Numbers in Arguments: Spotting Misleading Statistics

Evaluate how statistics are presented, not just whether they are accurate.

Statistics can be accurate yet misleading, depending on how they are framed. Watch for four common problems. Relative versus absolute change: 'Risk doubled' sounds alarming, but if risk rose from 1 in a million to 2 in a million, the absolute change is tiny. Missing base rates: '500 accidents at this intersection' means little without knowing how many cars pass through. Averages hiding spread: an average salary can be pulled up by a few very high earners, so the median may better represent a typical worker.

Truncated graphs: a chart whose vertical axis starts at 95 instead of 0 can make a small change look enormous. Worked example: an ad claims, 'Our toothpaste reduces cavities by 50 percent! ' A careful reader asks: 50 percent of what? If the comparison group averaged two cavities over five years and the toothpaste group averaged one, the claim is accurate but the benefit is one cavity in five years. Always ask what the number is compared to.

• 1Relative change can exaggerate small absolute changes.
• 2Numbers need base rates and context.
• 3Medians and full-scale graphs can reveal what averages and truncated axes hide.