In article <[EMAIL PROTECTED]>,
RD <[EMAIL PROTECTED]> wrote:
>On 13 Mar 2001 16:32:15 -0500, [EMAIL PROTECTED] (Herman
>Rubin) wrote:
>>In article <[EMAIL PROTECTED]>,
>>RD <[EMAIL PROTECTED]> wrote:
>>>On 13 Mar 2001 07:12:33 -0800, [EMAIL PROTECTED] (dennis roberts) wrote:
>>>>1. some test statistics are naturally (the way they work anyway) ONE sided
>>>>with respect to retain/reject decisions
>>>>example: chi square test for independence ... we reject ONLY when chi
>>>>square is LARGER than some CV ... to put a CV at the lower end of the
>>>>relevant chi square distribution makes no sense
>>>Hmm... do not want to start flame war but just can not go by such HUGE
>>>misconception about chi squared test. Indeed exactly reverse is true :
>>>chi squred test is always two tailed. There is nothing to prove just
>>>look at the definition : Khi^2(n)=sum(Z^2).
>>There is a way of looking at the chi-squared test otherwise.
>>In fact, a low chi-squared would constitute a question of
>>whether what purport to be random numbers really are.
>What do you exactly mean by that?
Suppose one has random numbers supposedly independent
and equally likely to be any of 0, 1, ..., k-1. Then
the chi-squared statistic has, for large sample size n,
approximately a chi-squared distribution with k-1 df.
Now suppose that the numbers are not independent, but
the process producing them tends very strongly to even
the proportions out. the statistic will tend to be much
smaller. In the extreme case in which the numbers are
produced in sets of k, with one of each in each set,
then none of the discrepancies between observed and
predicted is as large as 1.
--
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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