----- Original Message -----
From: Joe Ward wrote:
> Yep!!
>
> As you say:
> "Why are people so obsessed with T and Z? "
>
> Perhaps it would be even better (easier?) to focus on F since
>
> F(df1,df2) = t^2(df2)
>
> (Reminder: when using a t-table, the p-values usually involve ONE-TAIL...
It's an interesting trick, but not one I'd want to use in class.
If you are using a computer it is unnecessary.
If you are using tables in the back of a textbook you will typically get
your choice of one or two fixed alphas - I have seen as many as four but
that is unusual. Thus the whole idea of reporting p-values must be
abandoned. A high price to pay.
Moreover, the interpretation of the "t-square" test statistic is much
less concrete than the "standard deviations away from the mean" for t.
-Robert Dawson
PS: If we are going to do things like this I have a much more useful
suggestion - tabulate not \chi^2 but \chi^2/\nu, thus permitting easy and
accurate interpolation and extrapolation. Most small tables have continuous
values only up to (say) thirty degrees of freedom, and then perhaps skip by
tens or twenties for a bit; and this does not allow any good evaluation for
(say) 35 degrees of freedom, because f_{\chi^2_n}(x) does not converge
pointwise as n-> infinity. On the other hand, f_{\chi^2_n / n} (x) converges
pointwise nicely, so that a table with (say) thirty entries would cover all
chisquare distributions.
I can send a table of this form (Word document) to anybody who's
interested, fitting one legal page fairly easily. It has 26 DOF values
covering the range from 1 to 100 (effectively to infinity for larger
p-values, but for very small p this is still not quite enough) , and gives
45 high- and low-tail p-values
{.001,.002,....007,.01,.015,.02,...,.07,.1,.15,...,.999}
