9/19/2016

Wilcoxon Rank Sum Test

See p:\data\math\hartlaub\nonparametrics\MWW.csv
See p:\data\math\hartlaub\nonparametrics\MWW.R

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.

An Alternative Test based on Normal Scores (van der Waerden)

See code in p:\data\math\hartlaub\nonparametrics\MWW.R

Point and Interval Estimation for Shift Parameter

Examples - Return to MWW.R (the cotanine concentrations for children and exposure to second hand smoke).