Example 64.5 Exact Savage Multisample Test

A researcher conducting a laboratory experiment randomly assigned 15 mice to receive one of three drugs. The survival time (in days) was then recorded.

The following SAS statements create the data set Mice, which contains the observed survival times for the mice. The variable Treatment denotes the treatment received. The variable Days contains the number of days the mouse survived.

data Mice;
   input Treatment $ Days @@;
1 1 1 1 1 3 1 3 1 4
2 3 2 4 2 4 2 4 2 15
3 4 3 4 3 10 3 10 3 26

The following statements request a Savage test of the null hypothesis that there is no difference in survival time among the three drugs. Treatment is the CLASS variable, and Days is the analysis variable. The SAVAGE option requests an analysis of Savage scores. The SAVAGE option in the EXACT statement requests exact p-values for the Savage test. Because the sample size is small, the large-sample normal approximation might not be adequate, and it is appropriate to compute the exact test.

PROC NPAR1WAY tests the null hypothesis that there is no difference in the survival times among the three drugs against the alternative hypothesis of difference among the drugs. The SAVAGE option specifies an analysis based on Savage scores. The variable Treatment is the CLASS variable, and the variable Days is the response variable. The EXACT statement requests the exact Savage test.

proc npar1way savage data=Mice;
   class Treatment;
   var Days;
   exact savage;

Output 64.5.1 shows the results of the Savage test. The exact p-value is 0.0445, which supports a difference in survival times among the drugs at the 0.05 level. The asymptotic p-value based on the chi-square approximation is 0.0638.

Output 64.5.1 Savage Multisample Exact Test
The NPAR1WAY Procedure

Savage Scores (Exponential) for Variable Days
Classified by Variable Treatment
Treatment N Sum of
Under H0
Std Dev
Under H0
1 5 -3.367980 0.0 1.634555 -0.673596
2 5 0.095618 0.0 1.634555 0.019124
3 5 3.272362 0.0 1.634555 0.654472
Average scores were used for ties.

Savage One-Way Analysis
Chi-Square 5.5047
DF 2
Asymptotic Pr > Chi-Square 0.0638
Exact Pr >= Chi-Square 0.0445