Apparent Errors in StatXact 5
Below are comments about possible errors with
The asymptotic p-value seems to be incorrect. Instead of using ASE0
given by (23.18) on p. 829 of the User Manual, the z value that
is used to produce the asymptotic p-value makes use of ASE1.
I checked this out using the data in Table 8.1 on p. 367 of
Hollander & Wolfe (2nd Ed.).
StatXact matches the exact p-value obtained from Table A.30 in
H&W, but
StatXact's asymptotic p-value of about 0.021 for a one-tailed
test results from using the incorrect standard error (ASE1 instead of
ASE0). Note that it differs by more than a factor of 2 from H&W's
approximate p-value, with
StatXact's asymptotic p-value being the one that is farther from
the exact p-value. (Note: I have used a second data set to
seemingly confirm that StatXact's asymptotic p-value is based on
ASE1 instead of ASE0.)
If it is desired to have an asymptotic p-value which well approximates the
exact p-value, then I think it is clearly better to make use of the null
variance, and not use StatXact's ASE1.