One approach: (I assume that by "residual" you mean (O-E)/sqrt(E) for
each cell of a two-way frequency table, where O=observed frequency and
E=expected frequency under the null hypothesis). For the several (or
the single) largest residual(s), report O and E as proportions (of total
N). Express the residual in terms of proportions, which will turn out
to include N (or its square root) as a factor. Show that the residual
can be whatever it was (105.6, say) only if N is as large as it is in
your dataset, and that the same proportions for some smaller (more
reasonable?) N would _not_ produce a "significant" residual.
For purposes of this exercise, you could express the total chi-square
in terms of proportions and N, and show that for the observed proportions
only values of N larger than some value would produce a "significant"
result; or you could take, for any single cell, a critical value for
chi-square with one d.f.
(One could argue for d.f. = (r-1)(c-1)/(rc), since the table has rc
cells but only (r-1)(c-1) d.f., but 1 d.f. is arguably "conservative",
and finding critical values for fractional d.f. may be difficult.)
On 17 Aug 2001, JDriscoll wrote:
> I have a large dataset (N can be 2,000-9,000) with
> mostly categorical outcome variables. Any
> chi square is significant with residuals of 100+
> for tiny differences. I know one can determine
> effect size for continuous variables and show
> result is sign only due to size of the N, but...how
> do I do this for categorical outcome variables?
> Thanks!
Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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