1. 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

2. 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

3. 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

4. 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

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