PROC NPAR1WAY: Hodges-Lehmann Estimation :: SAS/STAT(R) 9.3 User's Guide

Example 64.4 Hodges-Lehmann Estimation

This example uses the SAS data set React created in Example 64.3. The data set contains the variable Stim, which represents Stimulant 1 or 2, and the variable Time, which contains the reaction times observed for subjects under the stimulant.

The following statements request Hodges-Lehmann estimation of the location shift between the two groups. Stim is the CLASS variable, and Time is the analysis variable. The HL option requests Hodges-Lehmann estimation. The ALPHA= option sets the confidence level for the Hodges-Lehmann confidence limits. The HL option in the EXACT statement requests exact confidence limits for the estimate of location shift. The ODS SELECT statement selects which tables to display. Output 64.4.1 shows the Hodges-Lehmann results.

proc npar1way hl alpha=.02 data=React;
   class Stim;
   var Time;
   exact hl;
   ods select WilcoxonScores HodgesLehmann;
run;

Output 64.4.1 Hodges-Lehmann Estimate of Location Shift

The NPAR1WAY Procedure

Wilcoxon Scores (Rank Sums) for Variable Time Classified by Variable Stim
Stim	N	Sum of Scores	Expected Under H0	Std Dev Under H0	Mean Score
1	13	110.50	130.0	11.004784	8.500
2	6	79.50	60.0	11.004784	13.250
Average scores were used for ties.

Hodges-Lehmann Estimation
Location Shift 0.3500
Type	98% Confidence Limits		Interval Midpoint	Asymptotic Standard Error
Asymptotic (Moses)	0.0000	0.8200	0.4100	0.1762
Exact	0.0000	1.3300	0.6650

The HL option automatically invokes the WILCOXON option, producing a table of Wilcoxon scores (Output 64.4.1). The Hodges-Lehmann estimate of location shift is 0.35, and the asymptotic confidence limits are 0.00 and 0.82. The confidence interval midpoint equals 0.41, which can also be used as an estimate of the location shift. The ASE estimate of 0.1762 is based on the length of the confidence interval. The exact confidence limits are 0.00 and 1.33.