The Wilcoxon Signed Rank Test calculator provides the Wilcoxon statistics and critical value for two groups of numeric observations based on an alpha value and whether it's a one or two tailed test.
INSTRUCTIONS: Enter the following:
Wilcoxon Stat and Critical Value: The calculator will return the Wilcoxon statistic (Wstat) and the critical value (Wcrit) associated with the sample size, alpha value and number of tails.
The Wilcoxon signed rank test is a non-parametric alternative to the paired samples t-test (Gravetter and Wallnau, 2013) that is useful when one or both of the observation groups are not normally distributed. Just like a paired-samples design, it measures the difference between two treatments on a sample that receives both treatments. Since it is non-parametric, it is only used if the data fail to meet the parametric assumptions; for instance, the data might not create a normal distribution. Therefore, instead of using the data points in the formula, the Wilcoxon test assigns every value a rank and uses the rank to compute the W value.
The numbers in the above table match the tutorial in the following YouTube video:.
The null hypothesis is in regard to the median of the two groups:
Ho MedianGroup1 = MedianGroup2
If you look up the Critical Value for a Wilcoxon two tailed test with alpha equal 0.05, you'll see a critical value of 17. Since Wstat of 16 is less than Wcrit of 17, the null hypothesis is rejected.
We will walk through another in-depth example of this so you can understand exactly how to perform a Wilcoxon signed rank test, if you need to. For this we will create a hypothetical set of data in vCalc called "Effects of Pain Relievers A and B" located. This example will explain a 10-rank Wilcoxon test, but you can do it with any number of ranks.
The first step to perform a Wilcoxon signed rank test is to convert your data from values into ranks. The ranks are based on the absolute values of the differences between the two treatments. To do this for the Pain Relievers example, we order the differences (which are -3, 3, 2, -5, -2, 11, -1, -8, 3, -6) in ascending order using the absolute values: 1, 2, 2, 3, 3, 3, 5, 6, 8, 11. And the ranks are assigned in ascending order, with 1 corresponding to 1 and 10 corresponding to 11.
If two or more of your values are the same, they are tied scores, and there are special instructions for ranking them. In the Pain Relievers example, we have two scores of 2 and three scores of 3. To get the tied rank, we simply take the average of the position ranks. For the scores of 2, the position ranks are 2 and 3. `2 + 3 = 5`, `5 /2 = 2.5.` For the scores of 3, the position ranks are 4, 5, and 6. `4 + 5 + 6 = 15`, `15 /3 = 5`. The final ranks used for this dataset are: 1, 2.5, 2.5, 5, 5, 5, 7, 8, 9, 10.
After the absolute values have been ranked, they have to be separated into the ranks associated with positive differences and those with negative differences. For the Pain Relievers example, the positive differences are 3, 3, 2, and 11. These values correspond to the ranks of 2, 5, 5, and 10. The other values are classified as negative differences, and the ranks are 1, 2, 5, 7, 8, and 9.
Next we have to add up the positive and negative difference ranks separately to get two sums of ranks, or `sum R`s. The `sum R` for the positive differences is `2.5 + 5 + 5 + 10 = 22.5`. The `sum R` for the negative differences is `1 + 2.5 + 5 + 7 + 8 + 9 = 32.5`.
The Wilcoxon T value is the smaller of the two sums of ranks. In this case, the Wilcoxon T = 22.5.
Now that we have obtained a T value of 22.5, we have to consult a. On this table, the critical T indicates the maximum value for there to be significance; obtained T values must be equal to or less than the value in the table in order for results to be considered significant. For a sample of 10, we see the critical T at alpha = .05 for a two-tailed test is 8, and for a one-tailed test is 10. We have a T value of 22.5, which means we do not have a significant Wilcoxon signed rank test.
Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the Behavioral Sciences. Wadsworth, CA: Cengage Learning.
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