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A nonparametric alternative to the Paired t-Test which is similar to the Fisher Sign Test. This test
assumes that there is information in the magnitudes of the differences between paired observations, as well as the signs.
Take the paired observations, calculate the differences, and rank them from smallest to largest by Absolute Value.
Add all the ranks associated with Positive differences, giving the 
statistic. Finally, the P-Value
associated with this statistic is found from an appropriate table. The Wilcoxon test is an R-Estimate.
See also Fisher Sign Test, Hypothesis Testing, Paired t-Test, Parametric Test