Is 1/10 > 10/100? The effect of denominator salience on perceptions of base rates of health risk

Abstract This paper examines how people process base rate information ( r = n / N ) to estimate risk. We propose that the more salient the denominator of a base rate ( N ) is, the more the information draws attention to the people on which it is based. Information concerning smaller populations or sample groups ( N = 1000 vs. 100,000), as well as geographically proximate populations, makes it easier for consumers to bring to mind the population involved. This increased salience of the denominator increases the attention paid to the numerator and translates into perceptions of greater risk. This investigation consists of three studies. Study 1 shows that when a constant numerator (viz., number of deaths by a certain cause in a given age group) is expressed in terms of a large denominator (viz., number of deaths by a given cause across all ages), the resulting smaller nominal rate, r , leads to a lower perceived risk than when expressed in terms of a larger denominator (viz., number of deaths by a given cause across all age groups). Studies 2 and 3 show that the smaller the nominal scale of the denominator (e.g., n /1000 vs. 100 n /100,000), the population size (e.g., a campus of 32,000 vs. a state of 35 million), and the geographical distance of the population group in question (e.g., closer vs. further), the higher the estimated risk for a given base rate. Combined, the studies show that risk estimates are biased towards the numerator information when the denominator on which they are compared against is salient, as information presented in this way allows consumers to more easily bring to mind the population on which it is based. Implications for health risk communication include restating percentage base rates in terms of levels of incidence in a population group that is easy to bring to mind (i.e., smaller, more proximate populations). “Seventeen million Americans have diabetes, and … nearly six million of them don't know it.” 1 “Percentage of Americans suffering from alcohol abuse or alcoholism in their lifetime: Men = 42%, Women = 19.5% … A previous report on the same data found that 4.7% of adults reported alcohol abuse in 2001–2002, and 3.8% reported alcoholism.” 2 “Eight out of 10 crashes involve drivers who are drowsy, chatting on cell phones, applying make-up or otherwise distracted from the road ahead …” 3 “Mental Illness will hit half in U.S.” 4 “Attention Deficit may affect 4 in 100 adults.” 5 “More than 11 percent of all Latino students – and 15 percent of Latino girls – said they had attempted suicide, according to the report issued Thursday by the U.S. Centers for Disease Prevention and Control…. In the category of drug use, 1 in 8 Latino students said they had used cocaine, 1 in 10 had used ecstasy, 1 in 11 methamphetamines, and 1 in 28 heroin.” 6 “According to the National Institutes of Health, an estimated 1,400 student deaths … are blamed on alcohol…. About 79 percent of UC students reported they had used alcohol in the past year.” 7 “Nearly one-third binge at least once a month… The behavior… is engaged in monthly by 5 million high school students … this number equals 31 percent of the nation's high school students.” 8 “In 1999, roughly 1 out of every 13 U.S. high school students reported making a suicide attempt in the previous 12 months. More teens and young adults die from suicide than cancer, heart disease, AIDS, birth defects, stroke, pneumonia, influenza, and chronic lung disease combined.” 9 “Did you know … More Americans die from suicide (28,332) than from homicide (16,137)?” 10 “Judge told VA stalls on care while 18 veterans a day commit suicide.” 11