Explaining Correlations by Plotting Orthogonal Contrasts

Abstract

This article describes a new plot that aids understanding the relationship between two response variables in a designed experiment. In addition to plotting the observed values directly, we make a scatterplot of orthogonal contrasts from the general linear model. This plot contains the same correlation information as the ordinary scatterplot. Therefore, one can interpret how the effects of the various design variables contribute to the correlation coefficient. This idea is also useful in more general cases. Any graphic presentation of the original observations can be accompanied by a corresponding plot of orthogonal contrasts that often will clarify the interpretation.

KEY WORDS :

• Design of experiments
• Fractional factorial design
• Scatterplot
• General linear model
• Partial least squares
• Principal component analysis