"Mark W. Humphries" wrote:
> If I understand correctly the t test, since it takes into account degrees of
> freedom, is applicable whatever the sample size might be, and has no
> drawbacks that I could find compared to the z test. Have I misunderstood
> something?
>From my class notes (which, in this case, are a reporting of
comments
made by Mosteller and Tukey)...
Frederick Mosteller and John Tukey, on pages 5-7 of Data Analysis
and Regression [Reading, MA: Addison-Wesley
Publishing Company, Inc., 1997] provide insight into what Student
really did and how it should affect our choice of test.
The value of Student's work lay not in great numerical change,
but in:
recognition that one could, if appropriate assumptions held, make
allowances for the "uncertainties" of small samples, not only in
Student's original problem, but in others as well;
provision of a numerical assessment of how small the necessary
numerical adjustment of confidence points were in Student's
problem...
presentation of tables that could be used--in setting confidence
limits, in making significance tests--to assess the uncertainty
associated with even very small samples.
Besides its values, Student's contribution had its drawbacks,
notably:
it made it too easy to neglect the proviso "if appropriate
assumptions held";
it overemphasized the "exactness of Student's solution for his
idealized problem";
it helped to divert the attention of theoretical statisticians to
the development of "exact" ways of treating
other problems; and
it failed to attack the "problem of multiplicity": the difficulties
and temptation associated with the application of large numbers of
tests to the same data.
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