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Re: st: sign test output


From   Nahla Betelmal <nahlaib@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: sign test output
Date   Thu, 17 Jan 2013 19:13:49 +0000

> Thank you so much everyone. Your comments were very insightful. I highly appreciate it.
>
> I performed qnorm and it seems that there is an outlier observation, so I will either winsorize or trim the data and run both tests again.
>
> Many thanks

> Nahla
>
>
> ----- Reply message -----
> From: "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
> To: <statalist@hsphsun2.harvard.edu>
> Subject: st: sign test output
> Date: Thu, Jan 17, 2013 3:10 pm
>
>
> 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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