In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (Donald Burrill) wrote:
> You have not stated how many subjects (Ss) receive each
> drug/dose combination. If all 20 Ss receive all 4 combinations, as
> implied by your assertion of 80 data points (below), then the design is
> not completely given: you must also have a factor representing the order
> in which the combinations were encountered by each S. If all Ss got the
> various drug/dose combinations in the same order, you have no way of
> telling whether (e.g.) the first combination affected responses to the
> later combinations, nor even in which direction. Also in this case, as
> one other respondent pointed out, you have a repeated-measures design:
> that is, instead of S(G x E) as in the usual 2-way ANOVA (using S for
> Subjects, G for druG, E for dosE), you have S x G x E, which implies
> (inter alia) different error terms for G, E, and GE.
>
Sorry, I assumed you would assume counterbalancing for order effects.
You're right, a repeated measures design was assumed (but not stated).
> (In that notation, using R for the raw data values within each S, the two
> designs above would be R(S(B x E) and R(S) x G x E . As remarked
> below, the same ratios of mean squares are computed, whether R is
> explicitly accounted for in the design or not.)
>
>
> As others have pointed out, it makes no difference. Your
> hypotheses are tested by comparisons among the cell means, and the
> denominator mean square for each hypothesis will be the estimated
> sampling variance of the means in question. Whether you use the mean of
> 25 trials for each S, or the 25 raw trials themselves, you get the same
> numbers.
>
> As remarked above, this is not true. One has the same numerical
> estimates, and the same numbers of degrees of freedom in numerator and
> denominator, for each hypothesis test. As other respondents have
> mentioned, if the raw data are a 0/1 dichotomy, there may be an advantage
> in using a logistic rather than a normal model; but if the proportions
> (the several cell means) are not very close to 0 or 1, say between .25
> and .75, there will not be much difference in the results of the
> analysis.
Many thanks to you and everyone else for your kind assistance. I think I
see the light now.
Jim
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