Example 92.3 Paired Comparisons

When it is not feasible to assume that two groups of data are independent, and a natural pairing of the data exists, it is advantageous to use an analysis that takes the correlation into account. Using this correlation results in higher power to detect existing differences between the means. The differences between paired observations are assumed to be normally distributed. Some examples of this natural pairing are as follows:

• pre- and post-test scores for a student receiving tutoring

• fuel efficiency readings of two fuel types observed on the same automobile

• sunburn scores for two sunblock lotions, one applied to the individual’s right arm, one to the left arm

• political attitude scores of husbands and wives

In this example, taken from the SUGI Supplemental Library User’s Guide, Version 5 Edition, a stimulus is being examined to determine its effect on systolic blood pressure. Twelve men participate in the study. Each man’s systolic blood pressure is measured both before and after the stimulus is applied. The following statements input the data:

   data pressure;
         input SBPbefore SBPafter @@;
         datalines;
   120 128   124 131   130 131   118 127
   140 132   128 125   140 141   135 137
   126 118   130 132   126 129   127 135
   ;
   run;

The variables SBPbefore and SBPafter denote the systolic blood pressure before and after the stimulus, respectively.

The statements to perform the test follow:

   ods graphics on;
   
   proc ttest;
      paired SBPbefore*SBPafter;
   run;
   
   ods graphics off;

The ODS GRAPHICS statement requests graphical output. The PAIRED statement is used to test whether the mean change in systolic blood pressure is significantly different from zero. The tabular output is displayed in Output 92.3.1.