Wilcoxon signed rank test

Question 1

What is the Wilcoxon signed rank test?

Answer 1

Paired/matched design

e.g.10 nurses were given a questionnaire that measured ratings for sympathy for minor injuries sustained by their family members pre and post-training

Hypothesis: There will be a significant difference in sympathy scores for pre- vs. post training

Question 2

How do you calculate the Wilcoxon signed rank test?

Answer 2

1) Calculate the difference between the 2 scores/data (after score - before score)

2) Arrange the differences from lowest to highest (ignoring negative signs)

3) Rank the differences

4) Split the rank of differences in terms of positives and negatives

5) Calculate the sum of positive ranks of differences and the sum of negative ranks of differences (T statistic)

Question 3

When the test statistic T is small, what p-value will we get?

Answer 3

We get a small p-value of obtaining this data by chance if there really was no difference between the two conditions

Question 4

T statistic will only be small if…?

Answer 4

One condition has consistently different (e.g. bigger) scores from the other condition

Question 5

How is T-statistic formed?

Answer 5

T is formed as the sum of ranks of the least occurring difference sign

Question 6

What are the p-values if we have small/non-normal data?

Answer 6

Exact Sig. (2-tailed)
or
Exact Sig. (1 tailed

Question 7

Exact Sig. (2-tailed)
or
Exact Sig. (1 tailed

What is this p-value for?

Answer 7

If the data is small or non-normal

Question 8

What does the p-value tell us if we had calculated the Wilcoxon signed rank test?

Answer 8

The P-value is the probability that the difference between the two sets of data could have occurred by chance under the null.

Question 9

You are interested in the efficacy of a new exercise-based intervention in reducing anxiety levels but you are limited to a small sample size of 12 people and you suspect the variable (a questionnaire score which provides a whole number anxiety rating between 0 and 10) is not normal. You collect anxiety rating data in your sample both before and after the exercise intervention. The data are summarised below (ordered by participant number):

Before: {4, 2, 6, 4, 6, 7, 5, 2, 2, 1, 5, 4}

After: {7, 5, 3, 5, 2, 8, 9, 3, 3, 6, 3, 6}

Based on the issues described above, you have decided to conduct a Wilcoxon signed rank test. Follow these steps to calculate the relevant T statistic:

First, take the difference between your scores within participants (After-Before), noting which differences are negative and which are positive.

Next, rank the absolute value (i.e. throw away the sign) of the difference scores, ignoring any 0 differences.

a) The sum of the ranks corresponding to the negative differences is:

b) The sum of the ranks corresponding to the positive differences is:

c) The T statistic (i.e. the smaller of the signed ranks) is:

Answer 9

a) 24
b) 54
c) 24

Question 10

You are interested in the effects of exaggerated language on perception. You show 12 participants 2 videos of cars hitting a wall (both are travelling at the same speed). In one condition the video is titled with the caption “Car hits a wall”. In the other video, the caption is “Car smashes into a wall”. The order of presentation was counterbalanced across participants. After seeing the video participants rate the perceived speed on a 10-point scale. After examining the data you are not convinced that your data follow a normal distribution and there appears to be more variability in the “Smashes” condition. The data are summarised below (ordered by participant number):

Hits: {4, 5, 3, 4, 5, 4, 3, 6, 4, 5, 3, 5}

Smashes: {7, 3, 9, 2, 6, 3, 7, 8, 2, 6, 5, 9}

Based on the issues described above, you have decided to conduct a Wilcoxon signed rank test. Follow these steps to calculate the relevant T statistic:

First, take the difference between your scores within participant (Smashes-Hits), noting which differences are negative and which are positive.

Next, rank the absolute value (i.e. throw away the sign) of the difference scores, ignoring any 0 differences.

a) The sum of the ranks corresponding to the negative differences is:

b) The sum of the ranks corresponding to the positive differences is:

c) The T statistic (i.e. the smaller of the signed ranks) is:

Answer 10

a) 20
b) 58
c) 20