How to Calculate Effect Size Correlation

Highly correlated variables produce steep graphs.

Variables' effect size correlation describe how closely they are related. For example, if each increase in one variable's value leads to an increase in the other variable, the variables have a correlation of 1. If each increase in one variable leads to two increases in the other variable's value, they have a correlation of 2. More weakly correlated variables might have decimal correlations. This correlation equals the gradient of the line that joins the variables' points on a graph.

Instructions

1. Plot the variables' data on a scatter graph, assigning each of the variables to one of the graph's axes.

2. Draw a line around all points on the graph except for those that stand far from the other points. If the points are correlated, this shape will appear oblong.

3. Bisect this shape, producing two oblong shapes that equal one another in size.

4. Identify the coordinates of two points on the line that bisect the shape. For example, two points may have coordinates of (8, 11) and (18, 12).

5. Divide the difference between these points' y-coordinates by the difference between their x-coordinates: (11 - 12) ÷ (8 - 18) = 0.1. This is the variables' effect size correlation.

References

• Carleton College; How Do I Construct a Straight Line Through Data Points?; 2009
• It's the Effect Size, Stupid; What effect size is and why it is important

Resources

• University of North Carolina; Linear Models and Scatter Plots; Dr. Jeff Brown
• West Texas A&M University; Graphing Linear Equations; Kim Seward; 2003
• Florida Institute of Technology; Point Slope Form of Line Equation; Priya Asokarathinam
• Rochester Institute of Technology: Graphing Linear Equations