"The statistically literate citizen has the right and the responsibility to refuse to quote a number that the data does not actually support."
The Asymmetry of Quotation
Quoting a number is fast. Adding the qualifications that make the number meaningful is slow. Refusing to quote takes social courage. The path of least resistance is therefore to repeat the unqualified number, which is exactly how misinformation spreads at scale through citizens who would otherwise object if asked. The citizen-statistician's discipline is to resist the path of least resistance when the number does not survive the lens.
When to Quote
- The shape is verified. If you know the underlying distribution is roughly bell-shaped (and you have grounds for that), the mean is meaningful and can be quoted with σ. Quote: 'IQ 130 is z = +2, roughly top 2% of the population.'
- The prior is named. If you state the base rate alongside the likelihood, the posterior is honestly computable. Quote: 'this test is 99% accurate but the disease is rare, so the posterior probability of disease given a positive is only about 2%.'
- The sample's filter is acknowledged. If the sample is filtered (which most are), quoting with that filter named is honest. Quote: 'among survey respondents (who self-selected), X% said Y.'
- The trade-off is visible. When citing a Type-I-vs-Type-II decision, quote both sides. Quote: 'lowering the standard would convict more guilty but also more innocent people.'
When to Refuse
- The mean of a power-law-shaped variable — refuse, or replace with the median and top-percentile distribution.
- A p-value without effect size, pre-registration status, and multiple-comparison context — refuse, or include all three qualifications.
- A 'risk' from a thin-tailed model when the underlying process is fat-tailed — refuse, or include the disclaimer that the model assumes thin tails.
- An 'X% chance' that smuggles in a prior nobody has named — refuse, or name the prior.
- A 'successful people do Z' generalization that ignores the failure rate — refuse, or explicitly name the missing failure data.
The Social Cost and Why It's Worth Paying
Refusing to quote a number is socially awkward. People want a clean number, not 'well, the underlying distribution is power-law-shaped so the mean is misleading...' The temptation to satisfy the social demand is real and constant. But citizens who refuse to quote inaccurate numbers, even when the audience would prefer them, are the citizens who eventually shift the social norm toward statistical honesty. The cost is paid in small social discomforts; the benefit is paid in long-run information quality.