Make uncertainty readable in a publication figure

A figure can be visually tidy while leaving the reader unsure what its error bars mean. Decide what quantity the bars communicate before choosing their appearance. The same measurements can legitimately produce different bars, provided the quantity, sample size and calculation method are stated.

One sample, three different summaries

Consider an illustrative set of five independent measurements: 8, 9, 10, 11 and 12 MPa. Their mean is 10 MPa, and the squared deviations sum to 10 MPa². Using the sample denominator n − 1 gives:

With four degrees of freedom, t ≈ 2.776; the illustrative interval is therefore 10 ± 1.963 MPa, or approximately 8.037 to 11.963 MPa. The NIST reference on confidence limits for the mean explains the t-based method. For this small-sample example, its interpretation assumes independent observations from an approximately normal population.

SD describes the spread of individual observations. SEM describes the estimated precision of the sample mean under the independence assumptions. The confidence interval adds a stated coverage procedure. None is interchangeable with another simply because one produces shorter bars. A 95% frequentist interval refers to the method’s long-run coverage, not a 95% probability assigned to this already-computed interval.

Map the quantity you actually calculated

Graph Studio Web takes supplied symmetric error magnitudes from a column. It does not compute SD, SEM, confidence intervals or statistical significance. For the example above, a mean column of 10 with a CI-error column of 1.963 draws the intended symmetric interval. Supplying 3.926, the full interval width, would double both arms.

Select CI as the error meaning and explain the method in the caption. A suitable illustrative caption is: “Mean and 95% t confidence interval; n = 5 independent measurements.” If multiple Y series share a panel, the browser edition uses the same selected error column for all of them; use separate panels when the uncertainty columns differ. Consult the web guide and limits before arranging the figure.

Review the artifact at its final size

As a unit check, an 85 mm-wide image at 300 pixels per inch needs 85 / 25.4 × 300 ≈ 1004 pixels across. That is an example size, not a journal requirement. Verify the target publication’s actual dimensions and file rules.

1. Inspect axis units, the legend, sample-size definitions and the stated uncertainty method.
2. Check excluded or missing data and whether a logarithmic scale removes non-positive values.
3. Open the exported SVG or PNG and inspect labels at the intended physical size. Keep markers and line patterns distinguishable.
4. For browser-generated PDF, inspect page dimensions, clipping and print scaling. Save a project download alongside the source data and analysis record.

Exporting a figure does not validate the experiment or guarantee publication acceptance. A useful figure makes its evidence and its limits inspectable.