1. Non-parametric tests Note: When valid use parametric Note: When valid use parametric Commonly used Commonly usedWilcoxon Chi square etc. Performance comparable to parametric Performance comparable to parametric Useful for non-normal data Useful for non-normal data If normalization not possible If normalization not possible Note: CI derivation-difficult/impossible 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 Exclude any differences which are zero Put the rest of differences in ascending order Put the rest of differences in ascending order Ignore their signs Ignore their signs Assign them ranks Assign them ranks If any differences are equal, average their 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 + 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 is no difference between drug (T + ) and placebo (T - ), then T + & T - would be similar If there were a difference If there were a difference one sum would be much smaller and one sum would be much smaller and the other much larger than expected the other much larger than expected The smaller sum is denoted as T The smaller sum is denoted as T T = smaller of T + and T - T = smaller of T + and T -

6. STEP 4 Compare the value obtained with the critical values (5%, 2% and 1% ) in table 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) N is the number of differences that were ranked (not the total number of differences) So the zero differences are excluded So the zero differences are excluded

7. Patient Hours of sleep DifferenceRank Ignoring sign DrugPlacebo 16.15.20.93.5* 27.07.9-0.93.5* 38.23.94.310 47.64.72.97 56.55.31.25 68.45.43.08 76.94.22.76 86.76.10.62 97.43.83.69 105.86.3-0.51 3 rd & 4 th 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 To compare two groups Consists of 3 basic steps 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 Rank the data of both the groups in ascending order If any values are equal average their ranks If any values are equal average their ranks

11. Step 2 Add up the ranks in group with smaller sample size Add up the ranks in group with smaller sample size If the two groups are of the same size either one may be picked If the two groups are of the same size either one may be picked T= sum of ranks in group with smaller sample size T= sum of ranks in group with smaller sample size

12. Step 3 Compare this sum with the critical ranges given in table Compare this sum with the critical ranges given in table Look up the rows corresponding to the sample sizes of the two groups Look up the rows corresponding to the sample sizes of the two groups A range will be shown for the 5% significance level A range will be shown for the 5% significance level

13. Non-smokers (n=15) Non-smokers (n=15) Heavy smokers (n=14) Heavy smokers (n=14) Birth wt (Kg) Rank Rank 3.99273.187 3.79242.845 3.60*182.906 3.73223.2711 3.2183.8526 3.60*183.5214 4.08283.239 3.61202.764 3.83253.60*18 3.31123.7523 4.13293.5916 3.26103.6321 3.54152.382 3.51132.341 2.713 Sum=272Sum=163 * 17, 18 & 19are tied hence the ranks are averaged