![]() Table 1 shows Steps 1 through 4 for the call time example. Calculate the sum of the ranks of the first sample (the W-value). ![]() Calculate and assign the average rank for the observations that are tied (the ones with the same value).Rank all the values, with the smallest observation given rank 1, the second smallest rank 2, etc.Combine the data from the two samples into one.The Mann-Whitney test can be completed in four steps: Handpicked Content: A Solution Template to Help in Hypothesis Testing How the Mann-Whitney Test WorksĪnother name for the Mann-Whitney test is the 2-sample rank test, and that name indicates how the test works. The test is significant at 0.0459 (adjusted for ties) ETA 1 not = ETA 2 is significant at 0.0460 Point estimate for ETA 1 – ETA 2 is 0.400ĩ5.0 percent confidence interval for ETA 1 – ETA 2 is (0.000 0.900) Mann-Whitney Test and Cofidence Interval: Before After The median call time of 1.15 minutes after the improvement is therefore significantly shorter than the 2-minute length before improvement. For the call times, the p-value is 0.0459 – less than 0.05. If the p-value is below the usually agreed alpha risk of 5 percent (0.05), the null hypothesis can be rejected and at least one significant difference can be assumed. When examining the plot, a practitioner might ask: Do the distributions look similar? Are they all left- or right-skewed, with only some extreme values? Completing the Testīecause the assumptions are now verified, the Mann-Whitney test can be conducted. If the probability plot does not provide distribution that matches all the groups, a visual check of the data may help. A dot plot (Figure 1) of the data shows a lot of overlap between the lead times – it is hard to tell whether there are significant differences.įigure 4: Test for Exponential Distribution of Before and After Improvement Effort Data Time is measured before and after the improvement. Comparing the medians of the number of injuries per month ( Y = discrete count) at two different sites ( X).Ī team wants to find out whether a project to reduce the time to answer customer calls was successful.Comparing the medians of the satisfaction ratings ( Y= discrete-ordinal) of customers before and after improving the quality of a product or service.Comparing the medians of manufacturing cycle times ( Y = continuous) of two different production lines ( X).Uses for the Mann-Whitney TestĮxamples for the usage of the Mann-Whitney test include: Of course, the Mann-Whitney test can also be used for normally distributed data, but in that case it is less powerful than the 2-sample t-test. The Mann-Whitney test compares the medians from two populations and works when the Y variable is continuous, discrete-ordinal or discrete-count, and the X variable is discrete with two attributes. If that assumption does not hold, the nonparametric Mann-Whitney test is a better safeguard against drawing wrong conclusions. When conducting the 2- sample t-test to compare the average of two groups, the data in both groups must be sampled from a normally distributed population.
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