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Non-parametric tests


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 l.jpg

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 l.jpg

Wilcoxon signed rank test

To test difference between paired data


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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


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STEP 2

  • Count up the ranks of +ives as T+

  • Count up the ranks of –ives as T-


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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-


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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


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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


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Wilcoxon rank sum test

  • To compare two groups

  • Consists of 3 basic steps


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Non-parametric equivalent of t test


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Step 1

  • Rank the data of both the groups in ascending order

  • If any values are equal average their ranks


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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


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