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Luis A. Afonso
Posts:
4,758
From:
LIsbon (Portugal)
Registered:
2/16/05


Limits of the *Welch Correction"
Posted:
Jun 19, 2013 2:49 AM


The socalled Welch correction for the twonormal samples difference niu= u/v, where u = [ssdx/(nx*(nx1))+ ssdy/(ny*(ny1))]^2 which if the samples have the same size n: u0= 1/(n^2*(n1)^2)*(ssdx+ ssdy)^2 v0= (ssdx)^2 /[(n^2*(n1)^3] + (ssdy)^2/[(n^2*(n1)^3] one have (u0/v0)/(n1) = = 1+ 2*(ssdx*ssdy) /[(ssdx)^2 + (ssdy)^2] < 2. __________ Corollary: Under samplepair, each size n, the socalled Welch correction, niu, is so that: 0 <= niu <= 2*(n1) ________________
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



