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 How to handle rows where the before and after values are identical

The Wilcoxon matched pairs test is a nonparametric test to compare two paired groups.

Like the paired t test, the first step in calculating this test is to subtract one paired value from the other. If the values are before and after a treatment, the difference is the change with treatment.

The next step is to rank the absolute value of those differences.

But what happens if, for one particular pair of values, the two values are identical, so the before value is identical to the after value.

When Wilcoxon developed this test, he recommended that those data simply be ignored. Imagine there are ten pairs of values. In nine pairs, the before and after values are distinct, but in the tenth pair those two values are identical (to the precision recorded). Using Wilcoxon's original method, that tenth pair would be ignored and the data from the other nine pairs would be analyzed.This is how InStat and Prism (up to version 5) handle the situation.

Pratt(1) proposed a different method that accounts for the tied values. Prism 6 and later offers the choice of using this method.

Which method should you choose? Obviously, if there are no ties among paired values (no differences equal to zero), it doesn't matter. Nor does it matter much if there is, for example, one such pair out of 200.

It makes intuitive sense that data should not be ignored, and that Pratt's method is better.  Connover (2) has shown that the relative merits of the two methods depend on the underlying distribution of the data, which you don't know.

1. Pratt, J.W. and Gibbons, J.D. (1981), Concepts of Nonparametric Theory, New York: Springer Verlag.

2. WJ Conover, On Methods of Handling Ties in the Wilcoxon Signed-Rank Test, Journal of the American Statistical Association, Vol. 68, No. 344 (Dec., 1973), pp. 985-988

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