Reading a figure

Lesson 3 33 minReading

In this lesson

By the end, you’ll be able to

  • Judge whether a chart's axes and scales represent the data honestly
  • Say what SD, SEM, and 95% CI error bars each mean
  • See what a bar of means hides that a distribution shows

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Most readers look at the figures and skip the math. That makes figures the place where a paper is most persuasive, and most easily misleading, on purpose or by habit. Reading a figure well means asking what choices were made in drawing it, because the same numbers can be drawn to tell opposite stories. Those choices are learnable, and once you see them you cannot unsee them.

Axis from 9090100ABlooks hugeAxis from 00ABbarely differs
The same two values, drawn twice. With the y-axis cut to start near the data (left) a tiny difference looks enormous; from a zero baseline (right) it nearly vanishes. Nothing about the numbers changed.

The first thing to check is the axis. A bar chart compares heights, so where the axis starts decides the story: truncate the baseline and a two-point gap becomes a chasm. For comparing magnitudes, a zero baseline is the honest default. Watch too for scale: a logarithmic axis is legitimate for data that grow by multiples, but each step is a factor (×10), so equal visual steps mean equal ratios, not equal amounts; read it accordingly, and never expect zero to appear on it.

Signature interactive

Same Data, Six Charts

Two groups, one dataset. Change how it is drawn and watch how different the groups look, while the actual numbers never move.

0204060Group AGroup B
The numbers never changed. Group A mean 50.0, Group B mean 54.0 (difference 4.0). SD ≈ 1.8, SEM ≈ 0.6, 95% CI ≈ ±1.1.

Which version would you submit, and how would you answer a reader who calls the flattering one “misleading”? The honest choice shows the spread (SD or the raw dots) on an axis that does not exaggerate the gap.

Error bars look precise but mean different things. Standard deviation (SD) describes how much individuals vary. Standard error of the mean (SEM) describes how precisely you have pinned down the mean, and it shrinks as the sample grows (SEM = SD/√n), so a large study can show tiny SEM bars while individuals vary wildly. A 95% confidence interval is a range of values compatible with the data for the true mean. Papers often plot SEM because it looks tightest; always check which bar you are seeing before you read confidence into it.

Categorize

Match each error bar to what it actually represents.

SD describes individuals; SEM shrinks with n and describes the mean's precision; a CI is a compatibility range for the true mean.

Standard deviation (SD)
Standard error of the mean (SEM)
95% confidence interval
How sure?

A bar of means is a summary, and summaries hide. The same mean can come from tightly clustered data, from a wide spread, or from two separate groups with almost no one in the middle. Showing the distribution (the individual points, a dot plot, a box or violin) reveals shape, spread, sample size, and outliers that a bar erases. When you can, show the data; when you read, ask what the summary is not showing you.

Which is better, and why?

Two charts show the same two groups, whose means differ by about 3 points. Which is the more honest figure, and why?

Which axis choice makes a 3-point gap look like a chasm? Which error bar hides the real spread?

How sure?

Categorize

Lab, four figures, one flaw each. Match each figure to the flaw it commits.

Ask of each: is the axis baseline honest? do the error bars show spread or precision? does a mean hide structure? are two scales forced to align?

Revenue bars with the y-axis starting at 4,900 instead of 0
Group bars with tiny error bars labelled 'SEM', making the groups look far apart
A single bar for the mean test score, when the scores are actually two separate clusters
Ice-cream sales and shark attacks plotted on two y-axes, rising together
How sure?

Checkpoint · item 1 of 5

A bar chart's y-axis starts at 95 instead of 0. What is the effect?

Picture two nearly-equal bars when the axis only covers 95–100.

How sure?

Reflection