Comparison and composition

Comparing discrete quantities and showing how parts make up a whole are the two most common charting tasks. Which format works is not a matter of taste — there is a body of perception research behind it, and it points fairly consistently in one direction.

The accuracy ranking of visual encodings

Work on graphical perception, beginning with Cleveland and McGill in the 1980s, established a fairly stable ordering of how accurately people extract quantity from different visual channels. Position along a common scale is best. Length against a shared baseline is next. Then angle and slope, then area, then volume, with colour intensity near the bottom.

A bar chart uses the top two channels at once: every bar has a length from zero and all bars sit on one axis. This is why it is rarely the wrong answer and why more elaborate alternatives should have to justify themselves.

The corollaries are unglamorous and worth stating. Three-dimensional bars add a perspective distortion that makes front bars look larger than they are. Radial layouts convert length into angle, moving down the ranking. Pictorial bars, where an icon is scaled to represent quantity, usually scale both dimensions and therefore encode value as area while looking like length — which overstates differences by roughly the square.

None of this means charts must be plain. It means the decoration should not be load-bearing: if removing the visual flourish would change how accurately the chart is read, the flourish is doing damage.

Getting a bar chart right

The zero baseline is the non-negotiable part. Bars encode value as length, so truncating the axis breaks the ratio between them. Values of 100, 102, and 104 from a baseline of 98 look like a threefold spread over what is actually 4 percent. Where the differences are genuinely small and genuinely important, a line chart, a dot plot, or a chart of the differences themselves are the honest alternatives.

Grouping beats stacking when the comparison is between series, because every grouped bar shares the same baseline while only the bottom segment of a stack does. The cost is horizontal space: categories multiplied by series is the bar count, and beyond about three series the bars get too thin to compare.

Category order is read as meaningful whether or not you intend it. Natural sequences — months, sizes, stages — should be preserved. Unordered categories such as products or regions are almost always better sorted by value, which makes the ranking visible instead of requiring the reader to reconstruct it. Alphabetical order is defensible only when readers need to look up specific items.

Horizontal bars are better for long labels and for many categories, since labels run in the normal reading direction and the chart can extend downward. The exception is time, which readers expect to run left to right, so a time series should stay vertical even with awkward labels.

On labels and gridlines, pick one. Gridlines support estimating values from the axis; direct labels make estimation unnecessary. Both together adds ink without information. But the reduction has a limit — the baseline, the axis, and the category labels look like furniture and are the parts doing the work.

The narrow case for a pie chart

Pie charts do communicate one thing better than bars: that the parts constitute a whole. The circle is closed, so readers grasp immediately that the slices sum to everything, which a bar chart does not convey without saying so.

They are also fine for a few slices at recognisable fractions. Half, a quarter, and three quarters are read accurately because the angles are familiar. Two or three clearly different slices is a case where a pie chart is defensible and arguably the better choice.

Everything else is where the criticism lands. Slices at 23 and 26 percent are indistinguishable, and it gets worse when they are not adjacent, since comparing two angles across the circle means holding one in memory. Orientation matters too: a slice starting at twelve o clock is read more accurately than the same slice further round, which is why the convention is largest slice first, clockwise, descending.

Five or six slices is the practical ceiling. Long-tailed data — twenty products where four are 80 percent of revenue — should have its tail combined into a single Other slice, since sixteen slivers convey nothing individually and, if the tail matters, it deserves its own chart.

One structural check: the values must sum to a meaningful whole. Counts from overlapping sets, or metrics of different kinds, produce a total that means nothing while the circle asserts completeness. Percentages summing to more than 100 are the obvious symptom.

And two pie charts side by side are very hard to compare, because it requires judging angles in one and holding them while judging another. Comparing across wholes is a grouped or stacked bar chart problem, and composition over time is a stacked bar chart problem — a row of pie charts by quarter is among the least readable things in business reporting.

Funnels, and the arithmetic underneath them

A funnel shows a sequential process where each stage is a strict subset of the one before it. The width encoding is correct and the silhouette adds a suggestion the data may not support.

The taper implies smooth, natural narrowing. Real funnels usually have one or two catastrophic steps and several harmless ones, and an 80 percent loss and a 5 percent loss both just look like tapering. Equal vertical spacing implies equal time or effort between stages, when the gap between visiting a page and signing up may be seconds and the gap between a trial and a purchase weeks. And the widest band draws the eye to the largest number, which is usually the least actionable.

The arithmetic is where the value is. Overall conversion is the bottom over the top; stage-to-stage conversion is each stage over its predecessor. A funnel of 10,000, 2,000, 800, 200 is 2 percent overall, which tells you nothing, and 20, 40, 25 percent by stage, which points straight at the first step. Because overall conversion is the product of the stage rates, moving that first step from 20 to 25 percent lifts overall conversion from 2 to 2.5 percent — a 25 percent gain in customers with nothing else changed.

A bar chart of the stage rates makes the problem stage obvious and loses the intuitive shape, which is a good argument for showing both.

One data trap outranks all of the display issues: cohort mismatch. If the top stage counts this month visitors and the bottom counts this month customers, some of those customers came from earlier visitors and some current visitors have not converted yet. For a long sales cycle this can move the apparent rate substantially, and only tracking a fixed cohort through the stages avoids it.

Frequently asked questions

Chart makers referenced in this guide