Slide 1 ### Non-parametric tests

- Note: When valid use parametric
- Commonly used
Wilcoxon

Chi square etc.

- Performance comparable to parametric
- Useful for non-normal data
- If normalization not possible
- Note: CI derivation-difficult/impossible

Slide 2 Wilcoxon signed rank test

To test difference between paired data

Slide 3 ### STEP 1

- Exclude any differences which are zero
- Put the rest of differences in ascending order
- Ignore their signs
- Assign them ranks
- If any differences are equal, average their ranks

Slide 4 ### STEP 2

- Count up the ranks of +ives as T+
- Count up the ranks of â€“ives as T-

Slide 5 Slide 6 ### STEP 4

- Compare the value obtained with the critical values (5%, 2% and 1% ) in table
- N is the number of differences that were ranked (not the total number of differences)
- So the zero differences are excluded

Slide 7 3rd & 4th ranks are tied hence averaged

T= smaller of T+ (50.5) and T- (4.5)

Here T=4.5 significant at 2% level indicating the drug (hypnotic) is more effective than placebo

Slide 8 ### Wilcoxon rank sum test

- To compare two groups
- Consists of 3 basic steps

Slide 9 ### Non-parametric equivalent of t test

Slide 10 ### Step 1

- Rank the data of both the groups in ascending order
- If any values are equal average their ranks

Slide 11 ### Step 2

- Add up the ranks in group with smaller sample size
- If the two groups are of the same size either one may be picked
- T= sum of ranks in group with smaller sample size

Slide 12 ### Step 3

- Compare this sum with the critical ranges given in table
- Look up the rows corresponding to the sample sizes of the two groups
- A range will be shown for the 5% significance level

Slide 13 * 17, 18 & 19are tied hence the ranks are averaged