Choosing What the Reader Will Judge

One row per category, with the value printed to the precision the measurement supports, optionally with a share column and the total stated.

This form is exact where every graphical form is approximate. A reader takes values off it without any perceptual judgement, so the accuracy ordering that governs plots does not apply: $102$ and $108$ are read as $102$ and $108$, and no baseline, aspect ratio or encoding stands between the number and the reader.

It is therefore the reference against which a display is checked. Computing the ratio the picture implies and comparing it against the ratio in the table is what exposes a truncated axis: bars drawn from a baseline of $100$ show heights in a ratio of $4.0000$ where the table gives $108/102=1.0588$.

What it cannot do is show shape. Pattern, trend, clustering and outliers are recoverable from a table only by reading every row and holding the values in mind, which fails past a dozen rows and fails entirely for the structure a scatter plot reveals at a glance. Four datasets agreeing on mean $x=9.000$, mean $y=7.501$, slope $\approx 0.500$ and $r\approx 0.816$ are one line in a summary table and four visibly different pictures.

The pairing with the dot plot is the useful one, and it runs both ways. Reading a ranking and the approximate gaps off the plot, and recovering exact values from the table, are different performances, and a report that needs both should carry both rather than choosing.

Which of eight regions had the highest revenue? A ranking question, answered by position along a common scale. A dot plot with regions sorted by value answers it in one glance; a pie chart asks the reader to compare eight angles and answers it poorly. Sorting is part of the encoding here, not decoration: an alphabetical ordering forces a search where a sorted one gives the answer by position.

Did the eight regions grow at the same rate? A ratio question. Revenue over time on a logarithmic axis makes equal growth rates parallel lines, so the comparison becomes "are these parallel" rather than "is this gap widening". The same series on a linear axis separates the large regions from the small ones and says almost nothing about rates.

How is response time distributed? Neither a mean nor a bar. The question is about shape, so it needs a display that shows shape: a histogram, or the points themselves when there are few. Reporting a mean of $240$ ms conceals whether that is a tight cluster or a bimodal split between a fast path and a slow one, which is usually the thing worth knowing.

Do these two variables move together? A scatter plot, which is a position judgement on two axes at once. A correlation coefficient answers a narrower question, how well a straight line fits, and four datasets sharing $r=0.816$ can be linear, curved, linear-with-an-outlier, or determined by a single point. The coefficient is not wrong; it is not sufficient.

What proportion of total cost is each category? The case where a part-to-whole encoding is genuinely apt, and it still competes with a sorted bar chart from zero. A pie is readable when there are two or three slices whose sizes differ by enough that the angle comparison is not what limits the reading; with seven similar slices the angle judgement fails and the labels do the work the picture was supposed to do.

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The pattern across the five. The question names a comparison, the comparison names a perceptual task, and the task names the encoding. Working the other way, choosing a chart and then deciding what it shows, produces displays that are accurate and unable to answer anything in particular.

A pie chart against a sorted dot plot, on the same shares.

The pie carries one thing the dot plot does not: the visual fact that the parts compose a whole. Where that is the point and the slices are few and unequal, it earns its place. Where the reader must rank or compare, it assigns a task the eye performs badly.

Linear against logarithmic, on the same growth series.

Both are faithful renderings of the same twelve numbers. The first is the right choice when the quantity added each period is the subject. A budget, a headcount. The second is right when the rate is the subject.

Zero baseline against truncated, on values of 102 and 108.

The truncated version is not a stronger presentation of a small difference; it is a different comparison. If $5.9\mathrm{\%}$ matters and is hard to see, the answer is a display where small differences are legible without being magnified. A dot plot on a restricted axis, where the reader reads values rather than comparing lengths.

Aspect ratios 0.25 and 1.0, on the same two slopes.

Segments rising $0.2$ and $1.0$ subtend $2.9°$ and $14.0°$ in the flat frame, a separation of $11.2°$; at a ratio of 1 they subtend $11.3°$ and $45.0°$, a separation of $33.7°$. The rates are identical in both. Banking is the deliberate version of a choice that is otherwise made by whatever canvas size the tool defaulted to.

A summary statistic against the points.

Four datasets agreeing on means of $9.000$ and $7.501$, slopes near $0.500$ and correlations near $0.816$ look nothing alike. The table treats them as one finding; the scatter plots separate them at a glance. The general lesson is not "always plot" but that every aggregation, including a plot that aggregates, discards the structure it summarises, and the author chooses which structure to discard.

That designing a display means picking a chart type that suits the data's shape, bars for categories, lines for time, pies for parts of a whole, after which the details are formatting. The chart type determines which elementary perceptual task the reader performs, and those tasks differ in measured accuracy: position along a common scale is judged far more accurately than angle or area. A pie chart asks for an angle judgement, so a difference of a few per cent between wedges is frequently misread, while the same values as a dot plot are read almost exactly. The question comes first, the perceptual task it requires comes second, and the chart type is what falls out of those two rather than what is chosen from a menu.

That the axis range, the baseline and the aspect ratio are presentation choices that leave the content of a display unchanged. Each one changes what the reader can conclude. Moving a bar chart's baseline from zero to 100 turns values of 102 and 108, whose true ratio is 1.0588, into bars whose heights stand in a ratio of 4.0000. The numbers are untouched and the comparison the reader performs is not. Switching a growth series from a linear to a logarithmic axis turns a curve that appears to accelerate into a straight line, because the increments rise by a factor of 2.1049 while the proportional change is constant at every step. Changing the aspect ratio alters the angles line segments subtend and therefore the slopes the reader judges. These are claims about which comparison matters, and they belong in the same category as the choice of statistic.