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Topic: The power of a test
Replies: 5   Last Post: Jun 13, 2013 6:29 PM

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Richard Ulrich

Posts: 2,928
Registered: 12/13/04
Re: The power of a test
Posted: Jun 8, 2013 11:26 PM
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On Sun, 09 Jun 2013 01:10:50 +0200, Cristiano <cristiapi@NSgmail.com>

>On 08/06/2013 1:56, Rich Ulrich wrote:
>> The text says that this is the empirical result of 1000
>> random samples. Apparently, there were 38 "rejections"
>> rather than 50, in this particular Monte Carlo experiment.
>> The 95% CI for 50 (as a Poisson, small count) is about (37, 65)
>> so this result is not too unusual.

>Can we suppose that they used an approximate critical value?

No. Why would they do that? JB is old enough that I
expect that the cutoffs they used are precise.

>I think that, because they say: "In this way, the ?rst column depicts
>the *actual size of the tests*, while the other columns represent their
>power.", which could be interpreted as: "using a good estimation of the
>critical value for JB, we get the actual size of the test with G_0,0.0".
>Does it make any sense?


They do a Monte Carlo randomization of 1000 trials under
the null condition; they use cutoffs for a test; they report
the observed "size" of the test for this test. Since they were
looking at a 5% tail, they expected 50, and this set of 1000
trials happened to give them 38 -- The other tests were
computed on the same set of 1000 and gave the same or
off by 1 in the count of rejections. They were all the same.

You need to study, read papers, contemplate, what-have-
you, to get used to this terminology and set of expectations.
For instance, it is technically a BAD performance for a RNG
if it does not produce "random variation" in every criterion
that you measure it against. And, 5 times out of 100, a
set of 1000 trials will result in less than/ greater than the
number of rejections specified by the CI -- if you have a
decent RNG.

The later columns in the table are called "power" because
(a) every sample is non-normal, by design, and (b) they
represent how often that non-normality is detected.

I hope that you recognize that this is a peculiar paper, in
a way. Most of the time, authors are proposing ways to
*detect* differences. These authors are proposing
"robust measures" that will NOT report samples as non-
normal when they are "merely" contaminated by outliers
of one sort or another. Thus, they are happy and proud
to point to the lack of power for detecting the specified
sorts of contamination, for certain "robust" tests.

If you want a test to detect non-normality in the form
of those contaminations ... the JB does fine. The power
of the so-called robust tests is going to be concentrated
elsewhere. Presumably.

I'm not sure I see much value in their paper. If the JB
rejects severely, and their robust tests do not, you might
conclude, "Well, the sample would be pretty normal if it
were not for 1%/5% contamination."

But then... I've never, ever, paid much attention to any
formal tests of normality. Maybe it is a lot more useful
to someone who has had data where other tests of normality
were useful.

Rich Ulrich

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