```Date: Jun 19, 2013 2:49 AM
Author: Luis A. Afonso
Subject: Limits of the *Welch Correction"

The so-called Welch correction for the two-normal samples difference niu= u/v, where u = [ssdx/(nx*(nx-1))+ ssdy/(ny*(ny-1))]^2which if the samples have the same size n:u0= 1/(n^2*(n-1)^2)*(ssdx+ ssdy)^2v0= (ssdx)^2 /[(n^2*(n-1)^3] + (ssdy)^2/[(n^2*(n-1)^3]one have(u0/v0)/(n-1) == 1+ 2*(ssdx*ssdy) /[(ssdx)^2 + (ssdy)^2] < 2.__________Corollary: Under sample-pair, each size n, the so-called Welch correction, niu, is so that:  0 <= niu <= 2*(n-1)________________In practice the degrees of freedom are exclusively function of data. Note that: __overestimating df we underestimate the amplitude of the C.I., which probably will be really wider: The danger is to reject unduly. We are more likely to found significant issues than it should be. __on contrary underestimating df one can be sure that alpha is shorter than you got: a significant value, if so, got a reinforced truthfulness.In fact the consideration above being correct does not include an important fact: the right tail fractiles of the Student t distribution (except for very small df) are sufficient close one another:Table of Student t critical values ______df=10 ___ 2.228(.975)__ 2.764(.99)__________20______2.086_______ 2.528____________30______2.042_______ 2.457____________40______2.021_______ 2.423____________60______2.000_______ 2.390___________120______1.980_______ 2.358__ Luis A. Afonso
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