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 @@; 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 ;

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; run;

Output 69.5.1 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 69.5.1: Savage Multisample Exact Test

The NPAR1WAY Procedure

Savage Scores (Exponential) for Variable Days Classified by Variable Treatment |
|||||
---|---|---|---|---|---|

Treatment | 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 |