Correlation Coefficient Calculator Using Z-score

Instructions: This calculator will compute Pearson's correlation coefficient for two give variables X and Y using the formula that involves z-scores. Please type your X and Y sample data, either in comma or space separated format (For example: "2, 3, 4, 5", or "3 4 5 6 7"), and the solver will show a detailed calculation:

X data (comma separated)
Y data (comma separated)
Name of X variable (optional)
Name of Y variable (optional)

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 .

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