On Sun, 15 Jul 2001, Melady Preece wrote:
> I have done a paired t-test on a measure of self-esteem before and
> after a six-week group intervention.
>
> There is a significant difference (in the right direction!) between
> the means using a paired t-test, p=.009. The effect size is .29 if I
> divide by the standard deviation of the pre-test mean, and .33 if I
> divide by the pooled standard deviation.
This implies that the effect size would be larger than .33 if you were to
divide by the s.d. of the post-test mean: which is evidently smaller
(although probably not significantly so?) than the s.d. of the pre-test
mean.
But if you have paired pre/post values, you are essentially calculating
the difference score (post minus pre), and constructing a t ratio using
the s.d. of those differences. This would ordinarily be expected to be
noticeably smaller than the s.d. of either pre-test or post-test means.
Do you have a reason for not using _that_ s.d.?
> Question 1: Which is the correct standard deviation to use?
Well, you have a choice of four: the s.d. of the pre-test mean,
the s.d. of the post-test mean, the s.d. of the difference, and the
pooled s.d. (resulting from pooling together the variances pre and post).
The pooled s.d. would be (at least possibly) appropriate if you were
performing a t-test for independent groups, but I cannot see how it could
be thought suitable for paired differences (unless, perhaps, you and I
mean different things by "pooled s.d.").
Of the other three, and in the absence of other considerations
which may apply to your situation that you haven't told us about, I'd be
inclined to report all three; unless circumstances (among the "other
considerations") led me to prefer one of them in particular. Using the
pre-test s.d. may make it possible for your readers to estimate what
differences they might expect to find, based on pre-test information,
before getting to the post-test stage; this might be of value to some
readers. Similar interpretations can be made of effect sizes calculated
from the other s.d.s.
I would also want to report the raw difference in means, if the
raw scores are (as I assume to be the case) values that are more or less
understood (e.g., number of right answers out of the number of items),
since it provides something like a common-sensical measure... I'd also
be interested (as a potential reader) in some summary information about
the difference scores, like what proportion were negative...
> Question 2: Can an effect size of .29 (or .33) be considered
> clinically significant?
Not enough information for me to tell. (And I just discovered my watch
had stopped -- forgot to wind it this morning -- and am in danger of
being late for today's next agendum. Good luck!)
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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