This Interpretation is based on work published in: https://doi.org/10.1098/rsos.201721
The analysis of the data - from 2,500 members of the UK general public who were asked to rate how risky they felt five different numerical risk levels were (0.1%, 1%, 5%, 12%, 20%) when presented to them in a random order - confirms the collected findings of previous studies.
The numbers were all presented in one of four formats: as percentages, as frequencies out of 100, as frequencies out of 1000, or in the ‘1 in X’ format. Percentages were rated as conveying the lowest risk, ‘x in 100’ as about 10 percentage points higher in risk, ‘x in 1000’ as higher again (about 13 percentage points higher than the percentage figure) and ‘1 in x’ as the highest risk.
Peters et al [1] had also found that frequencies (out of 100) were perceived as more risky than percentages, and this new study extends their findings over two orders of magnitude. In fact, our difference between the perception of percentages and frequencies out of 100 of about 10 percentage points seems to be very similar in a study by Windschitl [2]. The data also confirms the findings of ‘ratio bias’ that are well known from previous literature (see Denes-Raj et al [3] and Reyna & Brainard [4]), where 10 in 1000 is perceived as higher than 1 in 100. However, it is shown here that this effect appears to extend broadly across a range of ‘out of 1000’ figures.
Several psychological bases for these differences in perception have previously been suggested, as reviewed in Reyna & Brainard [4]. One theory is that the more ‘concrete’ a scenario – something that can easily be brought to the imagination – the more likely it seems. Under this theory the ‘1 in x’ numbers, where the ‘x’ is often small, are the most easily imagined as they involve only a small number of imaginary persons. A percentage is a more abstract concept, and so not so easily imagined - seeming less concrete and less likely [3-4]. For the frequencies expressed as ‘x out of 100’ or ‘x out of 1000’, people concentrate on the numerator, as this is a smaller number and so more easily imagined, and so they seem more concrete and riskier than the percentages, and the ‘x out of 1000’ has larger numerators so feels larger (the denominator tends to be neglected) [4]. Hopefully this new data comparing 4 formats directly will allow theorists to draw more conclusions about the psychological basis for these different perceptions (particularly, perhaps, comparing the responses of participants on the first number they saw versus the later numbers, where the analysis discussed here already shows that the response to later numbers was influenced by the context of the previous numbers).
The fact that the variance around the answers of those rating the risks displayed as a percentage was lower than those rating them as a frequency could indicate that these participants were perhaps using the answer slider as a 0–100 number line (even though it was not explicitly labelled), and hence were judging the percentage as a distance along this line. However, the fact that these results are in line with those found in other experiments – including those where participants were asked questions such as whether they would release a prisoner based on their chance of re-offending, with that chance being given as a percentage or a frequency [3] - suggests that they are likely to be robust.
1. Peters E, Hart PS, Fraenkel L. 2011 Informing patients: the influence of numeracy, framing, and format of side effect information on risk perceptions. Med. Decis. Mak. 31, 432–436. (doi:10.1177/0272989X10391672)
2. Windschitl, P. (2002). Judging the accuracy of a likelihood judgment: The case of smoking risk. Journal of Behavioral Decision Making, 15, 19−35.
3. Slovic, P., Monahan, J., & MacGregor, D. G. (2000). Violence risk assessment and risk communication: The effects of using actual cases, providing instructions, and employing probability vs. frequency formats. Law and Human Behavior, 24, 271−296.
4. Reyna, V.F. and Brainerd, C.J., 2008. Numeracy, ratio bias, and denominator neglect in judgments of risk and probability. Learning and individual differences, 18(1), pp.89-107.