Within-subject confidence intervals for pairwise differences in scatter plots.

Abstract

Scatter plots are a standard tool to illustrate the covariation of bivariate data. For paired observations of the same variable, they can also be used to illustrate differences in the central tendency. For these differences, it would be useful to draw confidence intervals (CIs) that correctly align with statistical analyses. Here, we describe a method to compute and draw a diagonal CI for pairwise differences in scatter plots. This CI can be compared to the identity line that marks coordinates with identical values in both observations. Such CIs offer advantages for both authors and readers: for authors, the CI is simple to compute and to draw; for readers, the CI is less ambiguous and more informative than other types of illustrations, because the three CIs of the standalone effects of x, y and their pairwise differences can be plotted simultaneously along horizontal, vertical and diagonal axes, respectively. A survey testing the interpretation of standalone effects and pairwise differences in bar and scatter plots by scientists showed that such effects can be interpreted with high certainty and accuracy from scatter plots containing horizonal and vertical CIs for standalone effects and diagonal CIs for pairwise differences.