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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.

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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

Wilcoxon signed rank test

To test difference between paired data

step 1
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
STEP 2
  • Count up the ranks of +ives as T+
  • Count up the ranks of –ives as T-
step 3
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
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
slide7

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
Wilcoxon rank sum test
  • To compare two groups
  • Consists of 3 basic steps
step 110
Step 1
  • Rank the data of both the groups in ascending order
  • If any values are equal average their ranks
step 211
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 312
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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