What are the key differences between Pearson and Spearman correlations?

3 Linearity vs. Monotonicity

One of the fundamental differences lies in what Pearson and Spearman correlations measure: linearity versus monotonicity. Pearson's r evaluates how well the relationship between two variables can be described by a straight line. In contrast, Spearman's ρ is concerned with monotonic relationships, where the variables tend to move in the same direction but not necessarily at a constant rate. This makes Spearman better suited for relationships that are consistently increasing or decreasing but not strictly linear.

4 Sensitivity to Outliers

Pearson's r can be heavily influenced by outliers—data points that deviate significantly from other observations. These outliers can skew the results and potentially provide misleading information about the strength of the relationship. On the other hand, Spearman's ρ, by virtue of using ranks rather than actual values, minimizes the impact of outliers. This makes Spearman a more robust choice in situations where outliers are present or cannot be reliably removed.

5 Data Requirements

The choice between Pearson and Spearman correlations also depends on the scale and distribution of your data. Pearson's r requires both variables to be measured on at least an interval scale and assumes a normal distribution. Spearman's ρ can be used with ordinal data or when the assumptions of normality are not met. Therefore, Spearman offers greater flexibility when dealing with non-parametric data or when parametric assumptions cannot be satisfied.

6 Choosing the Right Test

When deciding between Pearson and Spearman correlations, consider the nature of your data and the relationship you're investigating. Use Pearson's r for continuous data that meet the assumptions of normality and homoscedasticity and when you expect a linear relationship. Opt for Spearman's ρ when dealing with ordinal data, non-normal distributions, or when the relationship is monotonic but not necessarily linear. Your choice will significantly impact the validity of your findings and the conclusions you draw from your statistical analysis.

7 Here’s what else to consider

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