Mann-Whitney and Wilcoxon Tests

1. Mann-Whitney and Wilcoxon Tests

2. Types of Inferential Statistics • Inferential Statistics:estimate the value of a population parameter from the characteristics of a sample • Parametric Statistics: • Assumes the values in a sample are normally distributed • Interval/Ratio level data required • Nonparametric Statistics: • No assumptions about the underlying distribution of the sample • Used when the data do not meet the assumption for a nonparametric test (ordinal and nominal data)

3. Choosing Statistical Procedures

4. Mann Whitney U Test • Nonparametric equivalent of the independent t test • Two independent groups • Ordinal measurement of the DV • The sampling distribution of U is known and is used to test hypotheses in the same way as the t distribution. U

5. Mann Whitney U Test • To compute the Mann Whitney U: • Rank the scores in both groups (together) from highest to lowest. • Sum the ranks of the scores for each group. • The sum of ranks for each group are used to make the statistical comparison.

6. Non-Directional Hypotheses • Null Hypothesis: There is no difference in scores of the two groups (i.e. the sum of ranks for group 1 is no different than the sum of ranks for group 2). • Alternative Hypothesis: There is a difference between the scores of the two groups (i.e. the sum of ranks for group 1 is significantly different from the sum of ranks for group 2).

7. Computing the Mann Whitney U Using SPSS • Enter data into SPSS spreadsheet; two columns  1st column: groups; 2nd column: scores (ratings) • Analyze  Nonparametric  2 Independent Samples • Select the independent variable and move it to the Grouping Variable box  Click Define Groups  Enter 1 for group 1 and 2 for group 2 • Select the dependent variable and move it to the Test Variable box  Make sure Mann Whitney is selected  Click OK

8. Interpreting the Output The output provides a z score equivalent of the Mann Whitney U statistic. It also gives significance levels for both a one-tailed and a two-tailed hypothesis.

9. Generating Descriptives for Both Groups • Analyze  Descriptive Statistics  Explore • Independent variable  Factors box • Dependent variable  Dependent box • Click Statistics  Make sure Descriptives is checked  Click OK

10. Wilcoxon Signed-Rank Test • Nonparametric equivalent of the dependent (paired-samples) t test • Two dependent groups (within design) • Ordinal level measurement of the DV. • The test statistic is T, and the sampling distribution is the T distribution. T

11. Wilcoxon Test • To compute the Wilcoxon T: • Determine the differences between scores. • Rank the absolute values of the differences. • Place the appropriate sign with the rank (each rank retains the positive or negative value of its corresponding difference) • T = the sum of the ranks with the less frequent sign

12. Non-Directional Hypotheses • Null Hypothesis: There is no difference in scores before and after an intervention (i.e. the sums of the positive and negative ranks will be similar). • Non-Directional Research Hypothesis: There is a difference in scores before and after an intervention (i.e. the sums of the positive and negative ranks will be different).

13. Computing the Wilcoxon Test Using SPSS • Enter data into SPSS spreadsheet; two columns  1st column: pretest scores; 2nd column: posttest scores • Analyze  Nonparametric  2 Related Samples • Highlight both variables  move to the Test Pair(s) List  Click OK To Generate Descriptives: • Analyze  Descriptive Statistics  Explore • Both variables go in the Dependent box • Click Statistics  Make sure Descriptives is checked  Click OK

14. Interpreting the Output The T test statistic is the sum of the ranks with the less frequent sign. The output provides the equivalent z score for the test statistic. Two-Tailed significance is given.