Before a percentage becomes a conclusion

A percentage can make a report look settled before the questions have been asked. A rise appears encouraging; a fall prompts concern. Yet the figure alone cannot tell us who was counted, what changed or whether the comparison is fair. Before a number becomes a judgement about a service, a team or a public policy, it needs enough context to carry that judgement.

Ask what sits underneath

Start with the count and the total. In an invented example, eight positive responses from ten respondents produce 80%. Eighty positive responses from one hundred also produce 80%. The proportions match, but the amount of information behind them differs. With ten respondents, one different answer changes the result by ten percentage points.

Ask who could respond, who actually responded and whether anyone was excluded. A satisfaction figure describes the answers collected. Without further evidence, it should not be presented as the view of everyone who uses a service. Keep the underlying counts available in an appropriate form, while protecting confidentiality where small groups could make individuals recognisable.

Name the change accurately

The Office for National Statistics distinguishes percentage changes from percentage point changes. These describe different things, and confusing them can exaggerate or understate a result.

Suppose a hypothetical completion rate moves from 60% to 75%. That is an increase of 15 percentage points. Relative to the starting rate, it is a 25% increase: the difference of 15 divided by 60. Both calculations are correct, but they answer different questions. State which one you mean and show the starting and finishing values.

Choose language that allows the reader to follow the calculation. A dramatic relative increase from a small starting count may be mathematically accurate while giving an incomplete impression. Reporting the counts alongside the percentage makes the scale easier to judge.

Check whether the comparison holds

Before placing two periods beside each other, check the definitions. Did completion mean the same thing in both? Were the reporting windows equally long? Did the group being measured change? A new recording system or a revised eligibility rule can affect what enters the total.

These are questions to investigate, rather than automatic reasons to dismiss a result. If a definition changed, explain it close to the figure. Where a reliable comparison cannot be made, say so. A precise calculation cannot repair an unsuitable comparison.

Also separate the observation from the explanation. A figure moving after a new initiative does not, by itself, establish that the initiative caused the movement. Record what is known, identify possible explanations and seek evidence that could distinguish between them.

Give uncertainty a visible place

ONS guidance explains that survey estimates can vary because a sample, rather than the whole population, has been observed. Confidence intervals help communicate the precision of such estimates. Other problems, including non-response and inaccurate answers, can also affect the results.

When using published survey findings, read the accompanying methodology and uncertainty information before drawing conclusions from small differences. For technical comparisons, use the published assessment or seek suitable analytical advice. Do not improvise a statistical test from a chart.

An internal count of every recorded event is different from a sample survey. It may still be incomplete because events were missed or classified inconsistently. Describe the actual limitation. ONS chart guidance recommends showing uncertainty where it would materially affect interpretation; a written report should likewise place relevant limitations beside the claim.

Finish with a proportionate judgement

A useful reporting sentence connects the result, its basis and its limits. For an invented example: eight of ten respondents answered positively; this describes respondents only, and the reasons for the two other answers need further exploration. That gives a manager somewhere sensible to begin.

Before signing off a report, ask whether a reader could reconstruct the central comparison without guessing. Check the count, total, period, definition and source. Then explain what decision the evidence supports, what remains uncertain and what further information would help. The aim is a conclusion that earns the confidence placed in it.

Sources and further reading

• Office for National Statistics: Percentages and percentage points
• Office for National Statistics: Uncertainty and how we measure it for our surveys
• Office for National Statistics: Showing uncertainty in charts