IB DP Maths: AI HL复习笔记4.2.2 Correlation Coefficients

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
  • 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

• • 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

What is Spearman’s rank correlation coefficient?

How do I calculate Spearman’s rank correlation coefficient (PMCC)?

• Rank each set of data independently
  • 1 to n for the x-values
  • 1 to n for the y-values

Which correlation coefficient should I use?

• Pearson’s PMCC tests for a linear relationship between two variables
  • It will not tell you if the variables have a non-linear relationship
    • Such as exponential growth
  • Use this if you are interested in a linear relationship
• Spearman’s rank tests for a monotonic relationship (always increasing or always decreasing) between two variables
  • It will not tell you what function can be used to model the relationship
    • Both linear relationships and exponential relationships can be monotonic
  • Use this if you think there is a non-linear monotonic relationship

How are Pearson’s and Spearman’s correlation coefficients connected?

Are Pearson’s and Spearman’s correlation coefficients affected by outliers?

• Pearson’s PMCC is affected by outliers
  • as it uses the numerical value of each data point
• Spearman’s rank is not usually affected by outliers
  • as it only uses the ranks of each data point