I have been taught that p-value is a measure of the incapability between data and hypothesis. It is only used to disprove a (null) hypothesis. We do not accept all the things that Neyman and Pearson had proposed.

I also learned that p-value is a relative measure, with vague quantitative interpretation. Its numerical value is relative to the experimental conduct and to the hypothesis. Numerical comparisons of two p-values are meaningless if the sample sizes of the 2 experiments are different, or if the width of the 2 interval null hypotheses are different.

The American Statistician does not make their articles publicly available, so I can’t provide a link. You can access the journal’s archives if you are an ASA member. Also, the article is available via JSTOR; Your library may have access to JSTOR.

1st off, let me say i’ve enjoy your blogs.
can you provide a link to the article?

“So, first, the known measurement variation (SD=1) is at least 3 times that of the observed population variation…”

I too thought that Schervish’s values may not be representative, so i ran his experiment, this time using many randomly generated ranges and mean points (i.e. the 2.18). I find that in about 20% of the cases, the p-values associated with the tighter range are smaller than those associated with the larger range. So, Schervish’s point holds even for milder values of the mean point.

if you repeat the experiment with random values of
\mu_1,\mu_2,\mu_1′,\mu_2′ you will see that
the p-values of the first test are larger than those of the second test about
1 out of 5 times.

Best,

Of course, this completely ignores the lengths of the intervals, so I’m guessing that if I were to treat these as characterizing a (uniform?) prior, I’d get results closer to those of the post….

Where did these two (hypothetical) intervals come from? Presumably, they represent 95% CI for a population sample of some quantity in the subtype (bears), which was found to have mean 0 and SD 0.255; and in the type (mammals), having mean -0.15 and SD 0.342.

So, first, the known measurement variation (SD=1) is at least 3 times that of the observed population variation for either the type or the subtype; not an unimaginable situation if the population estimates were derived from repeated measures, but in that case, we haven’t been given the relevant intervals. Second, given either a N(0, 0.255) or N(-0.15, 0.341), the probability of observing 2.18 or greater is close to 0; i.e., you’re extremely unlikely to observe 2.18 if measuring an actual mammal.