Rates and the judgment of government performance

Many official statistics reported to the public appear in the form of rates, such as crimes or diseases per 100,000 people, with the choice of a base number (for example per 1,000,000, per 100,000, or per 1,000) remaining largely a matter of the choices or traditions of statistical agencies. Because prior studies have shown that people tend to judge the likelihood of an event based on the numerator alone (thus exhibiting denominator neglect), we hypothesize that ratio bias influences citizens’ perceptions of risks and conditions in society when interpreting real government statistics. To probe this hypothesis, we designed a pair of survey experiments in which a sample of US adults was randomly allocated to treatment groups receiving the same official statistics about violent crime (from the FBI) and infant mortality (from the CDC) but framed as rates with different base numbers (with an additional group receiving only the absolute number of events). We find some evidence of the expected ratio bias when violent crime is framed in terms of different base numbers, but the results for infant mortality were less consistent. For both violent crime and infant mortality, however, absolute numbers led to perceptions of the greatest risk and least favorable conditions, while individual rates (per person) led to perceptions of the least risk and the most favorable conditions. These findings suggest that citizens’ substantive judgments about risks and conditions in society may be influenced to some extent by the framing of rates by government statistical agencies when reporting official statistics to the public.