8.3 How Charts Mislead

Why This Is Examinable

PCPA task C-1 requires candidates to create and interpret statistical and graphical representations. Interpretation includes recognising when a chart is misleading — whether the chart came from a vendor, a competitor's filing, a colleague, or your own first draft. Cairo's How Charts Lie is the assigned reading, and its structure is a taxonomy of failures.

Most misleading charts are not fraudulent. They are produced by analysts using a default setting without thinking about what the default implies.

Failure 1: The Scale

Truncated bar axes. Covered in the previous section and worth repeating because it is the single most common distortion. A bar means length from a baseline; move the baseline and the meaning changes.

Aspect ratio. The same time series drawn tall and narrow shows a dramatic climb; drawn short and wide it looks flat. No number changes. When a trend's steepness is the point, the aspect ratio must be chosen deliberately and the axis range stated.

Dual axes. Two series on two scales in one frame can be made to cross, converge or diverge at will by choosing where each axis starts. A dual-axis chart implies a relationship that the analyst, not the data, selected. Use them only where the convention is established and expected — such as exposure bars behind a loss-cost line — and label both axes.

Inconsistent scales across panels. Comparing two charts whose y-axes differ is an invitation to a false conclusion. Identical axes are mandatory for small multiples.

Failure 2: The Denominator

Insurance is a business of ratios, and every ratio has a denominator that can be chosen badly.

• Counts instead of rates. "Territory 7 had the most claims" usually means Territory 7 has the most exposure. The interesting statistic is claims per car-year.
• Unweighted averages of rates. Averaging loss ratios across policies gives each policy equal weight regardless of premium volume. The portfolio loss ratio is sum(losses) / sum(premium), and the two answers can differ substantially.
• Changing denominators over time. A frequency series computed per policy in early years and per vehicle in later years has a trend that is entirely definitional.
• Percentages of small bases. "Claims up 200%" reads dramatically until the reader learns the count went from 1 to 3.

Failure 3: The Range

Starting a time series at a convenient year is the oldest trick in the collection. A loss-ratio series beginning in an unusually good year shows deterioration; the same data beginning three years earlier shows a cycle.

Related distortions:

• Immature periods. The most recent accident year's incurred losses are the least developed. Plotting them beside mature years shows an apparent improvement that is pure development lag. Either develop the years to a common maturity or plot them at a constant evaluation age.
• Truncated categories. A "top 10 territories" chart that omits the remaining 40 can imply the top 10 are the whole story.
• Excluded outliers shown without a note. Removing shock losses may be the right modelling decision, but a chart that does not disclose it overstates stability.

Failure 4: Aggregation That Reverses the Answer

The most serious version, because the chart is arithmetically correct and still wrong.

Simpson's paradox occurs when a relationship visible within every subgroup disappears or reverses when the subgroups are pooled. In insurance it is generally caused by a mix shift.

A worked example. An insurer's overall loss ratio rises from 62.0% to 67.8% between two years, and the portfolio chart shows deterioration. Split by line:

Both segments improved. The portfolio deteriorated because the book shifted toward the higher-loss-ratio segment. A chart showing only the total leads a reader to exactly the wrong action — tightening underwriting in segments that are in fact improving.

The defence is to show the segment detail, or at minimum to decompose the change into a rate effect and a mix effect.

Failure 5: Encoding a Pattern the Data Does Not Have

• Connecting unordered categories with a line. A line implies continuity between adjacent points. Territories, vehicle classes and construction types have no natural order, so a line across them invents a trend.
• Fitting a smooth curve through thin data. A trend line through eight points with wide confidence intervals asserts more than the data supports. Show the intervals, or show the points alone.
• 3-D effects and perspective. Depth distorts apparent length and area, so nearer bars read as larger. There is no case where a third dimension helps a two-variable comparison.
• Rainbow colour scales on a continuous measure. Non-monotonic colour ramps create apparent boundaries where the data changes smoothly.

A Review Checklist

Before any exhibit goes into a report, read it as a sceptic:

1. Axes — Are both labelled with units? Does the bar axis start at zero? Are compared panels on identical scales?
2. Denominator — Is this a rate or a count? Weighted by what? Is the weighting stated?
3. Range — Why does the series start there? Are all periods at comparable maturity?
4. Aggregation — Could a mix shift be driving this? Does the pattern hold within segments?
5. Volume — Can the reader see which points are credible?
6. What is missing — Which categories, periods or records were excluded, and is the exclusion disclosed?

[!WARNING] Apply this checklist to your own exhibits before you apply it to anyone else's. The project rubric asks the candidate to justify their choice of data and visual presentation, including clarity of purpose and appropriateness for the data, model, audience and business question. An exhibit that fails the checklist fails that criterion whether or not the underlying model is sound.