Framing & context

The heaped digit

The spike is where the pen stopped, not where the world piled up.

a.k.a. digit preference · terminal digit preference · end-digit bias · age heaping · the rounding artefact · Whipple’s index · recording granularity · the measurement lattice

Every number on a chart was written down by something — a person reading a dial, a form with a field on it, an instrument that steps. None of those can express every value, and the ones they favour are not the ones the world favours. Draw the distribution fine enough and what appears is the recording scale rather than the quantity: spikes where a human rounded to a comfortable number, and holes at the values the instrument or the form had no way to record. It is the near neighbour of the count that measures the looking and not the same thing — nothing here is undetected, nothing is missing, and every row in the file is drawn. The values are simply snapped to a lattice somebody chose, and a histogram is fine-grained enough to show you the lattice.

How to spot it

Look at the last digit. Ten bars, one per final digit, is the cheapest diagnostic in statistics: a clean scale gives roughly a tenth each, and anything else is the recording habit talking.
Watch for spikes at the round numbers — multiples of five, ten, twenty-five, a hundred — especially in anything self-reported, estimated by eye, or read off an analogue scale.
Watch for the opposite too. A comb of empty columns means a scale with fewer steps than your axis has ticks, and the gaps are as much an artefact as the spikes.
Ask what the measurement was recorded to the nearest of, and whether that is coarser than the difference the chart is asking you to see. A 1-unit finding on a 5-unit scale is not a finding.
Check the thresholds. A cut-point that lands on or just beside a favoured value is decided partly by the rounding rule, because everything within half a step of it moves across on somebody’s convention.
Suspect the bin width whenever it is not a whole multiple of the recording step: 5-wide bins over a 2-step lattice hold three values, then two, then three, and the bars alternate whatever the data does.
Read the publisher’s own notes. Data dictionaries, edit rules and interviewer manuals usually state the granularity outright, right next to the field.

The fix

Draw at the resolution the measurement actually has. One bar per step the instrument can take turns a comb back into a distribution, and the picture stops asserting a precision nobody recorded. Then print the granularity beside the unit the way you print the unit — "mmHg, to the nearest 2", "years, as reported" — because it is part of what the number means and it costs four words. Where the granularity is itself the question, give the last digit its own panel; ten bars beside the main chart settle in one glance what a paragraph of caveats cannot. Choose bin widths that are whole multiples of the recording step, so the bins hold equal numbers of reachable values and the sawtooth never appears. Where a second, finer measurement of the same thing exists — a scale beside the self-report, an automatic instrument beside the manual one — draw both, because the disagreement is the most honest error bar you will get. And before reading a spike or a gap as a fact about the world, check the form it was written on: a distribution is a statement about the recording system first and the population second.

In the gallery

Dark navy briefing slide. The masthead reads “Stroke prevention desk · clinic threshold review” on the left and “Systolic blood pressure · NHANES 2017–2018 · 19,959 readings” on the right. The headline is “Nobody in America has a blood pressure of 139.” Beneath it sits a bordered gold chip reading “Demonstration · drawn by us from published figures”. A standfirst says every reading on the chart is NHANES’s own — one national survey, one protocol, one field — 19,959 systolic measurements taken by certified physician examiners on 6,717 participants aged 8 and over; that nothing is smoothed, binned, indexed or rescaled, the count axis being linear and starting at zero with one bar for every whole millimetre of mercury from 80 to 200; and that read at that resolution the distribution turns out to be a comb, systolic pressure in this population not taking odd values in any of the 19,959 readings, with the empty column sitting directly beneath the threshold the clinic has been arguing about. The main panel, headed “Systolic blood pressure, one bar per millimetre of mercury” and subtitled “Count of readings at each whole mmHg · NHANES 2017–2018 auscultatory protocol · linear axis from zero · nothing smoothed, binned or rescaled”, is a gold histogram against a linear count axis running 0 to 1,000 in steps of 200, with the horizontal axis ticked every 10 mmHg from 80 to 200. Every second column is present and every other one is blank, producing a regular comb that rises from almost nothing at 80 to a peak of just over a thousand readings around 116 and falls away through a long right tail. An annotation at the upper left reads “Every odd millimetre is empty, all the way across” with a leader into one of the gaps between two tall bars. A dashed vertical line at 140 is labelled “Treatment threshold under review: 140”, and a second annotation beside it reads “139 mmHg — no readings. Its neighbours: 138 has 364, 140 has 345.” A caption along the foot of the panel reads “One national survey · one protocol · one field · every reading the examiners recorded”. Six cards run down the right. “The record, in one figure” prints a large gold 0 beside “readings at 139 mmHg”, and notes that the count is also zero at 137, at 141 and at every other odd millimetre between the lowest reading of 72 and the highest of 238, the bars either side of the gap being 364 at 138 and 345 at 140. “Read-out for the desk” says the distribution has a wall in it, that the column at 139 is not low but empty, and so is every other odd column across the whole range, so 140 is not a committee’s round number but where the data itself resumes; its recommendation is to hold the threshold at 140 and close the debate, to treat 1 mmHg differences as noise since pressure does not take those values, and to drop the odd integers from the clinic’s index. “What one bar is” explains that a bar is the number of systolic readings recorded at that whole millimetre of mercury, from NHANES 2017–2018, Blood Pressure (BPX_J), three readings per participant and four where one was interrupted, with bars covering 80–200 mmHg and 73 readings sitting outside the frame. “The lattice, in numbers” tabulates in monospace: readings 19,959; participants 6,717; range of readings 72–238; whole mmHg in that span 167; columns with a reading 82; columns standing empty 85; odd-numbered readings 0. “Why nothing here is bent” says the count axis runs from zero, nothing is indexed, rebased, logged or smoothed, the bars are one width and one colour, one per whole millimetre, nothing inside the plotted range has been dropped, and whatever makes the gaps it is not the drawing. “Basis of measurement” credits CDC / National Center for Health Statistics, NHANES 2017–2018, Blood Pressure (BPX_J), retrieved 16 September 2026, and says NHANES publishes the readings while the counts and the chart are ours. A method line runs along the foot: published readings, as recorded; one survey, one protocol, one field; linear count axis from zero; one bar per whole millimetre; nothing smoothed, binned or rescaled. A footnote credits the source, notes that every plotted value is a count of the survey’s own recorded readings, and states that the slide is a demonstration drawn by us in the manner of a hospital service briefing — the desk, the read-out and the recommendation are invented, and every figure behind them is real.

The zero readings at 139, and the 174 from the same visit

The heaped digit Phantom precision