1 / 2

Mann-Whitney Test

Mann-Whitney Test.

cicada
Download Presentation

Mann-Whitney Test

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mann-Whitney Test • If X1, X2, … Xm is a sample of size m from a population, and Y1, Y2, … Yn is a sample of size n from another population, then the Mann-Whitney statistic, U, is the number of (Xi,Yj) pairs for which Xi<Yj. U is used to test the same null hypothesis of equal population distributions and p-values are given in Table A4. • Go over Example 2.6.1 - use R • First note that W (sum of ranks, the Wilcoxon statistic) and U (the Mann-Whitney statistic) are equivalent: • Let W2=sum of ranks of the Y's and note that for any Yj, R(Yj)=# of X's <= Yj + #of Y's <= Yj • So W2= Sum over all j's{R(Yj)} =sum over all j's{# of X's <= Yj + #of Y's <= Yj } =U + (1+2+3+…+n) , since we may assume the Y's are ordered =U+n(n+1)/2 • NOTE: In R, the W given in wilcox.test is = U (or m*n - U ) • If there are ties, then U=#pairs of X<=Y + 1/2*(#ties)

  2. Review the relationship between a confidence interval and hypothesis testing in the parametric case… • If the null hypothesis of F1=F2 is rejected then one possible alternative is the so-called shift alternative: F1(x) = F2(x-D) where D can be thought of as the difference in means (or medians)… do a sketch. • A consequence of the truth of the shift alternative is that X and Y+ D have the same distribution. So think of D as the difference of the medians - we'll use the Hodges-Lehmann estimate of D : H-L=median(all pwds) • The 95% confidence interval for D is found by: • get all the pwds of X-Y • arrange them from smallest to largest • find 2 numbers ka, and kb s.t. P(ka<= U < kb ) = P(pwds(ka) < D <= pwds(kb)) = as close to the level of confidence as possible • for large samples, we'll use the normal approximation (more on this later) • Now go over Example 2.6.2 on page 46ff - use the R code in R4.doc… • Redo problem #4 on page 73 - get a 95% CI for D and its H-L estimate. Use R.

More Related