12.2.2.2 - Example: Body Correlation Matrix

This correlation matrix was constructed using the body dataset. These data are from the Journal of Statistics Education data archive.

 

Six variables were used: age, weight (kg), height (cm), hip girth, abdominal girth, and wrist girth.

Cell contents grouped by Age, Weight, Height, Hip Girth, and Abdominal Girth; First row: Pearson correlation, Following row: P-Value

Cell contents grouped by Age, Weight, Height, Hip Girth, and Abdominal Girth; First row: Pearson correlation, Following row: P-Value

Correlations
  Age Weight (kg) Height (cm) Hip Girth Abdominal Girth
Weight (kg) 0.207265        
  <0.0001        
Height (cm) 0.067883 0.717301      
  0.1269 <0.0001      
Hip Girth 0.227080 0.762969 0.338584    
  <0.0001 <0.0001 <0.0001    
Abdominal Girth 0.422188 0.711816 0.313197 0.825892  
  <0.0001 <0.0001 <0.0001 <0.0001  
Wrist Girth 0.192024 0.816488 0.690834 0.458857 0.435420
  <0.0001 <0.0001 <0.0001 <0.0001 <0.0001

This correlation matrix presents 15 different correlations. For each of the 15 pairs of variables, the top box contains the Pearson's r correlation coefficient and the bottom box contains the p value. 

The correlation between age and weight is \(r=0.207265\). This correlation is statistically significant (\(p<0.0001\)). That is, there is evidence of a relationship between age and weight in the population.

The correlation between age and height is \(r=0.0678863\). This correlation is not statistically significant (\(p=0.1269\)). There is not evidence of a relationship between age and height in the population.

The correlation between weight and height is \(r=0.717301\). This correlation is statistically significant (\(p<0.0001\)). That is, there is evidence of a relationship between weight and height in the population.

And so on.