This document explains how to perform the Wilcoxon signed-ranks test to analyze differences between pre- and post-ratings from church members assessing whether starring in a movie would negatively impact Joe's chances of going to heaven. It describes ranking the differences between pre- and post-ratings, with tied ranks getting the average rank. The ranks of negative differences are summed and compared to the ranks of positive differences; the smaller total is T. If T is equal to or below the critical value based on sample size from a table, there is a significant difference between pre- and post-ratings. Applying this to Joe's ratings, T=5 which is below the critical value of 6, so the church members see Joe as significantly more

1. Don’t worry, you can’t go
blind from ranking
Dr David Playfoot
d.r.playfoot@swansea.ac.uk

2. • Joe wants to know whether being in the
movie would affect his eternal soul
• He asks members of his church to rate how
likely he is to go to hell
• He asks members of his church to rate him
again after telling them about the movie
opportunity
Remember…

3. • We used the Sign test in the previous section
to see whether there was a change in Joe’s
likelihood of damnation
• It looked like this…
Remember…

4. Sign Test
Church member Pre-Orgazmo Post-Orgazmo Difference Sign of
difference
A 3 7 4 +
B 12 18 6 +
C 9 5 -4 -
D 7 7 0
E 8 12 4 +
F 1 5 4 +
G 15 16 1 +
H 10 12 2 +
I 11 15 4 +
J 10 17 7 +

5. • We can go one better by considering the ranks
of the differences.
• We organise the rows in terms of the size of
the difference between pre and post ratings
• We do this ignoring whether the difference
was +ve or –ve.
Wilcoxon Signed Ranks

6. Church member Pre-Orgazmo Post-Orgazmo Difference Rank of
difference
A 3 7 4 5
B 12 18 6 8
C 9 5 -4 5
D 7 7 0
E 8 12 4 5
F 1 5 4 5
G 15 16 1 1
H 10 12 2 2
I 11 15 4 5
J 10 17 7 9
Wilcoxon Signed Ranks

7. • Notice that church members A, C, E, F and I all
have the same rank.
• When there is the same size difference in
more than 1 pair of scores, you have to do
something about it.
• You can’t pretend that those pairs of scores
had different differences so you can’t give
them different ranks
Wilcoxon Signed Ranks

8. • So these pairs have to have the same ranks
• You can’t change the total number of ranks, or
the sum of all ranks by giving all pairs the next
available rank.
• In our example we’d used ranks 1 and 2
• The next available rank would be 3
• If we gave all tied scores a rank of 3, we
wouldn’t have the right total when we added
up all the ranks
Wilcoxon Signed Ranks

9. • So we give the tied scores the average rank
that they would have had.
• There are 5 tied pairs.
• We’ve used ranks 1 and 2
• If the tied pairs weren’t tied, we’d have ranked
them 3, 4, 5, 6, and 7
• Add up 3, 4, 5, 6, and 7 then divide by 5
• All the tied pairs can be ranked 5 without
making them seem different from each other
or affecting the sum of all the allocated ranks.
Wilcoxon Signed Ranks

10. • Next, we add up the ranks of all the pairs with
negative differences
Wilcoxon Signed Ranks

11. Church member Pre-Orgazmo Post-Orgazmo Difference Rank of
difference
A 3 7 4 5
B 12 18 6 8
C 9 5 -4 5
D 7 7 0
E 8 12 4 5
F 1 5 4 5
G 15 16 1 1
H 10 12 2 2
I 11 15 4 5
J 10 17 7 9
Wilcoxon Signed Ranks
Only
negative
difference

12. • Next, we add up the ranks of all the pairs with
negative differences = 5
• Then we add up the ranks of all the pairs with
positive differences
Wilcoxon Signed Ranks

13. Church member Pre-Orgazmo Post-Orgazmo Difference Rank of
difference
A 3 7 4 5
B 12 18 6 8
C 9 5 -4 5
D 7 7 0
E 8 12 4 5
F 1 5 4 5
G 15 16 1 1
H 10 12 2 2
I 11 15 4 5
J 10 17 7 9
Wilcoxon Signed Ranks
Positive
differences

14. • Next, we add up the ranks of all the pairs with
negative differences = 5
• Then we add up the ranks of all the pairs with
positive differences = 40
• Whichever is the smaller total becomes
known as T
Wilcoxon Signed Ranks

15. • If T is equal to or smaller than the value in the
critical values table (for the right N), there is a
significant difference.
• The critical value for N = 9 (N is the number of non-
zero differences) at p < .05 level is 6
• Our T = 5, so the church members think Joe is
significantly more likely to go to hell if he stars in
the film.
Wilcoxon Signed Ranks