Wilcoxin Signed Rank test

Question 1

What are the features of this test?

Answer 1

Ordinal level data
Used for testing differences between TWO CONDITIONS
Data from repeated measures/matched pairs - ranks difference between each pair of scores
If there is no difference between the two treatments there will be small difference values, but if there is a difference values will be larger and differences will either be mostly positive or mostly negative

Question 2

What are the 5 steps to the Wilcoxin procedure?

Answer 2

Subtract one condition’s score from the other
Rank all differences, ignoring signs at this point
Add up ranks for the positive and negative scores separately
The T value is the smaller of the summed rank values
Check T value for significance

Question 3

As with the Mann-Whitney U test, what is the sum of all ranks?

Answer 3

N(N+1)/2

Can use this to check answers

Question 4

What is the null hypothesis for this test?

Answer 4

Two populations from which scores are sampled are identical i.e. their medians are equal

Question 5

What are rank sums for a given sample size like?

Answer 5

Always add up to same number e.g. in sample of 14 the sum will be 105 (1+2+3+4…)
If there is no difference between conditions we would expect T to be roughly half of this over repeated sampling i.e. 52.5 - the null hypothesis suggests that if we were to draw 14 random score pairs repeatedly T values of 52 and 53 would occur most frequently because sums of ranks for positive and negative differences would be roughly equal

What we want to know is whether our calculated T value is random or if it is a significant value

Question 6

What do we do if a difference score for a participant is zero?

Answer 6

They need to be excluded from the ranking process and this needs to be reflected in the sum formula e.g. if remove two zeros, the sum of rankings for positive differences = N-2(N-1)/2