jim clark wrote:
> The problem is that one-tailed test is taken as synonymous with
> directional hypothesis (e.g., Ha: Mu1>Mu2). This causes no
> confusion with distributions such as the t-test, because
> directional implies one-tailed. This correspondence does not
> hold for other statistics, such as the F and Chi2. One can get a
> large F by either Mu1>Mu2 or Mu1<Mu2 (or by positive or negative
> R, ...). Therefore the one-tail of the distribution corresponds
> (normally) to a two-tailed or non-directional test. However,
> there is absolutely nothing wrong with making the necessary
> adjustment to make the test directional (i.e., equivalent to the
> one-tailed t-test), and therefore referring to it (confusingly,
> of course) as a one-tailed test. To make F directional, one
> simply halves p from the statistical output or looks up the
> critical value of F with 2*alpha (e.g., .10). The same would
> hold for Chi2 and is presumably what happened with the paper
> referred to initially (assuming knowledge of statistics). That
> is, the Chi2 under many applications would be insensitive as to
> the direction by which observed values differed from expected
> values, making it a non-directional/two-tailed test without some
> adjustment. But such adjustment would be appropriate if the
> direction of differences was predicted, just as for the F.
That's what I meant, sorry if I wasn't clear. Howell's text has a nice
explanation. I too prefer the term directional test when discounting
differences in one direction (i don't think prediction is sufficient to
justify use of a directional test).
F and Chi-square are also only suited to this kind of directional testing in
limited cases (i.e., when only 2 directions are possible).
Thom
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