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Topic: For nonrejection of H0, don't we want high signifance?
Replies: 7   Last Post: Apr 26, 2013 12:11 PM

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Posts: 493
Registered: 2/23/10
For nonrejection of H0, don't we want high signifance?
Posted: Apr 23, 2013 3:15 PM
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I'm perusing http://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test#Test_for_normality
for a statistical test of normality for my residuals. H0 is normality
of the residuals.

For typical hypothesis testing, we want small significance, which
means a small rejection region. Thus, and value of the statistic that
falls in the rejection region is less likely due to chance (in
combination with the truth of H0). In testing a drug for a medical
effect, that makes sense because we often want to demonstrate an
effect, and H0 is typically the absence of an effect. For values of
the statistic that fall in the small rejection region, we can say that
if H0 is true, it is highly unlikely for us to get this value for the
statistic. The smaller the significance, the smaller the rejection
region, and less we are able to attribute the chance any values in the
rejection region.

For normality, we often want the opposite. We want H0, which is
normality of the residuals. We can not accept H0 to any degree of
confidence using this setup of hypothesis testing, but at least we can
make it very easy to reject H0 so any non-rejection of H0 is seen to
be well founded. This implies large rejection region and high
significance. In fact, we might want to a 95% rejection region, the
counterpart of the wanting a 5% rejection region when the intent is to
demonstrate that rejection of H0 is not due to chance.

Is this reasonable? I ask because the table in the above link shows
significance values 1%, 2.5%, 5%, 10%, and 15%. These small values
seem more like the values that one might be interested in when wanting
to demonstrate valid rejection of H0.

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