Judging Numbers: Global and Local Contextual Effects in Individual and Group Data

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.