Pearson Correlation vs Spearman Correlation (With Graph Interpretations)

Introduction to Pearson and Spearman Correlation00:00:00

The video introduces Pearson (r) and Spearman (rho or rs) correlation tests, explaining their scale from -1 to 1. A value of -1 indicates an inverse relationship, +1 a direct relationship, and 0 no correlation. Pearson applies to continuous variables with a linear relationship, while Spearman is for monotonic variables (continuous or ordinal).

Assumptions of Pearson and Spearman Tests00:02:03

Pearson assumes a normally distributed data and homoscedasticity of error terms, meaning consistent variability. Spearman is non-parametric, assuming no specific distribution, making it suitable for smaller samples or when the central limit theorem cannot be applied. Spearman's variables are also ranked before analysis.

Interpreting Graphs: Positive Linear Relationship00:03:23

The first graph shows a strong positive linear relationship, resulting in a +1 coefficient for both Pearson and Spearman. This indicates that as one variable increases, the other increases at a constant rate (Pearson) and never decreases (Spearman).

Interpreting Graphs: Monotonic but Non-Linear Relationship00:03:57

The second graph depicts a sideways 'S' shape, representing a monotonic but non-linear relationship. Pearson's coefficient will be less than +1 because the rate of increase is not constant, while Spearman's will be +1 because as one variable increases, the other never decreases.

Interpreting Graphs: No Clear Relationship00:04:36

The third graph shows scattered data with no strong relationship, resulting in low correlation coefficients (e.g., -0.093) for both Pearson and Spearman, indicating no clear linear or monotonic trend.

Interpreting Graphs: Negative Linear Relationship00:05:00

The fourth graph illustrates a strong negative linear relationship, where both Pearson and Spearman coefficients are -1. This means as one variable increases, the other decreases at a constant rate (Pearson) and never increases (Spearman).

Interpreting Graphs: Negative Monotonic but Non-Linear Relationship00:05:26

The fifth graph shows a strong negative monotonic but non-linear relationship. Pearson's coefficient is less than -1 (e.g., -0.799) due to varying decrease rates, while Spearman's remains -1 because the relationship is consistently decreasing.

Interpreting Graphs: Non-Monotonic Relationship00:06:02

The final graph presents an inverse quadratic function, which is a non-monotonic relationship. Both Pearson and Spearman coefficients are near zero, as Pearson detects no linearity and Spearman's monotonic assumption is violated (the other variable decreases and then increases).