Statistics: Rank and Pearson Correlation

Study Notes

Rank Correlation

The Rank Correlation Coefficient measures the strength and direction of the linear relationship between two ranked variables.
It is used when data is ordinal or ranked.
The formula for calculating Rank Correlation is:
R = 1 - (6 * Σd²) / (n(n² - 1))*

Where:
- R is the rank correlation coefficient.
- d is the difference between the ranks of the two variables.
- n is the number of pairs of observations.

Karl Pearson's Coefficient of Correlation

This measures the strength and direction of the linear relationship between two variables.
Measured on a scale of -1 to +1. +1 indicates a strong positive linear correlation, -1 indicates a strong negative linear correlation, 0 indicates no linear correlation.
Two formulas:
r = Σ(X – X)(Y – Y) / √Σ(X – X)² √Σ(Y – Y)²*
- This formula uses deviations from the actual means.
- X is the value of the first variable.
- Y is the value of the second variable.
- X̄ is the mean of the first variable.
- Ȳ is the mean of the second variable.
r = (N × Σdx × dy - Σdx × Σdy) / √(N × Σdx² - (Σdx)²) √(N × Σdy² - (Σdy)²)*
- This formula uses deviations from assumed means, simplifying calculations.
- dx is the deviation of X from assumed mean (Ax).
- dy is the deviation of Y from assumed mean (Ay).
- N is the number of pairs of observations.

Description

Explore the concepts of Rank Correlation and Karl Pearson's Coefficient of Correlation through this quiz. Learn how these measures assess the strength and direction of relationships between variables. Test your knowledge on the formulas and applications of these statistical methods.