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Mann-Whitney and Wilcoxon Tests. Types of Inferential Statistics. Inferential Statistics : estimate the value of a population parameter from the characteristics of a sample Parametric Statistics :

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## Mann-Whitney and Wilcoxon Tests

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**Mann-Whitney**and Wilcoxon Tests**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)**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**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.**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).**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**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.**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**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**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**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).**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**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.

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