Re: Findining a P value from a T distribution


Bruce Weaver wrote:
> Jerry Dallal wrote:
>
> > It should be noted that Statable is not presented as a P value
> > calculator. Rather, it is described as providing "immediate access to
> > the twenty-five most commonly used statistical distributions.

Jerry pointed out the crux of the issue in our discussion. As a
general
probability calculator, that's a separate issue. When you recommended
it for use as a P value calculator, that was the entirety of my
objection,
that it didn't even consider the THREE Alternative hypotheses, which
is essential and fundamental in any p-value determination.

> > With just
> > a few keystrokes, the tail area or percentage point you want appears in
> > a pop-up window. StaTable eliminates hunting for books of tables,
> > interpolation, and the possibility of errors in calculation." Users
> > should be their own lookout for what they choose to do with it.
> >
> > The one thing I find lacking is that it can't handle handle tail areas
> > less than 0.001.
>
> --- snip the rest ---
>
> Just to clarify what Jerry is saying, you can enter a tail area and
> solve for z, t, or whatever (e.g., using the standard normal, entering
> 0.05 as the two-tailed area returns z = 1.96). But, the program will
> not accept a tail area less than 0.001 or greater than 0.999. (I agree
> that this is a curious limitation. of the program.)

I took a quick look at the program after seeing your comments, and
I quickly found many INCONSISTENCIES in its presentation of
probabilities OR the deviates corresponding to tail probabilities.

I would consider all those inconsistencies the work of "amateurs",
Cytel notwithstanding!
>
> But, when you enter a z or t or whatever, and solve for the tail area,
> it displays the result to 6 decimals. E.g., using the standard normal,
> and entering z = 3.5, I get the following values.
>
> Left tail: 0.999767
> Two tailed: 0.000465

That is another sign of amateurism. The program is CAPABLE
of calculating the probabilities to MORE than six significant
figures. But why present the two-tail probability as .000465
instead of .465258E-3, to be comparable in precision to the
6 significant digits in the left tail?

Actually the program is CAPABLE of accepting the value of z
greater than 6 digits and give the corresponding correct
probabilities.

For the left tail of 1.23456, it gives .891503
For the left tail of 1.23456789, it gives .891504

the latter of which is the rounded version of .89150431722664...

> And if I wanted the right tail area for z = 3.5, I could always use the
> left-tail value for z = -3.5, which is 0.000233. ;-)
>
> --
> Bruce Weaver
> bweaver@xxxxxxxxxxxx
> www.angelfire.com/wv/bwhomedir

which should have been given as .232639E-3, to 6 significant figures.


But it's the z value look-up corresponding to a given tail probability
that the true amateurism of the program showed itself -- in fact,
I would characterize its performance as BAD amateur work, to
be WRONG in the digits shown!

Example, for the left tail value of .891504, it gave a z value of
1.2373. As we had seen, the correct value of z should have been
1.23456789, or any of its correctly rounded values.

But if you gave the corresponding two-tail value of .21699137,
it gives the correct z value, shown as 1.2345.

1.2373 (wrong in the 4th digit) and 1.2345 (correct to the 5th digit)
on the SAME z, depending on whether the tail or two-tail
probability was given as input.

Is that amateurism or what?

So, while the StaTable is excusable for its inappropriateness as
a P-value computer, given Jerry's explanation of what that program
was meant to be, just a probability calculator.

As a probability calculator, the program also leaves MUCH to be
desired, as those few little examples above are meant to illustrate.

I'll have a much more substantive follow-up to Jerry post on
computer programs that do a MUCH better job than the StaTable
is intended to do, and address a few related issues, in response
to Jerry's questions and comments, and I'll change the SUBJECT
to Computer-Oriented Probabilities for Statistical Distributions.

I'll get to that later in the day.

-- Bob.

.

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