How to Calculate Correlation Coefficients With an Equation

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Pearson's r is a correlation coefficient used to measure the strength of association between two variables that fall into the interval ratio category. Interval ratio variables are those which have a numerical value and can be placed in rank order. This coefficient is used in statistics. There are other correlation coefficient equations, such as correlation determination, but the Pearson's r formula is most commonly used.

    View the following given information as an example:

    Covariance = 22.40

    Standard deviation x = 9.636

    Standard deviation y = 3.606

    Plug the given information into the following equation:

    Pearson's Correlation Coefficient r = covariance/(standard deviation x)(standard deviation y) or use r = Sxy/(S2x)(S2y).

    The result with the example is:

    r = 22.40/(9.636)(3.606)

    Calculate r = 22.40/(9.636)(3.606)

    r = 22.40/34.747

    r = .6446

    r = .65 (round to two digits)


    • The answer can be positive or negative. The positive or negative shows the direction of the relationship. The closer the answer is to -1 or +1 the stronger the relationship is between the variables.


    • If you are given the variances instead, you will need to use the following formula: r2 = covariance squared/(variance x)(variance y). Square root the answer. You will need to add a negative sign if the original covariance in the equation was negative.


About the Author

Aunice Reed is a medical science writer living in Los Angeles, Calif. With over 10 years previous nursing experience, Reed has been writing for over six years and has attended University of Northern Iowa, University of California, Los Angeles and Los Angeles Harbor College.

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