When Is Too Much Overlap Too Much? (Two Distributions)

This interactive GeoGebra example visualizes the overlap between two normal (or binomial) distributions and explores how to quantify when the overlap becomes too large to distinguish them. It demonstrates the concept of distribution overlap, mean absolute deviation (MAD), and statistical comparison using dot plots and box plots. The construction uses commands such as Sequence, DotPlot, mad, BoxPlot, LaTeX, Remove, and Length, with objects including sliders for parameters (p, left, right), buttons for interaction, and text displays for dynamic results. It also incorporates geometric elements like equilateral triangles and reflections to aid visualization. Suitable for high school or introductory college statistics courses, this example helps students understand the intuition behind hypothesis testing, effect size, and the role of variability in comparing distributions.