Statistics in Headlines

🧠 Thinking Clearly · Lesson 48 of 50 · about 8 minutes

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← Akademi · 🧠 Thinking Clearly · Lesson 48 of 50 · about 8 min

The relativity trick: “brain tumour risk doubles with X” sounds apocalyptic and may mean 1 in 10,000 becoming 2 in 10,000. Relative risk multiplies; absolute risk adds — and only the absolute version lets you decide anything sane. Whenever a headline gives you a percentage increase, hunt the baseline: the same result honestly stated as “an extra one case per 10,000 people” often reverses the emotional conclusion.

The subgroup trick: slice data enough ways and “significant” findings appear by chance alone. Screen 20 outcomes at the usual p<0.05 bar and statistically you expect about one false positive even when nothing is true; the “works only in men under 40” finding is usually that stray. This is not hypothetical — psychology and medicine have lived a replication crisis: landmark findings repeatedly failing retesting, p-hacking (collecting, slicing and modelling until the threshold trips) now estimated to inflate a substantial share of published positives. The 2010s correction — pre-registration, larger samples, open data — is real but incomplete.

The checklist that survives contact with any study article: how many subjects (a finding from 12 people is anecdote with decimals)? Compared against what (control group, or before-after with time confounds)? Measured or self-reported? Published in a venue that peer-reviewed it, or a press release? Who funded the analysis? And finally, the meta-rule the whole academy teaches: one study is never a verdict — science accumulates in the boring direction, and the trustworthy claim is the one several independent groups have now failed to knock down.

Key takeaways

  • Always convert relative risk back to absolute numbers before feeling anything
  • 20 cuts of nothing produce one “hit”: subgroups and p-hacking manufacture findings
  • Sample, control, funding and replication are the four footnotes that change conclusions

Check yourself

“Risk rises 100%!” from 0.01% to ___.

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