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Non-parametric tests


Wilcoxon signed rank test . To test difference between paired data. STEP 1. Exclude any differences which are zeroPut the rest of differences in ascending orderIgnore their signsAssign them ranksIf any differences are equal, average their ranks. STEP 2. Count up the ranks of ives as T

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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 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