Non-parametric tests

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

2. Wilcoxon signed rank test To test difference between paired data

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

4. STEP 2 • Count up the ranks of +ives as T+ • Count up the ranks of –ives as T-

5. STEP 3 • If there is no difference between drug (T+) and placebo (T-), then T+ & T- would be similar • If there were a difference one sum would be much smaller and the other much larger than expected • The smaller sum is denoted as T • T = smaller of T+ and T-

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

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

8. Wilcoxon rank sum test • To compare two groups • Consists of 3 basic steps

9. Non-parametric equivalent of t test

10. Step 1 • Rank the data of both the groups in ascending order • If any values are equal average their ranks

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

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

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