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## PowerPoint Slideshow about 'Non-parametric tests' - elom

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### Wilcoxon signed rank test

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

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

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