Correlation measures the strength of association between two variables. The correlation coefficient, r, ranges in value from -1 to +1, with 1 signifying perfect correlation. In real life, perfect correlations are rare. Simple experiments can test for correlation. For instance, you could take measurements of women's feet to see if average shoe size goes up one size for every inch of foot measurement, which would indicate +1 positive correlation. If cases of the flu drop 10 percent for every 10 percent of the population that is increasingly vaccinated over the course of a month, that is a -1 negative correlation.
Determine Equivalent Measures
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 Mean of Variables
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 that were observed.
Find Standard Deviation
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 Standardized Values
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.
Check Your Figures
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 Correlation Coefficient
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. Statistical software like IBM SPSS and spreadsheet programs such as Excel can calculate correlation coefficients, but doing it by hand aids comprehension.
About the Author
Shane Hall is a writer and research analyst with more than 20 years of experience. His work has appeared in "Brookings Papers on Education Policy," "Population and Development" and various Texas newspapers. Hall has a Doctor of Philosophy in political economy and is a former college instructor of economics and political science.