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# Non-parametric tests PowerPoint PPT Presentation

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. Wilcoxon signed rank test.

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Non-parametric tests

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### 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

## Wilcoxon signed rank test

To test difference between paired data

### 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

### STEP 2

• Count up the ranks of +ives as T+

• Count up the ranks of –ives as T-

### 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-

### 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

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

### Wilcoxon rank sum test

• To compare two groups

• Consists of 3 basic steps

### Step 1

• Rank the data of both the groups in ascending order

• If any values are equal average their ranks

### 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

### 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

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