Re assumptions for inference...
----- Forwarded message from Robert J. MacG. Dawson -----
What is needed in the small-sample case is outside _knowledge_ (not
"well, it _might_ be true" or "in this discipline we usually assume..."
assumptions!) about the distribution - without this we should not be
making any distributional assumptions.
----- End of forwarded message from Robert J. MacG. Dawson -----
Much of this problem arises from treating statistics out of context.
I think of the early applications in agriculture. I'm sure by now
Iowa State, for example, has tons of data on how corn yields are
distributed, and knows what transformations, if any, are needed to
stabilize variances or normalize shape. However, someone working a
homework problem in a textbook has no such fund of knowledge to rely
upon. (No, a textbook that declares things are normally distributed
by fiat is NOT a solution!-)
Similarly, in our graduate schools, students are trying to apply
inferential procedures prematurely in areas where not enough data has
been accumulated to establish what the relevant distributions look
like (nor to suggest reasonable hypotheses to test, for that matter).
We need to look at the data we do inference on, to see if our sample
deviates from what is usual for this type of data. But first we must
know what is usual. A sample large enough to establish "close enough
to normal" is probably also so large that we don't need normality very
badly anyway. Looking at a single sample is not a very efffective way
to see if a population is normally distributed, but it may draw our
attention to the fact that the very low response from one of the
experimental rats was because that rat was something the cat dragged
in.
_
| | Robert W. Hayden
| | Work: Department of Mathematics
/ | Plymouth State College MSC#29
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