Plotting the Differences Between Data and Expectation

TL;DR

This paper introduces a method to enhance histogram plots by adding an inset that displays the statistical significance of deviations between data and expectation, aiding in better visual interpretation of potential significant differences.

Contribution

It proposes a novel visualization technique with an inset showing statistical significance, improving the detection of meaningful deviations in histograms.

Findings

The inset helps identify statistically significant deviations that are otherwise invisible.

The routines are based on formulas suitable for proper statistical inference.

Implementation available at https://github.com/dcasadei/psde.

Abstract

This article proposes a way to improve the presentation of histograms where data are compared to expectation. Sometimes, it is difficult to judge by eye whether the difference between the bin content and the theoretical expectation (provided by either a fitting function or another histogram) is just due to statistical fluctuations. More importantly, there could be statistically significant deviations which are completely invisible in the plot. We propose to add a small inset at the bottom of the plot, in which the statistical significance of the deviation observed in each bin is shown. Even though the numerical routines which we developed have only illustration purposes, it comes out that they are based on formulae which could be used to perform statistical inference in a proper way. An implementation of our computation is available at https://github.com/dcasadei/psde .