In article <8cd9g3$c5d$[EMAIL PROTECTED]>,
Madewell <[EMAIL PROTECTED]> wrote:
>Let me ask you guys this. If you calculated the power for
>the Chi-Squared test using both a small and then a large numbers and did
>the same for the KS test what would you find?
The power of the KS test, as usually defined, cannot be
calculated except by simulation with few exceptions, and
is a function of the significance level, even asymptotically.
There is the asymptotic limit as the significance level
goes to zero, but not too quickly, and this is also
obtainable in other ways, such as the rather easily
calculated asymptotic Bayes risk efficiency; see my
paper with Sethuraman in Sankhya 1965. At any rate,
it has reasonable power in the classical sense.
The chi-squared test with a FIXED number of cells has
an efficiency in the classical sense, and at least in
principle it can be calculated. However, as the number
of cells increases, this efficiency goes to zero.
This is because the chi-squared test ignores adjacency,
and for reasonable alternatives, adjacent regions are
likely to differ from the null in similar ways.
In practice, the difference is surprising.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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