The Phistogram

Abstract

This article introduces a new kind of histogram-based representation for univariate random variables, named the phistogram because of its perceptual qualities. The technique relies on shifted groupings of data, creating a color-gradient zone that evidences the uncertainty from smoothing and highlights sampling issues. In this way, the phistogram offers a deep and visually appealing perspective on the finite sample peculiarities, being capable of depicting the underlying distribution as well, thus, becoming an useful complement to histograms and other statistical summaries. Although not limited to it, the present construction is derived from the equal-area histogram, a variant that differs conceptually from the traditional one. As such a distinction is not greatly emphasized in the literature, the graphical fundamentals are described in detail, and an alternative terminology is proposed to separate some concepts. Additionally, a compact notation is adopted to integrate the representation’s metadata into the graphic itself.

KEYWORDS:

• Color-gradient technique
• Data visualization tool
• Equal-area histogram
• Perception
• Smoothing uncertainty
• Statistical graphic

Supplementary Materials

Supplementary document:The file phistogram_supplement.pdf contains additional application examples (including real cases), as well as transcripts of code scripts instructing the implementation of the technique in R, Scilab, and Python. It also includes the manuscript’s figures with the theoretical distribution curve superimposed on the graphics. (PDF file).

Datasets:The file phistogram_datasets.zip provides the real samples used in the examples of the supplementary document. (ZIP file).

Color Palette:The cividis_light.pal file is the lightened and trimmed version of the cividis palette for GNUplot. (PAL file).

Acknowledgments

I am deeply grateful to my Work Director, Dr. Andrea Carolina Monaldi, and to the Director of my Institute, Dr. Alejandro Luis Hernández, for allowing me to dedicate the necessary time to the development of the phistogram and all the work related to this article, as well as for their comments and support. I would like to thank all those whose encouraging comments about the phistogram inspired me to write about it, and especially the one whose kindness and almost-infinite patience motivated me in continuing this task. I cannot fail to thank Dr. Joshua Tebbs and the anonymous reviewers, who have given me the opportunity to learn from them, wisely guiding me with their questions and concerns to achieve this improved revision. I also want to thank Dr. Alejandra Méndez and Dr. Juan Pablo Aparicio for all their suggestions and corrections, and Dr. Javier Gutierrez for his help with Python, as well as to Ricardo Echazú and Dr. Andrés Diaz for providing the data used in the code example in the supplementary document.

Disclosure Statement

The author report there are no competing interests to declare.

Additional information

Funding

The author is financed by the Institute for Research in Non-Conventional Energy (INENCO), dependent on the National Council for Scientific and Technical Research of Argentina (CONICET), and this work was partially supported by the National Agency for Scientific and Technological Promotion of Argentina (ANPCyT) under grant PICT2017 2397.