The HPCORR Procedure

Example 4.1 Computing the Pearson Measure of Association in Single-Machine Mode

The Fitness data set created in the section Getting Started: HPCORR Procedure contains measurements from a study of physical fitness of 31 participants. The following statements request the Pearson measure of association for the variables Weight, Oxygen, and Runtime:

title 'Measures of Association for a Physical Fitness Study';
proc hpcorr data=Fitness pearson;
   var Weight Oxygen RunTime;
run;

The Simple Statistics table in Output 4.1.1 displays univariate descriptive statistics for the analysis variables. By default, observations that have nonmissing values for each variable are used to derive the univariate statistics for that variable.

Output 4.1.1: Simple Statistics

Measures of Association for a Physical Fitness Study

The HPCORR Procedure

Performance Information
Execution Mode Single-Machine
Number of Threads 4

3 Variables: Weight Oxygen RunTime

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
Weight 31 77.44452 8.32857 2401 59.08000 91.63000
Oxygen 29 47.22721 5.47718 1370 37.38800 60.05500
RunTime 29 10.67414 1.39194 309.55000 8.17000 14.03000


The Pearson Correlation Coefficients table in Output 4.1.2 displays the Pearson correlation statistics for pairs of analysis variables. The Pearson correlation is a parametric measure of association for two continuous random variables. When the data have missing values, the number of observations used to calculate the correlation can vary.

Output 4.1.2: Pearson Correlation Coefficients

Pearson Correlation Coefficients
Prob > |r| under H0: Rho=0
Number of Observations
  Weight Oxygen RunTime
Weight
1.00000
 
31
-0.15358
0.4264
29
0.20072
0.2965
29
Oxygen
-0.15358
0.4264
29
1.00000
 
29
-0.86843
<.0001
28
RunTime
0.20072
0.2965
29
-0.86843
<.0001
28
1.00000
 
29


The table shows that the Pearson correlation between Runtime and Oxygen is $-$0.86843, which is significant with a $p$-value less than 0.0001. This indicates a strong negative linear relationship between these two variables. As Runtime increases, Oxygen decreases linearly.