# The NPAR1WAY Procedure

## 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

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.