Percentage estimation of proportion as a function of element type, exposure time, and task.

What very small numbers mean.

“…Most psychophysical research on the relation between perceived and estimated proportions has concentrated on quantities between 1% and 99% (e.g., see Begg, 1974;Brooke & MacRae, 1977;Shuford, 1961;Teigen, 1973;Tversky & Fox, 1995;Varey et al, 1990). Generally, researchers present different auditory or visual stimuli and ask participants to estimate the proportion of a target stimulus.…”

“…The implicit assumption of numerical equivalence is prevalent in studies of psychophysics (e.g., Gescheider, 1988;Marks, 1974;Marks & Algom, 1998;Stevens, 1956Stevens, , 1986, risk estimation (e.g., D. J. Cohen & Bruce, 1997;Gladis, Michela, Walter, & Vaughan, 1992;Hansen, Hahn, & Wolkenstein, 1990;Mickler, 1993;van der Velde, van der Plight, & Hooykaas, 1994), mathematics (e.g., Ashcroft, 1992;Ashcroft & Kirk, 2001;Campbell & Xue, 2001), reasoning (e.g., Kahneman & Tversky, 1972;Tversky & Kahneman, 1974;Wanke, Schwarz, & Bless, 1995), and probability estimation (e.g., Begg, 1974;Brooke & MacRae, 1977;Hollands & Dyre, 2000;Shuford, 1961;Spence, 1990;Teigen, 1973;Tversky & Fox, 1995;Varey, Mellers, & Birnbaum, 1990), to name just a few. The assumption of numerical equivalence, however, should not be made lightly because people's interpretation of numbers likely affects the data they produce, and thus the conclusions that researchers draw.…”

“…Nevertheless, researchers often make an implicit assumption that people interpret these numerical formats equivalently (termed the assumption of numerical equivalence). The implicit assumption of numerical equivalence is prevalent in studies of psychophysics (e.g., Gescheider, 1988;Marks, 1974;Marks & Algom, 1998;Stevens, 1956Stevens, , 1986 Schwarz, & Bless, 1995), and probability estimation (e.g., Begg, 1974;Brooke & MacRae, 1977;Hollands & Dyre, 2000;Shuford, 1961;Spence, 1990;Teigen, 1973;Tversky & Fox, 1995;Varey, Mellers, & Birnbaum, 1990), to name just a few. The assumption of numerical equivalence, however, should not be made lightly because people's interpretation of numbers likely affects the data they produce, and thus the conclusions that researchers draw.…”

“…We report five experiments that assess how people interpret and represent relative frequencies and decimals that denote very low proportions (i.e., proportions below 1%). We chose to examine very low proportions for three reasons: (a) There is extensive evidence that people do not interpret numerical labels (i.e., any individual symbol representing quantity) symbolizing very low proportions accurately (for a review, see Rothman & Kiviniemi, 1999), (b) numerical labels symbolizing very low proportions are vital to the communication of issues ranging from health risks to pollution (e.g., Environment Protection Agency, 1991), and (c) people's interpretation of relatively common quantities (between 1% and 99%) has been studied (e.g., see Begg, 1974;Brooke & MacRae, 1977;Hollands & Dyre, 2000;Shuford, 1961;Spence, 1990;Teigen, 1973;Tversky & Fox, 1995;Varey et al, 1990) and therefore can serve as a comparison group.…”

Error patterns in the judgment and production of numerical proportions

“…Because subjects considered that they had made a mistake on these occasions, their recorded judgments were adjusted by subtracting the response from 100. Shuford (1961) had also noted that such errors occur. He did not associate them with any particular response strategy, though he commented that "the extreme errors were due not to random fluctuations in S's perception of the matrix but rather to reversals in the association of element type and proportion" (p, 435).…”