The HPCORR Procedure

Example 5.1 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 5.1.1 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 5.1.1: Simple Statistics

 Measures of Association for a Physical Fitness Study

The HPCORR Procedure

Performance Information
Execution Mode Single-Machine

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 5.1.2 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 5.1.2: 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.