14 Nonparametric Statistics

STEP-BY-STEP TECHNOLOGY GUIDE: Wilcoxon Signed Rank Test

Neither TI-83/84 calculators nor Excel has a built-in function for the Wilcoxon signed rank test.

MINITAB

Step 1 If you have two samples, enter the values in C1 and C2. If you have one sample, enter the values in C1.
Step 2 For two samples, click Calc > Calculator…. For Store result in variable, type C3. For Expression, type C1– C2. Click OK.
Step 3 Click Stat > Nonparametrics > 1-Sample Wilcoxon….
Step 4 For Variables, type C3. Select Test Median, and enter the hypothesized value of the median M₀. Select the form of the Alternative hypothesis, and click OK.

SPSS

We use the data in Example 12 to illustrate the procedure.

Step 1 Enter the data into the first column. Under the Variable View tab, rename the variable Age and change Measure to Scale.
Step 2 Click Data > Select Cases…, click If condition is satisfied, and click If….
Step 3 In the empty formula box, type Age ≅ 6. Click Continue then OK.

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Step 4 Click Analyze > Nonparametric Tests > One Sample….
Step 5 Select the Fields tab, and move Age to Test Fields.
Step 6 Select the Settings tab, select Customize tests, and check Compare median to hypothesized (Wilcoxon signed-rank test). Enter the Hypothesized median, 6, and click Run.
Step 7 Double-click the table of results in the Output window to open the Model Viewer, and observe the right-hand side. The results are shown in Figure 15 of Example 12.

CRUNCHIT!

We use the data in Table 7 to illustrate the procedure.

Step 1 Enter the 2013 data into Var1 and the 2014 data into Var2.
Step 2 Select Insert > Evaluate Formula. Enter |Var2|−|Varl| and click Evaluate. The differences appear in Var5.
Step 3 Select Statistics > Non-parametrics > Wilcoxon Signed Rank. For Sample, select Var5. Enter the Median under null hypothesis, 0, and for the Alternative hypothesis choose Less than. Click Calculate.