The following statements create the data set Fitness1
. This data set contains an ordinal variable Oxygen
that is derived from a continuous measurement of oxygen intake which is not directly observed.
* Data on Physical Fitness *  These measurements were made on men involved in a physical   fitness course at N.C. State University.   The variables are Age (years), Weight (kg),   Runtime (time to run 1.5 miles in minutes), and   Oxygen (an ordinal variable based on oxygen intake,   ml per kg body weight per minute)   Certain values were changed to missing for the analysis.  **; data Fitness1; input Age Weight RunTime Oxygen @@; datalines; 44 89.47 11.37 8 40 75.07 10.07 9 44 85.84 8.65 10 42 68.15 8.17 11 38 89.02 . 9 47 77.45 11.63 8 40 75.98 11.95 9 43 81.19 10.85 9 44 81.42 13.08 7 38 81.87 8.63 12 44 73.03 10.13 10 45 87.66 14.03 7 45 66.45 11.12 8 47 79.15 10.60 9 54 83.12 10.33 10 49 81.42 8.95 9 51 69.63 10.95 8 51 77.91 10.00 9 48 91.63 10.25 9 49 73.37 10.08 . 57 73.37 12.63 7 54 79.38 11.17 9 52 76.32 9.63 9 50 70.87 8.92 10 51 67.25 11.08 9 54 91.63 12.88 7 51 73.71 10.47 9 57 59.08 9.93 10 49 76.32 . . 48 61.24 11.50 9 52 82.78 10.50 9 ;
The following statements compute Pearson correlations and polyserial correlations:
proc corr data=Fitness1 pearson polyserial; with Oxygen; var Age Weight RunTime; run;
For the purpose of computing Pearson correlations, the variables in the WITH and VAR statements are treated as continuous variables. For the purpose of computing polyserial correlations, the variables in the WITH statement are treated as ordinal variables by default, and the variables in the VAR statement are treated as continuous variables.
The “Simple Statistics” table in Output 2.5.1 displays univariate descriptive statistics for each analysis variable.
Output 2.5.1: Simple Statistics
1 With Variables:  Oxygen 

3 Variables:  Age Weight RunTime 
Simple Statistics  

Variable  N  Mean  Std Dev  Median  Minimum  Maximum 
Oxygen  29  8.93103  1.16285  9.00000  7.00000  12.00000 
Age  31  47.67742  5.21144  48.00000  38.00000  57.00000 
Weight  31  77.44452  8.32857  77.45000  59.08000  91.63000 
RunTime  29  10.67414  1.39194  10.50000  8.17000  14.03000 
The “Pearson Correlation Coefficients” table in Output 2.5.2 displays Pearson correlation statistics between Oxygen
and the other three variables. The table shows a strong correlation between variables Oxygen
and RunTime
.
Output 2.5.2: Pearson Correlation Coefficients
Pearson Correlation Coefficients Prob > r under H0: Rho=0 Number of Observations 


Age  Weight  RunTime  
Oxygen 



The “Polyserial Correlations” table in Output 2.5.3 displays polyserial correlation statistics between Oxygen
and the three continuous variables. The variable Oxygen
is treated as an ordinal variable derived from oxygen intake (the underlying continuous variable), assuming a bivariate normal
distribution for oxygen intake and each of the three continuous variables Age
, Weight
, and RunTime
. The CORR procedure provides two tests for a zero polyserial correlation: the Wald test and the likelihood ratio test. The
table shows a strong polyserial correlation between RunTime
and the underlying continuous variable of Oxygen
from both tests.
Output 2.5.3: Polyserial Correlation Coefficients
Polyserial Correlations  

Continuous Variable 
Ordinal Variable 
N  Correlation  Wald Test  LR Test  
Standard Error 
ChiSquare  Pr > ChiSq  ChiSquare  Pr > ChiSq  
Age  Oxygen  29  0.23586  0.18813  1.5717  0.2100  1.4466  0.2291 
Weight  Oxygen  29  0.24514  0.18421  1.7709  0.1833  1.6185  0.2033 
RunTime  Oxygen  28  0.91042  0.04071  500.0345  <.0001  38.6963  <.0001 