Non-parametric tests

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

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Presentation Transcript
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