What very small numbers mean.

Abstract

This article presents a theoretical and experimental framework for assessing the biases associated with the interpretation of numbers. This framework consists of having participants convert between different representations of quantities. These representations should include both variations in numerical labels that symbolize quantities and variations in displays in which quantity is inherent. Five experiments assessed how people convert between relative frequencies, decimals, and displays of dots that denote very low proportions (i.e., proportions below 1%). The participants demonstrated perceptual, response, and numerical transformation biases. Furthermore, the data suggest that relative frequencies and decimals are associated with different abstract representations of amount.

Evidence for direct retrieval of relative quantity information in a quantity judgment task: Decimals, integers, and the role of physical similarity.

“…Furthermore, Cohen et al (2002) has demonstrated that people's understanding of decimals are seemingly independent of their understanding of relative frequencies (e.g., 50 in 120). This reveals a close link between numerical format and quantity representation, at least in the case of decimals and relative frequencies.…”

“…It is therefore not unreasonable to assume that the mental representation of decimals is different from that of integers. My colleagues and I have previously demonstrated the uniqueness of decimal representation by revealing that the mental representation of decimals is different from and perhaps independent of the mental representation of relative frequencies (Cohen, Ferrell, & Johnson, 2002). In addition, there is some evidence that fractions are processed by the individual integer components, rather than the holistic proportion they represent (Bonato, Fabbri, Umilta, & Zorzi, 2007).…”

Cross-Format Physical Similarity Effects and Their Implications for the Numerical Cognition Architecture

“…1 is a simplified depiction of a strict Multiple Quantity Representation model (e.g., Cohen, 2009Cohen, , 2010Cohen, Ferrell, & Johnson, 2002;Gonzalez 1 Dehaene's (1992) Triple Code model assumes that the format modules link to one and other and each format module links to the same abstract representation. This architecture is a version of Seidenberg and McClelland's (1989) distributed model of word recognition.…”

Effects of comparative claims in prescription drug direct-to-consumer advertising on consumer perceptions and recall

“…For example, we did not examine risk-related comparisons, such as "Drug X does not require blood tests." Given our finding that introducing comparative benefit claims may influence beliefs about the risks of the drug, a direct comparison of riskrelated information would reveal whether the opposite would also be true, as suggested in previous research (Bowman, 2002;Cohen et al, 2002;Davis, 2007;Hoek, 2008;Kees et al, 2008).…”

“…Nonetheless, these findings illustrate the potential for comparative DTC ads to influence perceptions of the benefits and risk of advertised drugs, possibly leading consumers to magnify benefit and minimize risk. In fact, previous DTC research has consistently found that various DTC advertising strategies that increase perceptions of benefit also decrease perceptions of risk (Bowman, 2002;Cohen et al, 2002;Davis, 2007;Hoek, 2008;Kees et al, 2008). Consequently, a comparative claim that focuses on the superior effectiveness of a drug may also influence risk perceptions.…”