A 50% increase in quitting—or five percentage points?

01

Start with the people counted, not the headline

Here is an entirely invented arithmetic exercise, not a real trial or a claim about any support. A report compares arrangements A and B, with 600 people in each analysis. At six months, 90 in A and 60 in B report no cigarette smoking during the preceding seven days. Assume this exercise has no missing outcomes. The proportions are 90/600 = 15% and 60/600 = 10%.

Now imagine two headlines: ‘50% higher’ and ‘five percentage points higher’. Both can describe this same comparison. Neither means that 50 of every 100 people quit, nor does a six-month assessment mean six months of continuous abstinence.

02

Do the subtraction and division separately

For the absolute difference, subtract 10% from 15%: five percentage points. In equal-sized groups of 600, that is an observed difference of 30 people meeting the stated endpoint, equivalent to five per 100. It does not identify 30 people whose outcome was caused by A.

For the risk ratio, divide 15% by 10%: 1.5. A's proportion is 150% of B's proportion, or 50% higher relative to B: (15 − 10)/10 × 100. ‘150% of’ and ‘150% higher’ are not interchangeable. The table keeps the units visible.

03

What a trial report should put beside those figures

CONSORT 2025 calls for group results, analysed and available counts, effect estimates and precision. For a binary outcome like this one, it calls for both absolute and relative effects. Look for the actual outcome table, not just a headline.

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04

The same ratio can hide a much smaller headcount difference

Change only the invented numbers: nine of 600 versus six of 600 meet the same endpoint. These are 1.5% versus 1%, again a risk ratio of 1.5 and a relative increase of 50%. This time the absolute difference is 0.5 percentage points—three people across the equal-sized groups, not 30.

That contrast explains why ‘50% higher’ without the comparison proportion is incomplete. It does not make the second arrangement worse or better than the first: these are fabricated numbers without evidence about real services. Likewise, a ratio from one setting cannot simply be multiplied by a guessed local quit rate to make a personal forecast.

05

If the paper says OR, do not relabel it RR

An odds ratio compares odds, not outcome proportions. In the first exercise, A has odds 90/510, while B has odds 60/540. Their ratio is about 1.59, not 1.5. It uses the people who did not meet the endpoint as well as those who did.

Do not read OR 1.59 as ‘59% more people quit’. Also do not expect an adjusted estimate from a statistical model to reproduce simple arithmetic on a rounded results table. Check which measure and analysis the report actually presents.

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06

A complete sentence carries its limits

Absolute and relative presentations should be read together, with uncertainty and the comparison baseline. Changing units does not remove uncertainty.

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07

Write only what the exercise permits

A faithful sentence is: ‘In this invented six-month assessment, 15% under A and 10% under B met the preceding-seven-day cigarette endpoint: an absolute difference of five percentage points and an unadjusted risk ratio of 1.5.’ The exercise supplies no real support, causal evidence or confidence interval. Do not add ‘proven effective’ or treat this as an estimated clinical benefit.

For a real paper, attach its reported confidence interval to the matching estimate. Keep the population, comparator, endpoint, assessment time and analysis together; comparing scales within one result is different from ranking rates from unrelated studies. Public group counts are sufficient for this reading task—no personal smoking or health information is needed.

08

When the question becomes about your care

In England, NHS Better Health provides a route to local Stop Smoking Services. Ask a qualified professional about personal support choices; this arithmetic cannot select one for you. Readers elsewhere need their own local service, not an assumed entitlement to NHS care.

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09

What to keep in mind

• Recover both proportions before interpreting ‘higher’.
• Name the unit: percentage points, risk ratio, or relative percentage.
• Keep the baseline, endpoint and reported uncertainty beside the comparison.

10

Common questions