Correlation Coefficient Using Z-scores

Pearson's correlation coefficient can be calculated using different formulas, based on the sample data. One way of doing is taking the sample data \((X_i)\) and \((Y_i)\) and normalize the scores to the corresponding z-scores \((Z_i^X)\) and \((Z_i^Y)\) and by calculating Pearson's correlation coefficient with z scores the, using the following formula:

\[r =\frac{1}{n} \sum_{i=1}^n Z_i^X Z_i^Y \]

This calculator allows you to understand how to calculate correlation coefficient by hand, using z-scores and a tabulation to organize those scores. The usefulness of using z-scores for this calculation is that once the z-scores are already compute the calculation of the correlation coefficient follows very directly.

You can also compute the coefficient correlation using this calculator .