Pearson’s Sample Correlation Coefficient, r, is used to measure the strength and direction of the association between two numerical paired variables.

• Direction of the Association: The association can be either positive or negative.
  • Positive Correlation: as the x variable increases so does the y variable. Example: In the summer, as the temperature increases, so does thirst.
  • Negative Correlation: as the x variable increases, the y variable decreases. Example: As the price of an item increases, the number of items sold decreases.
• Strength of the Association:  The strength of the association is measured by the sample Correlation Coefficient, r.  r can be any value from –1 to +1.   
  • The closer r is to one (in magnitude) the stronger the linear association is.  
  • If r equals zero, then there is no linear association between the two variables.  
• See the two charts below for some guidelines in interpreting the correlation coefficient.
  

*  No other values of r have precise definitions of strength. See the chart below.

Note:  All of the values in the second table are positive. Thus the association is positive. The same strength interpretations hold for negative values of r, only the direction interpretations of the association would change.

Click here for  visual representation links of different strengths and directions of linear correlation.  They are very useful for understanding correlation.

Learn the Procedure for calculating correlation coefficients

         

Correlation Menu  Dictionary

STATS @ MTSU