Pearson's Product-Moment Correlation Coefficient (DP IB Analysis & Approaches (AA)): Revision Note

PMCC

What is Pearson’s product-moment correlation coefficient?

• Pearson’s product-moment correlation coefficient (PMCC) is a way of giving a numerical value to a linear relationship of bivariate data

• The PMCC of a sample is denoted by the letter 

  • r can take any value such that 

  • A positive value of r describes positive correlation

  • A negative value of r describes negative correlation

  • r = 0 means there is no linear correlation

  • r = 1 means perfect positive linear correlation

  • r = -1 means perfect negative linear correlation

  • The closer to 1 or -1 the stronger the correlation

How do I calculate Pearson’s product-moment correlation coefficient (PMCC)?

• You will be expected to use the statistics mode on your GDC to calculate the PMCC

• The formula can be useful to deepen your understanding

• is linked to the covariance

•  and  are linked to the variances

• You do not need to learn this as using your GDC will be expected

When does the PMCC suggest there is a linear relationship?

• Critical values of r indicate when the PMCC would suggest there is a linear relationship

  • In your exam you will be given critical values where appropriate

  • Critical values will depend on the size of the sample

• If the absolute value of the PMCC is bigger than the critical value then this suggests a linear model is appropriate