8.2 Chart Selection & Graphical Perception

Start From the Relationship, Not the Chart Menu

The most common charting mistake is choosing a chart type first. Few's approach inverts it: identify the relationship you need the reader to see, and the chart type follows.

For PCPA, the last two matter most. Actual versus predicted is a deviation question. A quantile plot of loss cost by model decile is a ranking-and-deviation question. Residuals against fitted values is a correlation question.

How Accurately People Decode Visual Encodings

Not all visual channels are read equally well. Ranked from most to least accurately decoded:

1. Position along a common scale — points or bars on the same axis
2. Position along non-aligned scales — small multiples with separate panels
3. Length — bar height
4. Angle and slope — line direction
5. Area — bubble size
6. Colour saturation and hue — heat maps

Two practical consequences:

• Use position and length for the comparison that matters. If the reader's job is to compare loss ratios across ten territories, put them on a common axis as dots or bars. Do not encode them as bubble sizes or colour intensity.
• Use colour for grouping, not for magnitude. Colour is the weakest quantitative channel and the one most likely to fail for colour-blind readers or in a black-and-white printout of a rate filing.

This ranking is also why the pie chart is a poor default: it forces readers to compare angles and areas, the two channels they read least accurately. A sorted bar chart of the same data is read faster and more precisely.

Axis Rules That Actually Matter

Bar charts must start at zero. A bar encodes value by its length, so a truncated axis makes a 3% difference look like a 300% difference. This is not a stylistic preference — it makes the encoding lie.

Line charts may be truncated. A line encodes change through slope, not absolute value through length, so starting the axis near the data range is legitimate and often necessary to make a real pattern visible. Label the axis clearly so the reader is not misled about the baseline.

Use log scales for insurance loss data. Severity spans orders of magnitude. On a linear axis a single $4 million claim compresses every other point onto the baseline. The Monograph makes this point explicitly about actual-versus-predicted plots, which are usually drawn on a log scale.

Keep axes identical across compared panels. If a quantile plot for Model A and one for Model B use different y-ranges, the visual comparison is meaningless.

Small Multiples

When a pattern must be compared across many segments — twelve territories, five vehicle classes, four policy years — the instinct is one chart with twelve lines. The result is an unreadable tangle.

The better structure is small multiples: the same simple chart repeated once per subgroup, with identical axes, arranged in a grid. Each panel is trivially readable, and because the axes match, differences between panels are read as position differences, the most accurate visual channel. Small multiples are the native form of statistical graphics and one of the highest-value techniques available to an actuarial report.

Show Volume Alongside the Statistic

The standard actuarial one-way plot is a dual-encoding exhibit: exposure as bars on one axis, the observed and fitted statistic as lines on the other. The bars are not decoration; they are what lets a reader dismiss an apparent spike in a thin band.

When using dual axes, be careful: two different scales in one frame can imply a relationship that does not exist, and the reader has no way to know where the two axes were anchored. Use dual axes only for the exposure-plus-statistic convention, where the pairing is standard and expected, and label both axes explicitly.

Infovis Versus Statistical Graphics

Gelman and Unwin's assigned paper separates two traditions that have different goals:

Both are legitimate, and PCPA needs both: statistical graphics during exploratory work and diagnostics, and a more communicative style for the non-technical audience in the project report. The failure mode is confusing them — a decorative chart that hides a diagnostic problem, or an unlabelled six-panel residual grid shown to a business audience that needed one sentence.

[!WARNING] Every chart needs four things before it is finished: both axes labelled with units, a scale whose baseline is honest for the encoding used, a legend or direct labels that do not require colour discrimination alone, and a title that states the finding. An exhibit missing any of these is incomplete, and the project rubric explicitly asks candidates to justify their choice of presentation including proper labelling and clarity of purpose.