On Wed, 2 Aug 2000, Rich Ulrich wrote:
> I have a question of my own - I think FAMILY is not, in general, the
> same as EXPERIMENT.
[Thanks to Jerry Dallal for that lovely quote from Rupert Miller!]
I have always understood "experimentwise" to refer to post hoc multiple
comparisons carried out without any restrictions on WHICH comparisons one
chose to look at; and the techniques that apply are ordinarily called
the Scheffe' method and the Tukey method; both are discussed in Scheffe'
(1959) and Guenther (1964). Some more recent authors use "familywise" or
"family-based" for these methods (Glass & Hopkins 1984, Keppel 1982).
Although the Tukey method was devised for pairwise comparisons in
particular, and it is usually used only for such contrasts, it applies
as well to all possible contrasts; the Scheffe' method applies to all
possible contrasts, and it is a theorem that iff the omnibus ANOVA
hypothesis is rejected at the alpha level of significance, there exists
at least one contrast that is significant at alpha by the S-method.
(One is of course not guaranteed that the significant contrast(s) be
of especial interest to the investigator!)
I have understood "familywise", when not used synonymously with
"experimentwise", to refer to a restricted subset (or "family") of all
possible contrasts: for example, all possible pairwise (aka simple)
contrasts; or simple comparisons with a "control" group; or pairwise
contrasts taken sequentially from the largest difference between means
to the smallest, but stopping as soon as one encounters a nonsignficant
contrast; or the set of planned comparisons; or a set of orthogonal
comparisons.
> On 01 Aug 2000 19:54:26 GMT, [EMAIL PROTECTED] (EAK5COLUMB) wrote:
>
> > I am trying to find a definition of "familywise error".
> > Am running a number of regressions on the same set of data. Assume
> > "familywise error" means the chance of Type I error increases.
I think what you should be looking for is "familywise error rate", since
"familywise error" simply means the Type I error associated with a
family of (multiple) comparisons. As Rich Ulrich observed, the
familywise error rate is the probability of rejecting the null hypothesis
(that the value of a contrast is zero) for one or more of the comparisons
in the family, using the procedure that defines the family.
> > Is a solution Bonferroni?
It may be. The Dunn method uses Bonferroni, for example.
> > Are there other solutions?
Yes, in ANOVA contexts.
> "familywise error" is contrasted to "comparisonwise error."
>
> An online search with Google shows that "experimentwise error" is
> often used exactly the same as "familywise error" and a large number
> of references (online) happen to use one term or the other. The
> definition for each is, approximately: the chance rejecting at least
> once, by chance, across a family of tests.
< snip, the rest >
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
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