Pearson's R measures the strength or degree of association between two interval ratio variables ranging from .0 to 1 either positive or negative. It is the square root of correlation determination. The closer the measure is to 1 or -1, the stronger the relationship. Thus, 80 or 90 in either direction indicates a strong relationship exists. Zero means there is no correlation. Pearson's R is the most commonly used correlation measure. It uses the following formula:
R = covariance/(standard deviation x)(standard deviation y).
Correlation determination measures the proportional reduction error resulting from linear regression. According to the text "Social Statistics for a Diverse Society," correlation determination also shows "the proportion of the total variation in the dependent variable y, which is explained by the independent variable x." If r = .60, then 60 percent of the variation of y is explained by x. It is also referred to as the coefficient of determination. The formula used to calculate correlation determination is as follows:
R squared = covariance squared/(variance x)(variance y).
A negative sign is added to the answer if the original covariance was also negative.
The scatter diagram (also called a scatter plot) shows the relationship of two interval ratio variables on a coordinate grid. Only points are shown. It is the first step of regression analysis. It is a quick way to see if the variables are associated and the strength of the association. A scatter diagram also shows the direction of the relationship. All points clustered together in a straight line suggests there is a strong relationship. Even if a few points are outside of the line, a relationship can still exist. If the points are not clustered and are scattered, it is random and there is no relationship.
Associations between variables can be positive or negative. This only refers to the direction of the relationship. A positive correlation means that both variables are increasing, while a negative correlation means that as one variable increases the other decreases. Perfect positives in Pearson's R will equal +1 and a perfect negative will equal -1. In a scatter diagram, if the points form a line from bottom left to the upper right on the grid, the correlation is positive. If it goes from upper left to bottom right, it is negative.