Example 47.3: The Exact Savage Multisample Test

The NPAR1WAY Procedure

Example 47.3: The Exact Savage Multisample Test

A researcher conducting a laboratory experiment randomly assigned fifteen 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 all the mice. The variable Trt denotes the treatment received by a mouse. The variable Days contains the number of days the mouse survived.

   data Mice;
      input Trt $ Days @@;
      datalines;
   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
   ;

PROC NPAR1WAY tests the null hypothesis that there is no difference in the survival times among the three drugs against an alternative hypothesis of difference among the drugs. The SAVAGE option specifies that Savage scores are to be used. The variable Trt is the CLASS variable, and the VAR statement specifies that the variable Days is the response variable. The EXACT statement requests the exact test.

   proc npar1way savage data=Mice;
      class Trt;
      var Days;
      exact;
   run;

Output 47.3.1: Results of the Savage Multisample Test

The NPAR1WAY Procedure

Savage Scores (Exponential) for Variable Days Classified by Variable Trt
Trt	N	Sum of Scores	Expected Under H0	Std Dev Under H0	Mean Score
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

Output 47.3.1 shows the results of the Savage test. The exact p-value is 0.0445, which is significant at the 0.05 level. However, the p-value based on the chi-square approximation is 0.0638, which results in nonrejection of the null hypothesis at the 0.05 level.

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