This module discusses the three main types of correlational relationships and correlation coefficients.

Learning Objectives

• Describe the three basic types of correlations
• Identify the type of correlation based on the direction of the relationship
• Define correlation coefficient and describe how it is used

Begin this module by viewing the following video, Measures of Relationships, which describes the three main types of correlational relationships and discusses how the strength of the relationship is determined. This video is an excellent introduction to the topics in this module.

Following is a discussion of the three main types of correlational relationships, including examples of each.  These correlations indicate the direction of the relationship.

• A positive correlation occurs whenever the change in the variables is occurring in the same direction. If an increase in variable A occurs and results in an increase in variable B, there is a positive correlation. For example, an increase in the number of hours that student’s study could result in an increase in test scores or lower ACT scores may indicate poorer performance in college. These are both examples of positive correlations because the variables are moving in the same direction. 
• A negative (inverse) correlation occurs when one variable increases and the other variable decreases. An example would be the relationship between increasing exercise and reducing the number of doctor visits for colds and common illnesses. 
• Finally, there may be zero correlation when there is no identifiable pattern for determining a relationship. For example, there may be no relationship found between the number of cups of coffee drank per day and intelligence.

The data from a correlational study is often represented graphically using a scatterplot or scatter diagram. Scatterplots are used to summarize the relationship between two variables (X and Y) by plotting the discrete data points and then looking for overall trends. The following graph represents the three main types of correlational relationships:

The strength of the relationship is measure of how consistently the values of each variable change in relation to each other. Graphically, the stronger the relationship, the closer the data points will fall along a line as seen in the example below:

A Correlation Coefficient (r) is used to statistically determine the strength of the relationship. The correlation coefficient is calculated in such a way that the numerical values range from -1.00 to +1.00.  In general, r>0 indicates a positive relationship while r<0 indicates a negative relationship. When r=0, there is no relationship. A perfect relationship occurs when all data points fall along the line precisely and the r value is either -1.00 or +1.00. Most relationships are not perfect; however, and therefore the r values fall along a continuum. The chart below demonstrates the strength of a relationship based on r values. The r values in the scatterplots above serve as examples of how the r value corresponds to a set of data points.

There are a variety of correlation coefficient calculation models. The most common one is the Pearson Correlation Coefficient. The calculations can be performed by most statistical software, but there are also free, simple online calculators that allow researchers to enter data points (x,y) and it will calculate the r value. A link for the Pearson calculator is included in the Resource Links on this page. The next module in this series will look at more advanced statistical analyses of correlational data.