can actually
> understand what is going on. Let the population ***cell means*** be
> mu_ij (i = 1, ..., m, j = 1, ..., n) and forget about the confusing
> and misleading over-parameterized model.
>
> Testing for the significance of the ``row factor'' by Type III
> sums of squares (with interaction in the model of course) tests
>
> H_0: mu_{1.}-bar = mu_{2.}-bar = ... = mu_{m.}-bar
>
> I.e. that the means of the population cell means, over columns, are
> all equal. I.e. that ``when rows are averaged over columns'' there
> is no row effect.
>
> This could, at least conceiveably, be of interest. Note that the
> average is not a weighted average, saying that all columns are
> equally important. If all columns are NOT equally important (e.g.
> if an item randomly drawn from the population is more likely to
> ``come from'' column 1 than from column 2 etc.) then this hypothesis
> is less likely to be of interest.
>
> But it isn't nonsensical.
>
> It is true, however, that most of the time when people test things
> using Type III sums of squares they don't understand what they are
> really testing. But then (said he cynically) people don't understand
> what the hell they are really testing in most situations, not just
> in the context of Type III sums of squares.
>
> cheers,
>
> Rolf Turner
>
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