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Topic: About the T test statistics
Replies: 2   Last Post: Jan 3, 2014 1:45 PM

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Luis A. Afonso

Posts: 4,518
From: LIsbon (Portugal)
Registered: 2/16/05
About the T test statistics
Posted: Dec 26, 2013 12:35 PM
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Around the T test statistics


From the formula, for the Population difference on means:

T=
=(mX-mY)/Sqrt[ssd/(nX+nY-2)*(1/nX+1/nY)]

Where
mX, mY = observed sample means, sizes nX, nY,
ssd = ssdX+ ssdY= sum of square deviations.

One can easily obtain a good approximation

T= (mX-mY)/Sqrt [(ssd)/(nX * nY)]

In fact
__(1/nX+1/nY)/[nX+ nY- 2] =
__[(nX+ nY)/(nX+nY-2)]* 1/(nX * nY) =
__[1/(1- 2/(nX+nY)]* 1/(nX * nY)
It can be seen that, unless the total sample is small, the square bracket is very close to 1.

Luis A. Afonso



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