Data Visualization

Study guides: Exam PA, Exam PCPA

Data Visualization is showing quantitative information as a graph or a table, so that a reader can see the pattern the numbers hold. Choosing the display is a modelling decision like any other: the right one depends on the message, the data and the audience. The same chart can inform one reader and mislead another.

\text{Data-ink ratio} = \frac{\text{ink used to display the data}}{\text{total ink used in the graphic}}

• The data-ink ratio (Tufte's term) is the case for decluttering. Gridlines, borders, 3-D effects and redundant labels cost the reader attention and carry no data, so push the ratio up by removing what does not inform
• Exploratory vs. explanatory (Knaflic): exploration is looking at a hundred views to find the two that matter. Explanation shows those two to someone else. A model report is explanatory: the EDA plots that led somewhere belong in an appendix, and most belong nowhere
• Table or graph? (Few): use a table when the reader needs precise individual values, such as a model's coefficients. Use a graph when the message is in the shape of the data — a trend, a ranking, a comparison
• How charts mislead (Cairo): a bar chart whose axis does not start at zero, two series on dual axes, dubious or insufficient data, hidden uncertainty, and patterns that suggest a relationship the data do not support
• Different goals (Gelman and Unwin): a graphic built to grab attention and one built to support statistical comparison make different trade-offs, and it is better to use two graphs than to cram both jobs into one
• For a predictive model, the exhibits that justify it to a business audience sort and aggregate the data to show segmentation: a lift (quantile) plot, a double lift chart, a Lorenz curve with its Gini index. Policy-level residual plots and QQ plots are working diagnostics, not the evidence

A Truncated Axis A bar chart shows two territory relativities, 0.95 and 1.05, with the vertical axis starting at 0.90. How much bigger does the second bar look than the first, and how much bigger is it actually?

Answer

\begin{align*}
\text{Apparent ratio} &= \frac{1.05 - 0.90}{0.95 - 0.90} \\
&= \frac{0.15}{0.05} = 3.0 \\
\text{Actual ratio} &= \frac{1.05}{0.95} \\
&= 1.105
\end{align*}

The bar is drawn three times as tall, but the relativity is only about 10.5\% higher. Bars encode value by length, so a bar chart's axis must start at zero. For small differences, plot the points instead, or show the differences from 1.00 directly.

Choosing Exhibits for a Non-Technical Audience A candidate's model report to underwriting management includes a histogram of fitted values, a QQ plot of deviance residuals, and a table of 40 coefficients with standard errors. What should replace them?

Answer None of the three shows the one thing management needs: whether the model separates good risks from bad on data it has not seen. Replace them with:

• a quantile (lift) plot on the hold-out data, showing actual loss cost rising from the best to the worst bucket;
• a double lift chart against the current rating plan, showing where the new model is more accurate;
• a short table of the few rating factors that drive the result, with their relativities in plain terms ("+25\% for …").

State which data set each exhibit was built on. The residual diagnostics belong in a technical appendix.