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How to Interpret the Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is a non-parametric alternative to the t-test. That is, it compares two paired groups on some continuous variable. For example, it might be used to compare the incomes of husbands and wives. "Non-parametric test" is a statistical term used for tests that rely on fewer assumptions than their parametric alternatives. Data is paired when the two data points in a pair are not independent, as with pretty much any data from married couples. A nonparametric test would be useful for comparing incomes, since income is not normally distributed.

Instructions

- 1
  Examine W, which is the value of the Wilcoxon test. W is the sum of the signed ranks between the two groups. In the example, you would take the difference between the husband and wife in each couple, then rank the absolute value of these differences, and then sum the signed ranks.
- 2
  Compare W to the minimum and maximum values for W. The minimum possible W is 0, the maximum possible W is n*(n+1)/2, where n is the number of pairs. For example, if you had 10 couples, the maximum W would be 10*11/2 = 55.
- 3
  Calculate the standard deviation of W. This is the square root of n*(n+1)*(2n+1)/6. For example, if you had 10 pairs, this would be (10*11*21/6)^0.5 = 385^0.5 = 19.62.
- 4
  Subtract 0.5 from W.
- 5
  Divide the result in Step 3 by the result in Step 4. This gives a value for z.
- 6
  Test the statistical significance of z. Tables for doing this are in many statistics books, it can also be done on some scientific calculators or in Excel.

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