Comparison of Correlation Coefficients (DP IB Applications & Interpretation (AI)): Revision Note

Appropriateness & Limitations

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?

• If there is linear correlation then the relationship is also monotonic

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  • However the converse is not true

• It is possible for Spearman’s rank to be 1 (or -1) but for the PMCC to be different

  • For example: data that follows an exponential growth model

    • as the points are always increasing

    • as the points do not lie on a straight line

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