Track 15 · Applied Statistics for Professionals · Lesson 11 of 12
Reading published results
Extract the estimate, its uncertainty and its practical size from a published result, check that the numbers agree with each other, and spot the red flags that should lower your trust.
A vendor's white paper says its wellbeing programme “cut sick leave by 25% (p < 0.05)”. Before your organisation spends a budget on it, you need to know: 25% of what, how uncertain that is, how the study was designed — and whether the reported numbers even agree with each other.
Every quantitative finding in a report, paper or slide deck should give you four things:
- An estimate of the effect (a difference in means, a risk ratio, an odds ratio, a correlation).
- Its uncertainty, usually a 95% confidence interval (CI).
- A test result, usually a p-value, which says how surprising data like these would be if there were truly no effect.
- Enough context to judge size: the baseline, the units, or a standardised effect size.
The first three are linked by simple arithmetic, so you can recover a missing one and check that the reported ones agree. The fourth is where most over-selling happens.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Recover a standard error and p-value from a reported confidence interval, including ratio measures on the log scale
- Check that an estimate, interval and p-value agree
- Translate relative effects into absolute risk reductions and numbers needed to treat
- Judge practical importance with real units and standardised effect sizes
- Recognise red flags: small samples, selective reporting, surrogate and composite outcomes, and causal language from observational data