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.