Pearson correlation coefficient

Pearson's correlation is a mathematical formula for calculating the correlation coefficients between two datasets. Most computer programs have a command to calculate this such as CORREL(dataset x: dataset y). The coefficient can be calculated by

• Step 1: Find the mean of x, and the mean of y
• Step 2: Subtract the mean of x from every x value (call them "a"), and subtract the mean of y from every y value (call them "b")
• Step 3: Calculate: ab, a² and b² for every value
• Step 4: Sum up ab, sum up a² and sum up b²
• Step 5: Divide the sum of ab by the square root of [(sum of a²) × (sum of b²)]

Examples of scatter diagrams with different values of Pearson correlation coefficient (ρ).

Karl Pearson came up with the formula in the 1880s when he contributed to research in statistics.