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Title: The Paired t-Test
Author: Keith M. Bower
Publication Source: Scientific Computing & Instrumentation, Vol. 18 No. 3, February 2001, pp 62-63

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Abstract

General guidelines are provided for using and interpreting the results using the paired t-test procedure. In particular, the example addresses:

(1) Anderson-Darling Normality test
(2) Paired t-test interpretation (including p-value)
(3) Confidence interval results

Notes

The motivation for this paper was to address a misunderstanding of many practitioners regarding when and why a paired-t vs. a two-sample t-test should be employed. Disturbingly, I had encountered several organizations that did not even teach the paired-t procedure, and only discussed a two-sample t-test despite obvious instances for the obvious employment of a paired t-procedure for the analysis.

In hindsight, I see that I was remiss in discussing the loss of degrees of freedom when using the paired t-test vs. the two-sample t-test. My defense would be that the more refined error term used in the test should adequately compensate for this, though there is an obvious trade-off. In practice, this needs to be considered case-by-case.

I was also interested in showing the fact that a paired t-test is merely a one-sample t-test using the differences. Even among those using the procedure I found that this statistical fact had been overlooked.

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© Keith M. Bower. All rights reserved.