Abstract
This study examined the generality of the result that linear or logarithmic functions best describe the relationship between numerical stimuli and people’s judgments about those stimuli. In Experiment 1, one group of participants was told that 2 was a perfect example of category x and 6 was a perfect example of category y; another group was told the same about 6 and 18. The participants then rated how well logarithmically spaced numbers matched the category x number. Exponential and logarithmic functions best fit the data of individual participants who did the “2 vs. 6” task; power functions did the same in the “6 vs. 18” task. When participants’ data were averaged, a logarithmic function was the best fit for the ratings produced by the “2 vs. 6” task; power and exponential functions were the best fits for the ratings produced by the “6 vs. 18” task. In Experiment 2, two groups of participants were given similar rules about two numbers (2 vs. 4 or 4 vs. 6) and then rated how well linearly spaced numbers matched the category x number. For both tasks, most individuals’ ratings best fit a linear function. When the data were averaged, though, a logarithmic function was the best fit for the ratings produced by both tasks. The results highlight the importance of presenting individuals’ data and suggest that global and local numerical contexts influence people’s judgments about the numbers. Stimulus generalization may be a mechanism by which the local influence occurs.
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Notes
Exactly what represents (a verb) and representation (a noun) mean is unclear; see Greco (1995) for a discussion of the many meanings of these terms. In cognitive psychology, representation (O) refers to hypothetical physiological or computational mechanisms. The characteristics of a representation are inferred from responses (R) to stimuli (S). Or we can use the terms represents and representation simply as shorthand for the production of—or in reference to—the functional relation between real numbers (S) and judgments (R) based on those numbers. That is the usage we adopt here.
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We thank Armando Machado for this helpful comments and insightful discussions related to an earlier version of this manuscript.
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Silva, F.J., Silva, P.N. & Silva, K.M. Judging Numbers: Global and Local Contextual Effects in Individual and Group Data. Psychol Rec 72, 285–304 (2022). https://doi.org/10.1007/s40732-021-00467-w
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DOI: https://doi.org/10.1007/s40732-021-00467-w