Writing Science: the Figure, the Error Bar and the Claim
Report a measured estimate with units and defined uncertainty. Present figures and captions that state only what the evidence supports. Identify statistical and systematic contributions and describe the method so another group can repeat the procedure and check the analysis.
What a learner can do afterwards
- Drafts a figure whose caption states the claim it supports
- Reports a result with statistical and systematic uncertainties kept separate
- Writes a method description detailed enough for another group to repeat
1 · Read
Report a measured estimate with its unit and an uncertainty whose meaning is defined. Exact counts need no measurement uncertainty. Accuracy concerns agreement with a reference; precision concerns agreement among repeats. Three scale readings of 183 g agree with each other but miss a 180 g reference. Correct known offsets where appropriate and include uncertainty in the correction.
With independent readings under stable conditions, more data can reduce statistical uncertainty in the mean. Averaging does not narrow the underlying spread of individual readings or remove a shared fixed offset. Report statistical and systematic contributions separately by source. You may also give a total uncertainty if you explain the combination method and correlations. Better calibration or design can reduce systematic uncertainty.
State your rounding convention. Here, round uncertainty to one significant digit, then the estimate to the same decimal place. An estimate of 6.283 s with uncertainty 0.047 s becomes 6.28 ± 0.05 s. Some conventions retain two significant digits in uncertainty. Keep extra working digits during calculations and round the reported result at the end.
Name plotted variables and give their units. Add a legend when groups or markers need identifying. Define error bars: they might show spread, standard uncertainty or a confidence interval. Give a confidence level when applicable. Show uncertainty where readers need it to judge the finding. Make axis limits clear and consider their effect on interpretation; a nonzero axis is not automatically misleading.
A caption identifies the measurement, groups or sample size, and the supported finding. State its limits. If an observational sample shows two variables rising together, describe an association in that sample. Association alone does not establish that one variable caused the other to change. Other causes may explain the pattern.
Document instruments, settings, calibration and sample sizes. State exclusions and when their rules were chosen. Give analysis steps or accessible code with versions. Define symbols, give units and provide access to data needed to check reported numbers. Another group should be able to repeat the procedure, without an identical estimate being guaranteed. Before calling estimates contradictory, compare uncertainty definitions, conditions, calibration and analysis.
Define the estimate and uncertainty, make the figure interpretable, limit claims to their evidence, and document how the result can be checked.
Lesson, questions and flashcards written for this dataset. Supplied OpenStax measurement and units sections informed factual and teaching-design study; their prose was not reused.
Readings and flashcards written for this dataset. Supplied OpenStax sections were used for factual study; the reporting and method guidance is original text.
More to read
Explaining an estimate's uncertainty
A reader needs to know what a reported uncertainty represents. A ± value could describe a standard uncertainty or an interval constructed by a stated procedure. Define it and provide a confidence level where applicable. Do not present it as a guaranteed range for the true value.
Agreement with a reference and agreement among repeats answer different questions. A set of tightly clustered readings can share a calibration offset. Repeating those readings does not identify or remove that offset.
Under stable conditions, adding independent measurements can reduce statistical uncertainty in their mean. The underlying distribution of individual readings need not become narrower. Calibration, background checks and experimental design address other uncertainty sources.
Report statistical and systematic contributions so readers can see what they include. If you also provide a combined uncertainty, explain the calculation and any correlations. A shared source can affect several results together, which matters when comparing them.
Correct known offsets where appropriate and include uncertainty in the correction. Distinguish measured values from exact quantities. An exact count of intact objects needs no measurement uncertainty, whereas their measured mass does.
Choosing reported digits and explaining a figure
Retain working digits during a calculation. Round the reported result using a convention that you state. For example, under a one-significant-digit uncertainty convention, 8.746 s with uncertainty 0.083 s becomes 8.75 ± 0.08 s. The rounded uncertainty ends at hundredths, so the estimate ends there too. Other conventions may retain two significant digits in uncertainty.
A figure also needs a stated interpretation. Give variable names and units, and identify any groups or markers that would otherwise be unclear. Define error bars. Spread among observations, uncertainty in an estimate and a confidence interval communicate different information.
Make axis limits clear. A nonzero axis can help readers inspect small differences in measured values, but the scale must not conceal their size or uncertainty. Consider what impression the chosen range creates.
The caption should identify what was measured and describe the finding the figure supports. If an observational sample shows an association, name that association and its scope. Do not turn it into an isolated causal effect or a claim about an unstudied population.
Making a procedure checkable
A method should explain how the reported numbers were obtained. Describe sampling, instrument settings, calibration, corrections and analysis. Identify relevant software versions or accessible code. Define symbols and units so another group does not have to guess what a quantity means.
Selection decisions belong in this account. State which records were excluded, the exclusion rule and when it was chosen. Readers need to distinguish a planned rule from a decision made after inspecting outcomes. Both require a clear record.
Provide access to the data and analysis information needed to check the result. A short description does not replace missing operational details, data or code. Another group should be able to follow the procedure and examine how its choices affect the estimate.
Repeating the procedure need not yield an identical estimate. Before declaring two results contradictory, compare their uncertainty definitions and included sources. Check measurement conditions, calibration and analysis differences too. A discrepancy can motivate further investigation without establishing that either report is false.
2 · Watch
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Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.