replying to mine, and catching an error,
(My apologies for the error, please, and my
thanks to Jim for the catch.... ),
On Tue, 03 Apr 2001 15:05:20 -0700, James H. Steiger
<see_my_address@end_of_post> wrote:
> Things are not always what they seem.
>
> Consider the following data:
>
> A B A/B Log A Log B Log A - Log
> 3 1 3 .477 0 .477
> 1 3 .333 0 .477 -.477
> 2 2 1 .301 .301 0
>
>
> The t test for the difference of logs obviously
> gives a value of zero, while the t for the hypothesis
> that the mean ratio is 1 has a positive value.
>
> This seems to show that the statement that the
> two tests are "precisely, 100% identical"
> is incorrect.
[ snip, more ... ]
Yep, sorry -- I fear that I left out a step, even as I sat
and read the problem. And when I read my own 1st draft
of an answer, I saw that it was worded a bit equivocally.
I made that statement firmer, but I forgot to make sure it
was still true, in detail.
{ 1/2, 1/1, 2/1 }
( equal to .5, 1.0, 2.0) clearly does not define equal steps.
Except, if you first take log(X).
The automatic advice for "ratios" -- not always true, but
always to be considered -- is "take the logs". When you have
a ratio ( above zero), there is far less room between 0-1 than
above 1. Is this asymmetry ever desirable, for the metric?
Well, it *ought* to be desirable, if you are going to use a ratio
without further transformation. But I think it is not apt to be
desirable for human reaction times.
For log(A) and log(B), consider: log(A/B) = log(A) - log(B).
The one-sample test on *LOG* of A/B is the same as the
difference in logs.
Those are the tests I had in mind... or should have had in mind.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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