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Correlation, Pearson
The Pearson correlation coefficient (also known as Pearson product-moment correlation coefficient) r is a measure to determine the relationship (instead of difference) between two quantitative variables (interval/ratio) and the degree to which the two variables coincide with one another—that is, the extent to which two variables are linearly related: changes in one variable correspond to changes in another variable. In fact, a variety of different correlation coefficients (such as phi correlation coefficient, point-biserial correlation, Spearman’s rho, partial correlation, and part correlation) have been developed over the years for measuring relationships between sets of data, and the Pearson correlation coefficient (also referred to Pearson’s r) is the most common measure of correlation and has been widely used in the sciences as a measure of the degree of linear dependence between two paired data. This entry provides an overview of the Pearson correlation coefficient, specifically the types and assumptions of a correlation. It also explains correlation computation and interpretation. Finally, the entry discusses some potential problems that may arise with the use of a correlation.
What Is a Correlation?
Pearson’s correlation coefficient was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s. Researchers have widely used it in many applications such as time-delay estimation, pattern recognition, and data analysis, to name a few. Pearson correlation is also extensively used in real-life situations. For instance, it has been used to measure the linear correlation between national income and household savings/deposits, the height and weight of humans, high school grades and college entrance examination scores.
Correlation Objectives
The main purpose of a correlation is to determine the relationship between two quantitative variables (data that can be anything from a range of salaries, years of education, scores on a test, or height and weight): whether as the score on one variable changes (goes up or down), the score on a second variable also changes (goes up or down). To conduct a Pearson product-moment correlation, a researcher needs to obtain two scores from each numerical variable. If the correlation coefficient r is significant, there exists some type of relationship between the two quantitative variables. However, if the correlation coefficient r is not significant, then the researchers cannot draw any conclusions about the nature of the relationship between the two variables.
Types of Relationships
In statistics, there are four theoretical types of relationships that can occur from testing correlation. The first type is positive/direct—this type of relationship has a positive slope indicating that as one variable increases the other variable also increases, or as one variable decreases the other variable also decreases. An example of a positive correlation can be as an instructor’s use of humor increases, so does his or her students’ perceived popularity toward him or her. The second type is negative/inverse (identified by negative signs before correlation coefficients)—values of this relationship will have a negative slope indicating that as one variable increases the other will decrease, or as one variable decreases the other variable will increase. An example of a negative correlation can be as a person’s education goes up, his or her encountered discrimination goes down.
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