Correlation measures the strength of association between two variables. Examples include the correlation between education and income, or between crime rates and house prices. The correlation coefficient, r, ranges in value from -1 to +1, with 1 signifying perfect correlation (positive or negative). An important step in measuring correlation is to standardize the values of the two variables. This eliminates differences between the two variables, such as differences of scale. Another example would be two variables measured in prices, in which the values of one variable are expressed in dollars and other in euros.

Calculate the means of the two variables of interest. The mean is the arithmetic average, obtained by adding the values of each case in a set of observations and dividing the sum by the total number of cases.

Obtain the standard deviations of the two variables. The standard deviation is a measure of dispersion in a set of scores. Calculate the sum of squared differences divided by the number of cases in each variable to obtain the variance. The square root of the variance is the standard deviation.

Calculate the standardized values by subtracting the mean from the scores of the individual cases and dividing the resulting values by the standard deviation. The standardized values will tell you, in units of standard deviation, how far the individual values are above or below the mean.

Ensure that you have calculated the standardized values correctly by calculating the means and standard deviations for them. The mean of a standardized variable should be zero, and the standard deviation should be 1.

Calculate the correlation coefficient, r, for your standardized variables. Multiply the individual standardized values of variables x and y to obtain the products. Then calculate the mean of the products of the standardized values and interpret the results. The higher the value of r, the stronger the correlation is between the two variables. A correlation coefficient of zero indicates no correlation.

#### Tip

- Statistical software and spreadsheet programs such as Excel can calculate correlation coefficients.

#### References

- Dictionary of Statistics and Methodology, W. Paul Vogt, 1993
- David Salomon: Correlation in Statistics and Data Compression

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