Wilcoxon Matched Pairs Signed Ranks test When should we use it? At least ordinal data Repeated measures design Nominal Ordinal Interval Independent Chi-Square (association) Mann-Whitney U test (difference) Repeated Sign test (difference) Wilcoxon Matched Pairs Signed Ranks test (difference) Spearman Rank Correlation test (correlation) Matched pairs

Wilcoxon Signed-Rank Test A firm is selecting one of two express delivery services to provide next-day deliveries to the district offices. To test the delivery times of the two services, the firm sends two reports to a sample of 10 district offices. Is there a difference in the two services? District Office Overnight (hrs.) NiteFlite Seattle 32 25 Los Angeles 30 24 Boston 19 15 Cleveland 16 New York 13 Houston 18 Atlanta 14 St. Louis 10 8 Milwaukee 7 9 Denver 11 Difference |Difference| Rank Sign + Rank 7 10 6 9 4 1 1.5 2 3 -1 -1.5 -2 -4 5 8 Positive = 49.5 Negative = 5.5 Difference Rank of difference Difference and sign Total

Wilcoxon Signed-Rank Test H0 : The two populations are equal i.e., no difference in service times Rejection Region: Using a 0.05 level of significance, Reject if o=5.5 is greater than the critical value n is the number of participants, ignoring those with a difference of 0. Based on the rejection region above, we reject the null hypothesis and conclude that the two populations are not equal N = 10

Memory Study 12 people were tested in a repeated measures study examining the effects of music on memory. Each person was given one minute to memorise a list of 20 items before being asked to recall them. They did this twice, once with music in the background and once without. Silence 6 18 12 9 14 13 17 8 15 Music 11 10 16 5

Not Significant Total positive: 45.5 Total negative: 9.5 Obs = 9.5, n = 10, Critical = 8 Not Significant Difference -2 3 4 2 -1 1 Rank 7.5 10 1.5 Sign and Rank -4 -1.5