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Re: st: sign test output


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: sign test output
Date   Thu, 17 Jan 2013 10:10:07 -0500

The role of normality of the sample in many of statistical tests is
overstated. As long as the data distributions are reasonably unimodal,
symmetric, have roughly the same degree of dispersion, and don't have
excessively heavy tails, the central limit theorem says that the
sampling distribution of the sample mean is normal for "sufficiently
large" n, where "sufficiently large" can often be sample sizes of no
more than a few dozen. The central limit theorem says nothing about
measured variables' distributions, which are frequently not normal.

Tests for normality of sample are, unfortunately, much less robust
than the t-test itself and I am 100% with Nick that -qnorm- will be
very helpful in diagnosing problems much more so than any hypothesis
tests.

If the data are substantially asymmetric I'd question whether the
difference of means is even the right measure of group difference. If
a difference of means is sensible, might I suggest bootstrapping?
Given what you have here it probably won't matter for the p-value of a
hypothesis test but the confidence interval would be slightly more
accurate. Bootstrapping is now very simple, especially in Stata, so
there's no good reason not to use it.
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