The Pearson product-moment correlation coefficient (or just Pearson correlation coefficient) is used in statistics to evaluate the linear relationship between two continuous and quantitative variables. Pearson’s correlation coefficient (r) reflects the degree, or strength, of that relationship.
You will first plug in your variables for X and Y into the table below. Remember, these two variables can be measured in two different units, but both must be measured on an interval or ratio scale. Your data will then be plotted and the Pearson correlation coefficient, a number between -1 and +1 representing the strength of the correlation, will be determined.
- Value of 0: Indicates no correlation or association between the two variables.
- Positive Correlation: Any value greater than zero is considered a positive correlation, meaning as X increases, Y increases as well. A value of +1 is a perfect, positive correlation between X and Y.
- Negative Correlation: Values less than zero indicates a negative correlation, meaning as X increases, Y tends to decrease. A value of -1 is a perfect, negative correlation between X and Y and the changes in Y can be attributable to X.
Each set of variables are plotted on the chart and the Pearson correlation looks at how these points relate to a line of best fit. The coefficient indicates variation around the line of best fit; the stronger the association of the two variables the closer the coefficient will be to +1 or -1. Achieving a value of exactly +1 or -1 will plot your data points exactly on the line of best fit.
The Pearson correlation coefficient is an important element of Six Sigma. It allows you to analyze cause and effects between variables and conduct correlation tests. Correlation tests are used in the first three phases of the DMAIC cycle and help to identify what variable changes in a process or product can be made for improvement.