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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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David Jones

Posts: 62
Registered: 2/9/12
Re: For nonrejection of H0, don't we want high signifance?
Posted: Apr 26, 2013 4:35 AM
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"Jeff Miller" wrote in message
news:9de41597-61aa-4417-b5e7-2a293c689f19@googlegroups.com...

The confidence interval approach is much more informative in most such
situations, because they allow conclusions of the form "Ho is not wrong by
more than X units". CIs are not easily adapted to your original question of
checking for normality, though, AFAIK.

========================================================================

CIs are "easy" to apply here, in one of two ways. CIs are just things that
contain the set of all null hypotheses that are not rejected based on the
data. So either:

(i) form a discrete collection of possible families of distributions, test
each of these as the null hypothesis and form a list of all those that are
not rejected. This list would indicate how much non-normality is not
excluded by the data available.... but it clearly requires both wide-ranging
behaviours in the original list and an understanding of these behaviours if
the CI s to be useful.

(ii) embed the normal distribution in a 3 or 4 parameter family of
distributions, with the extra parameters representing departure from
normality. Then an "ordinary" confidence region can in indicate how much
non-normality is not excluded by the data available.

David Jones




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