1. Non-parametric test Introduction, Wilcoxon rank sum test and Man-Whitney U test Reporter: Shao-Li Han

2. Non-Parametric Test  Parametric tests: certain assumptions  Non-parametric tests: fewer assumptions need

3. Advantage  Few or no assumption  Reduce the effect of the outlies  Even for ordinal and sometimes even nominal data Nominal data: Ex. Marriage status: single, marriage, devoiced, widow… Ordinal data: Ex. The academic performance: A, B, C, D and E

4. Statistic Character  No estimate of variance  No confidence interval  Fewer measures of effect size  Chi-Square test of independence is one of non-parametric statitics  Median, instead of the mean Not as powerful as parametric alternatives!!

5. Sign Test  When to apply: conditions that single sample t-test are not met.  Binomial test  Example 1

6. Observation  Use less number  One tail or 2 tails =>excel function, =binomdist provided one tail probablity  Not for ranked-signs, for example 1, there should be different influence in “50” and “25” on the result, although the signs of the two value are all “1”. Wilcoxon’s ranked-sign test!

7. Wilcoxon Rank Sum Test for Independent Samples  2 independent samples are drawn from populations with an ordinal distribution.  H0: the observations come from the same population.  The probability when x 0 > y 0 and x 0 <y 0 is just the same  They have the same medians. W left tail statistc  Example 2 Nominal data: Ex. Marriage status: single, marriage, devoiced, widow… Ordinal data: Ex. The academic performance: A, B, C, D and E

8. Different sample size  A bit more care is required  W represents the left tail static; W’ for right tail statictic  Using reverse ranking  Example

9. If 2 samples are sufficiently large  Sample size > 10 or greater than 20  Wilcoxon table  W statistic is approximately normal N(μ,σ)  Example 3

10. Effect Size  Given by the correlation coefficient  (M1-M2)/Standard deviation

11. Mann-Whitney U Test  Alternative form of Wilcoxon rank-Sum test  No matter which sample is bigger!!  Mann-Whitney TablesTables  Observed value of U Reject the hypothesis  Mathematic processing …ex. U1+U2=n1*n2…  Examples…

12. Example  ADHD vs non-ADHD children  Academic performance, A, B, C among students from a given grade 1 elementary school.  By using Wilcoxon rank sum test or Mann-Whitney U test  Sample size > 20 (in excel file)