Principles of Data Visualization

A chart is an argument made with ink, and the reader believes it before they read a word of your caption. That power cuts both ways: the same numbers can be drawn to reveal a pattern or to manufacture one. This page is about drawing them so the picture is both easy to read and honest.

Figure 1. A misleading bar chart with a truncated y-axis makes four nearly equal site positivity rates look dramatically different; the honest version beside it draws the same means from zero with standard-error intervals.

Match the chart to the question#

Pick the chart from what you are asking, not from habit or from what a spreadsheet offers by default. A distribution wants a histogram or density; a relationship wants a scatter; a trend over time wants a line; a comparison across groups wants points with intervals. If you cannot say in one sentence what the reader should take away, the chart is not ready. More on the chart-to-question mapping lives in Graphing Data.

The perceptual hierarchy#

People do not read every visual channel equally well. Cleveland and McGill ranked how accurately we judge the channels a chart can use, and the ordering is stable.

Position along a common scale is read most accurately, then length.
Angle and slope come next, which is why pie charts are hard to compare.
Area is worse still, so bubble sizes mislead.
Color hue is near the bottom for encoding a quantity.

The practical rule follows directly: encode the number you most want the reader to compare as a position or a length, and reserve color for grouping, not for magnitude.

Color for everyone#

Roughly one in twelve men has some form of color vision deficiency, so a chart that leans on red-versus-green fails a real slice of your audience. Two habits fix most problems.

Use a colorblind-safe palette: viridis for continuous scales, Okabe-Ito for categories.
Never use the default rainbow (jet) colormap, which invents false boundaries where the data is smooth and hides real ones.

Do not let color carry meaning alone. Pair it with a redundant channel — position, shape, or a direct label — so the chart survives grayscale printing and color blindness both.

Avoid distortion#

Small choices in the axes and decoration can change the story without changing the data.

Do not truncate the axis on a bar chart; bars encode length, so a y-axis that starts above zero exaggerates every difference, as the left panel above shows.
Avoid dual y-axes, which let you slide two series until they appear correlated when they are not.
Cut chartjunk: 3-D effects, heavy gridlines, and background images add ink without information and often mislead.

Show uncertainty#

A point estimate with no interval invites the reader to over-read noise. Show the spread — a confidence or credible interval, an error bar, or the raw points behind a mean — so the eye can tell a real gap from sampling scatter. The honest panel in the figure adds standard-error bars, and the near-equal sites stop looking different.

Small multiples and direct labels#

When you compare many groups, many small panels sharing one scale beat one crowded chart; Tufte called these small multiples. And where a legend forces the reader to bounce between a color key and the lines, put the label next to the line instead. Direct labeling keeps the reader’s eye on the data.

A worked example#

Suppose you measure test positivity at four field sites and want to show whether they differ. A first draft draws four colored bars on a y-axis running from 0.40 to 0.48, and the bars look wildly unequal. The redesign makes three decisions.

Start the axis at zero so bar length is proportional to the value; the sites now look as similar as they are.
Drop the per-bar rainbow for one color, since the site is already encoded by position on the x-axis.
Add standard-error bars, which show the differences are within noise.

The numbers a good chart would show are exactly the group means and their standard errors, computed below.

In code#

Compute the summary the chart should display before you draw anything.

Python#

Python

import numpy as np
import polars as pl

rng = np.random.default_rng(1834)
sites = ["A", "B", "C", "D"]
base = {"A": 0.42, "B": 0.45, "C": 0.47, "D": 0.44}

rows = []
for s in sites:
    draws = rng.binomial(1, base[s], size=60)
    rows += [{"site": s, "positive": int(v)} for v in draws]

df = pl.DataFrame(rows)
summary = (
    df.group_by("site")
    .agg(
        n=pl.len(),
        mean=pl.col("positive").mean(),
        se=(pl.col("positive").std() / pl.len().sqrt()),
    )
    .sort("site")
    .with_columns(pl.col("mean", "se").round(3))
)
print(summary)

shape: (4, 4)
┌──────┬─────┬───────┬───────┐
│ site ┆ n   ┆ mean  ┆ se    │
│ ---  ┆ --- ┆ ---   ┆ ---   │
│ str  ┆ u32 ┆ f64   ┆ f64   │
╞══════╪═════╪═══════╪═══════╡
│ A    ┆ 60  ┆ 0.45  ┆ 0.065 │
│ B    ┆ 60  ┆ 0.467 ┆ 0.065 │
│ C    ┆ 60  ┆ 0.5   ┆ 0.065 │
│ D    ┆ 60  ┆ 0.383 ┆ 0.063 │
└──────┴─────┴───────┴───────┘

R#

library(data.table)
set.seed(1834)
base <- c(A = 0.42, B = 0.45, C = 0.47, D = 0.44)
dt <- rbindlist(lapply(names(base), function(s) {
  data.table(site = s, positive = rbinom(60, 1, base[[s]]))
}))
dt[, .(n = .N,
       mean = mean(positive),
       se = sd(positive) / sqrt(.N)), by = site]

Why it matters#

Field data on positivity, incidence, or dose response usually differs by small amounts against a noisy background, which is precisely the regime where a truncated axis or a rainbow palette can invent a finding. Drawing the intervals and starting bars at zero is not decoration; it is the difference between reporting a signal and reporting an artifact. A chart that respects the perceptual hierarchy lets a collaborator or reviewer reach the right conclusion in a glance.