Paired comparisons and regression to the mean - with emphasis on graphical illustrations

To review methods for graphical illustration of paired comparisons in the pretest-posttest design and present a new and simple plot, based on the waterfall plot combined with evaluation of vertical symmetry. The plot includes changes in the raw data, median changes with confidence zones and allows easy visualization of correction for regression to the mean to guide subsequent analysis of covariance or mixed effects modeling and for final presentation. The methods are demonstrated using a publicly available clinical dataset and simulations of illustrative example data performed in R. Compared to previous methods such as 1) the simple scatter plot of pretest vs. change, 2) the tilted line-segment plot, 3) Galton's squeeze plot, and 4) a one-dimensional scatter plot, the waterfall plots have several advantages: no overlap of data, ease of interpretation, independence of sample size, and the ability to clearly visualize regression to the mean and a possible intervention effect. The combination of vertical symmetry, waterfall plots, box plot summaries, and confidence zones allows for quick decoding and comparison of pre- and post-test data. This approach effectively visualizes and helps evaluate the occurrence of regression to the mean and/or a possible intervention effect, regardless of sample size.