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Mann-Whitney U Test

Mann-Whitney U Test. Nonparametric test for independent subject designs P. Regoniel Advanced Statistics I. Topics. Mann-Whitney U-Test Defined and Related Concepts Difference Between t-test and Mann-Whitney U Test When Should Mann-Whitney U Test be Used? Example of Mann-Whitney U Test

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Mann-Whitney U Test

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  1. Mann-Whitney U Test Nonparametric test for independent subject designs P. Regoniel Advanced Statistics I

  2. Topics • Mann-Whitney U-Test Defined and Related Concepts • Difference Between t-test and Mann-Whitney U Test • When Should Mann-Whitney U Test be Used? • Example of Mann-Whitney U Test • Application of the Mann-Whitney U Test

  3. Mann-Whitney U Test Defined and Related Concepts • A nonparametric test for use with independent subject designs. • Independent subjects design (or independent samples design)— a design in which • groups of subjects experience different experimental conditions; • there is comparison of a control group versus an experimental group, or • two distinct groups are measured

  4. Difference Between T-test and Mann-Whitney U Test • t-test determines significant differences between means while Mann-Whitney U Test uses the medians to test for a significant difference in the location of the sample data. • t-test uses data directly while MWUT uses data in the form of ranks

  5. When Should Mann-Whitney Be Used? • When data are in the form of ranks • When data are not normally distributed (also implies that data are few) • When the variances of the two groups being compared are greatly different (as indicated by the F-test)

  6. Example Data: Bird Song Duration

  7. Formula Used for Mann-Whitney U Test • US = NSNL + [NS (NS + 1)/2] – T • UL = NSNL - US where NS = number of measures in the smaller sample; NL = number of measures in the larger sample

  8. Steps • Rank the data using both groups. Lowest score gets rank 1. • Calculate the US first before the UL. • Look up the tabular value for NS and NL in the Mann Whitney U Test Table. • If either the observed values is equal to or less than the tabular value, there is a significant difference between two groups.

  9. Answer: • US = NSNL + [NS (NS + 1)/2] – T • UL = NSNL - US So US = (7)(9) + [7(7 + 1)/2] – 68 = 63 + 28 – 68 = 23 UL = (7)(9) – 23 = 40

  10. Tabular Value for NS and NL (two-tailed)

  11. Conclusion • The tabular value is 12 at  = 0.05. • Since US and UL are greater than 12, the song durations therefore are not significantly different between the two populations. • There is a significant difference if either of the observed values (US or UL) is equal to or less than the tabular value. • By ocular inspection, we can notice that there is such variability in Sample B that it overlaps the values in Sample A. • An F-max test would be expected to show a significant difference in the variation of bird-song duration between the two populations.

  12. Exercise • Identify a situation where the Mann-Whitney U Test can be applied. • Requirements: Minimum number of observations for two groups = 20 • Present results to the class. • First group that presents correct answer gets additional two points in their quizzes. • Next groups with correct answer, 1 pt each.

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