In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>At 08:03 PM 11/15/01 +0000, Radford Neal wrote:
>>Radford Neal:
>> >> The difference is that when dealing with real data, it is possible for
>> >> two populations to have the same mean (as assumed by the null), but
>> >> different variances. In contrast, when dealing with binary data, if
>> >> the means are the same in the two populations, the variances must
>> >> necessarily be the same as well. So one can argue on this basis that
>> >> the distribution of the p-values if the null is true will be close to
>> >> correct when using the pooled estimate (apart from the use of a normal
>> >> approximation, etc.)
>>Jerry Dallal:
>> >But, if the null hypothesis is that the means are the same, why
>> >isn't(aren't) the sample variance(s) calculated about a pooled
>> >estimate of the common mean?
>>An interesting question.
>i think what this shows (ie, these small highly technical distinctions) is
>that ... that most null hypotheses that we use for our array of
>significance tests ... have rather little meaning
>null hypothesis testing is a highly overrated activity in statistical work
Agreed. The question is how to act.
>in the case of differences between two proportions ... the useful question
>is: i wonder how much difference (since i know there is bound to be some
>[even though it could be trivial]) there is between the proportions of A
>population versus B population?
Now this is a difficult problem. It is only in translation
parameter problems that it is even clear that this is what
should be asked. Confidence intervals for a binomial proportion
are a major headache, although for large samples, the usual
asymptotic expressions give a good approximation.
>to seek an answer to the real question ... no notion of null has to even be
>entertained
If the means are far apart, one definitely should NOT use the
pooled mean to estimate the precision; the estimate of
precision from that is always too large. If the means are
close, the difference might be unimportant.
--
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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