Skip to article frontmatterSkip to article content
Site not loading correctly?

This may be due to an incorrect BASE_URL configuration. See the MyST Documentation for reference.

Data Visualization

(Some) Principles of data visualization

The importance of visual information cannot be understated, and statisticians (and similar) aim to build figure that communicate easily a concept, thought, novel finding etc. Visuals can be simple and compelling, complex but worth the fight to understand. However, visuals can be misleading, damaging, and meant to persuade despite the evidence to the contrary.

There are too many data-visual (data-viz) principles to discuss. Scientists have written books attmepting to cover all of the aspects of the scientific communication of visual information.

Instead, we will explore four famous individuals and the most prominant ideas about statistical and visual communication that they put forth. We will also spend time looking at visuals that were (whether intentional or not) misleading.

Cleveland & McGill: Build plots that humans are best set up to understand (why the pie chart is stupid)

https://www.youtube.com/watch?v=i9XU6wk_mWY (minute 9)

Bertin: One visual aspect for one statistical aspect. No doubling up.

https://callingbullshit.org/tools/tools_misleading_axes.html

Tukey: Plot for exploration

The first human we will study is John Tukey. XX XX XX

An important principle Tukey emphasized was using visuals to explore your dataset. Tukey wrote that summary statistics (like our measures of central tendancy, measures of dispersion, and any other summary statisticsw) are meant to describe the typical observation in a target population. Visuals, on the other hand, can be useful to discover the atypical, outliers, unexpected observations, and relationships between two variables that may not have been expected.

A good example of the use of visuals to explore one’s dataset is Anscombe’s quartet. At the time (in the 70s) there was an impressions among statistician’s that numerical algorithms and their results were exact. Figures, graphs, visuals were a lesser type of communication that gave the reader a rough estimate. In fact, some statisticians considered looking at your data as sort of “cheating”. The original article is here: http://www.lithoguru.com/scientist/statistics/Anscombe_Graphs in Statistical Analysis_1973.pdf

Anscombe intended to show how important graphs can be for statistical analysis and study. He illustrated this importance by showing his audience how a graph can be used to understand the (perhaps trickier than you would expedct) relationship between two variables xx and yy.

Below is the original figure. In the upper left was presented a fairly typical linear relationship between xx and yy. In the upper right is a nonlinear relationship that, if you had not plotted your data would return the same calculated slope and intercept for a best-fit line. The lower left figure also returns the same best fit line. However, the data visualized has a massive outlier. Finally, the bottom right (which also returns the same best fit line) only has two possible xx. If you had plotted just tghe best fit line you would never know. The visual immediatly reveals whether the numerical best fit line and your assumptins about the relationship match.

This is what Tukey was talking about. Visuals are a useful mechanism for understanding how variables in your data relate. How information in your data may be typical and, even more important, atypical.

In research papers visuals feel like the end product. But, to get to those polished final results likely took many many many visuals to represent what was happening in the data itself. Plot away.

Part I — Statistical Machinery
Experiments, Outcomes, and Datapoints
Part I — Statistical Machinery
Exploratory Data Analysis