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Re: st: VEC: t- instead of z-statistics


From   John Luke Gallup <jlgallup@pdx.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: VEC: t- instead of z-statistics
Date   Fri, 22 Jul 2011 00:34:51 -0700

I am puzzled why -svy: logit- report t-statistics, since -logit- without svy: reports z-statistics.  A mechanical answer may be that the variance of the errors, which is part of the t- and z-statististic formulas, are calculated differently in each case.  The variance, sigma squared, is calculated with a factor of 1 / (N-K) when calculating a t-statistic, but sigma squared is often calculated with a factor of 1 / N for a z-statistic.  The two formulas for sigma squared are both consistent, but the first is unbiased.

The main point is that there is no good reason to think that a t-statistic is better than a z-statistic unless you are using a linear estimator and you believe that your errors are actually normal.  Otherwise you only know the asymptotic properties of the estimator. The t-statistic and the z-statistic are both asymptotically normal, but have an unknown small sample distribution.

John
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