This example uses the SAS data set React
created in Example 65.3. 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 HodgesLehmann estimation of the location shift between the two groups. Stim
is the CLASS variable, and Time
is the analysis variable. The HL option requests HodgesLehmann estimation. The ALPHA= option sets the confidence level for
the HodgesLehmann 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 65.4.1 shows the HodgesLehmann results.
proc npar1way hl alpha=.02 data=React; class Stim; var Time; exact hl; ods select WilcoxonScores HodgesLehmann; run;
The HL option invokes the WILCOXON option, which produces a table of Wilcoxon scores (Output 65.4.1). The HodgesLehmann 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.
Output 65.4.1: HodgesLehmann Estimate of Location Shift
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. 
HodgesLehmann Estimation  

Location Shift (2  1) 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 