Abstract
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.
Highlights
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 remaining largely a matter of the choices or traditions of statistical agencies
A sample of US adults was randomly allocated to treatment groups receiving the same official statistics about violent crime and infant mortality but framed as rates with different base numbers
We report regressions that test the difference of treatment group means from a reference group, defined as the government’s standard reporting ratio used in actual public reports by the Federal Bureau of Investigation (FBI) and Centers for Diseases Control and Prevention (CDC)
Summary
We designed and implemented a pair of survey experiments and embedded them in an omnibus online survey of US adults conducted in February 2018 Both experiments had the same design with one presenting statistics on violent crime and the other infant mortality (see Supplement, Appendix A). Infant mortality is reported as deaths per 100,000 live births, with a nationwide rate at the time of survey design of 582.1 (National Center for Health Statistics, 2015). It should be noted that infant mortality is sometimes reported in the form of deaths per 1,000 live births (see National Center for Health Statistics, 2016) In both experiments, we preserved the real ratio but varied the base of the ratios across experimental groups as follows: 1,000,000; 100,000; 10,000; and 1,000. The two experiments were part of the same block of questions within the survey instrument, which included other short survey experiments (in separate blocks randomized within the survey)
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