9/15/2023

Section 4.1 - see GoogleDrive\Stat216-Nonparametrics-F2023\!Class Notes\Section4.1-Notes-BH.pdf

Two Sample Location Problem

Models for location alternatives

Wilcoxon Rank Sum Test

The null distribution of the Wilcoxon rank sum statistic

Class Exercise - Find the null distribution of W when we have m=3 X observations and n=2 Y observations.

Ties Corrections

The W* LSA test in the case of ties is conservative if we do not use the correction. i.e., If we reject the null hypothesis without the correction, then we would also reject the null hypothesis with it.

General recommendation:

• Compute W* without the ties correction
• Find the p-value for this uncorrected W*. If the p-value is less than or equal to alpha, reject the null hypothesis and do not mess with the ties correction.
• If the p-value is greater than alpha, but close to alpha, then use the ties correction and recompute alpha.
• If the p-value is greater than alpha, but not close to alpha, ignore the ties correction.

We will have a problem session and lab on Monday. Please complete your reading of Chapter 4 for class on Wednesday.