Example 67.3: Paired Comparisons

The TTEST Procedure

Example 67.3: 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. Utilizing 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

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 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. Their systolic blood pressure is measured both before and after the stimulus is applied. The following statements input the data:

   title 'Paired Comparison';
   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.

   proc ttest;
      paired SBPbefore*SBPafter;
   run;

The PAIRED statement is used to test whether the mean change in systolic blood pressure is significantly different from zero. The output is displayed in Output 67.3.1.

Output 67.3.1: TTEST Results

Paired Comparison

The TTEST Procedure

Statistics
Difference	N	Lower CL Mean	Mean	Upper CL Mean	Lower CL Std Dev	Std Dev	Upper CL Std Dev	Std Err	Minimum	Maximum
SBPbefore - SBPafter	12	-5.536	-1.833	1.8698	4.1288	5.8284	9.8958	1.6825	-9	8

T-Tests
Difference	DF	t Value	Pr > \|t\|
SBPbefore - SBPafter	11	-1.09	0.2992

The variables SBPbefore and SBPafter are the paired variables with a sample size of 12. The summary statistics of the difference are displayed (mean, standard deviation, and standard error) along with their confidence limits. The minimum and maximum differences are also displayed. The t test is not significant (t=-1.09, p=0.2992), indicating that the stimuli did not significantly affect systolic blood pressure.

Note that this test of hypothesis assumes that the differences are normally distributed. This assumption can be investigated using PROC UNIVARIATE with the NORMAL option. If the assumption is not satisfied, PROC NPAR1WAY should be used.

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