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Topic: Re: Is n=30 large enough?
Replies: 0

 Bob Hayden Posts: 2,384 Registered: 12/6/04
Re: Is n=30 large enough?
Posted: Feb 11, 1997 5:38 PM

Some of the discussion from this list got copied to EdStat-L and
people have been responding there. Here is one response I thought was
worth repeating.

----- Forwarded message from David S. Moore -----

>>The text book we are using says use the z- distribution when ever the
>sample size exceeds 30 and the distribution is normal. Let sample s
>approximate population sigma. How come the t- table in the AP booklet
>has degrees of freedom entries way past 30 ??? what am I missing??

The AP stat tables come directly from The Basic Practice of Statistics.
I didn't stop at df = 30 for the obvious reason given by Paul Velleman:
whenever you estimate sigma from the data, for any n, you are using t
not z.

As n increases, t approaches z, but rounding all the way to df=infty
for any n > 30 may not be reasonable. A selection of intermediate
df's allows rounding up to the next largest df and also assessing
what the effect of rounding to df=infty would be. Many texts (like
BPS) have 1-page t-tables that allow this, as Don Burrill remarks.
If your text bases t vs z on n rather than on s versus sigma, and
doesn't discuss the robustness of t to non-normality that makes t
procedures often reasonable in practice, you should look at more
modern texts. (And I think we should all be using software or
capable calculators that make tables anachronistic in any event.)

David

----- End of forwarded message from David S. Moore -----

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