How to check percentages in an AI research answer

An AI-generated sentence can cite the right table and still describe the numbers incorrectly. A share can become a growth rate. A change in percentage points can become a percent increase. Two groups with very different sizes can receive equal weight in a combined result.

Before using a numerical claim, reconstruct it from the underlying values. You need a source, a definition, a denominator and a calculation that another person can repeat. This guide covers ordinary research arithmetic, using entirely fictional workshop-registration data. None of the examples describes a real organization, study or product result.

1. Translate the sentence into a calculation

Consider the fictional statement: “Workshop completion increased by 10%.” It is incomplete. Does it describe the number of completions, the completion rate, or a ten-percentage-point change in that rate?

Write down four things before accepting it:

• Numerator: What is being counted?
• Denominator: Out of which total?
• Period: When were the observations made?
• Unit: Is the result a count, a share, a percentage-point difference or relative growth?

Suppose an invented workshop recorded 40 completions among 200 registrations in one period and 60 completions among 200 registrations in the next. The completion rates are 20% and 30%. The number of completions rose by 20. The completion rate rose by 10 percentage points. Relative to the starting rate, it rose by 50%.

Those statements use the same inputs but answer different questions. Choose the one your research actually needs and retain the underlying values in your notes.

2. Distinguish percentage points from percent change

To find a percentage-point difference, subtract one percentage from the other:

30% − 20% = 10 percentage points.

To find relative percent change for a positive starting value, divide the change by that starting value and multiply by 100:

(30 − 20) ÷ 20 × 100 = 50%.

The Bureau of Labor Statistics' explanation of percent change uses the same subtract, divide and multiply sequence for changes in index values. It also explains why an index-point difference is not interchangeable with a percent change.

A clear description of the fictional workshop is: “The completion rate rose from 20% to 30%, an increase of 10 percentage points, or 50% relative to the earlier rate.” In a short report, the starting rate, ending rate and percentage-point difference may be enough.

Check the baseline before using the formula. Growth from zero has no defined relative percentage under this calculation because it requires division by zero. Report the count change and starting value instead. For negative baselines or specialized statistics, use the source's documented method rather than applying a familiar formula automatically.

3. Recheck the denominator when the group changes

Now change the fictional second period: there are still 60 completions, but registrations have risen to 400. Completions increased from 40 to 60, while the completion rate fell from 20% to 15%.

Neither result cancels the other. More people completed the workshop, and a smaller share of registrants completed it. A summary that says only “completion improved by 50%” hides a choice about which measure matters.

Read the source's definition of registration, too. Does it include cancellations? Duplicate signups? People still enrolled when the reporting period closes? Preserve the publisher's definitions. If one period includes active participants and another contains only finished cohorts, a rate comparison needs more investigation before it becomes a trend claim.

This is also where to stop an AI assistant from filling gaps. If the total number of registrations is missing, ask for that missing input. Do not let a plausible-looking percentage stand in for an unavailable denominator.

4. Combine counts before averaging rates

Suppose two fictional workshops report:

• Workshop A: 9 completions from 10 registrations, or 90%.
• Workshop B: 10 completions from 100 registrations, or 10%.

The simple average of their rates is 50%. But the combined completion rate across all registrations is 19 ÷ 110 × 100, or about 17.3%.

The first calculation gives each workshop equal weight. The second gives each registration equal weight. If the question is “What share of all registrations resulted in completion?”, use the combined counts, assuming the groups do not overlap and use the same definition.

Equal weighting can be appropriate when the intended unit is the workshop itself. State that choice explicitly. Also check for duplicate people if the intended question concerns unique participants rather than registrations. Adding two registration totals does not automatically produce a unique-person total.

5. Keep the time basis attached

A monthly change, a year-over-year change and an annualized rate are different measures. Carry the label with the number whenever you shorten a source's wording.

BLS's percent-change guidance distinguishes changes between matching months a year apart from changes in annual averages. It also warns that adding monthly percent changes does not give the over-the-year change.

For another important distinction, the Bureau of Economic Analysis explains annualized quarterly rates as the result of compounding a quarterly rate for four quarters. That rate describes what the change would be if the quarterly pace continued; it is not an observation that a full year has already passed at that pace.

You do not need to recalculate every official statistic yourself. You do need to preserve the published period, adjustment and unit. If the source says “seasonally adjusted annual rate,” removing those words can change the meaning of the claim.

6. Ask for a calculation record before a polished summary

Give Neutron Says or another research assistant the relevant public table or a short, permitted excerpt. Ask it to organize the inputs before writing the conclusion:

For each numerical claim, list the source URL, table or passage, numerator, denominator, units and period. Show the arithmetic from the supplied values. Distinguish percentage points from relative percent change. Explain any weighting. Mark missing inputs as missing. Do not infer causation or statistical significance. Then draft one sentence whose wording matches the calculation.

This is a suggested review workflow, not a claim that Neutron automatically audits calculations or guarantees their correctness. Verify the inputs against the original source and check the arithmetic independently with a calculator or spreadsheet.

Keep full precision during the calculation and round the reported result at the end. If the inputs were already rounded, avoid presenting additional decimal places as new accuracy. A correct calculation also does not establish why something changed or whether an observed difference exceeds sampling uncertainty.

A final check before using the number

Can another reader recover the same result from your source and notes? They should be able to find:

1. The exact definition and reporting period.
2. The starting and ending values, or numerator and denominator.
3. The calculation and any weighting choice.
4. The rounding used in the final sentence.
5. Any unresolved issue with comparability, missing values or uncertainty.

If the source itself needs checking, use the citation verification guide. If two sources genuinely conflict, use the source comparison workflow. The calculation check here comes after you have identified what the source actually reports.

Ready to organize a public-source research question? Open Neutron Says and ask for the inputs and reasoning alongside the answer. Keep the final numerical check in your own review process.