Correlation

A correlation is an index of the strength of the relationship between two variables.

Correlation coefficients (typically denoted by the statistic "r") describe the strength of the relationship between two variables. Correlations range from -1.0 to +1.0 in value.

A correlation coefficient of 1.0 indicates a perfect positive relationship in which high values of one variable are related perfectly to high values in the other variable, and conversely, low values on one variable are perfectly related to low values on the other variable.

A correlation coefficient of 0.0 indicates no relationship between the two variables. That is, one cannot use the scores on one variable to tell anything about the scores on the second variable.

A correlation coefficient of -1.0 indicates a perfect negative relationship in which high values of one variable are related perfectly to low values in the other variables, and conversely, low values in one variable are perfectly related to high values on the other variable.

If a correlation coefficient is squared (multiplied by itself), the resulting number is the "percentage of the variation" in the two variables that is in common. Thus, a correlation of .7 (or -.7) indicates that about 50% (or .7 times .7 = .49; -.7 times -.7 = .49) of the variation in one variable can be predicted from the other.

Typically we use three kinds of correlations here.

Pearson Product Moment Correlations (or "r") assume the two variables being considered are measured on continuously- measured scales (like the numbers 1, 2, 3, 4, 5, 6, 7 or height or weight).

Spearman Rank Order Correlations (or "rho")  and Kendall's Tau-b (or "tau") Correlations are used when the variables are measured as ranks (from highest-to-lowest or lowest-to-highest).

In practice, the amount of correlation estimated with any of these three types of coefficients is fairly similar. The Pearson Product Moment Correlation is the most commonly-used method.

When one looks at correlation between more than one pair of variables in a single analysis, the resulting coefficients are usually arranged in a "Correlation Matrix." The Correlation Matrix shows all possible pairwise  correlations, has 1.0s on the diagonal, and is symmetric (the values shown above the diagonal also appear below the diagonal).