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.

这项研究检验了线性或对数函数最能描述数字刺激与人们对这些刺激的判断之间的关系的结果的一般性。在实验1中，一组参与者被告知2是类别x的完美示例，6是类别y的完美示例；另一组被告知相同的6和18。然后，参与者评估了以对数间隔的数字与类别x匹配的程度数字。指数和对数函数最适合执行“ 2 vs. 6”任务的单个参与者的数据；幂函数在“ 6 vs. 18”任务中的作用相同。将参与者的数据平均后，对数函数最适合“ 2 vs. 6”任务产生的评分；幂和指数函数最适合“ 6对18”任务所产生的等级。在实验2中，给两组参与者关于两个数字的相似规则（2对4或4对6），然后评估线性间隔数字与类别x匹配的程度数字。对于这两个任务，大多数人的评分最适合线性函数。但是，当对数据进行平均时，对数函数最适合两个任务所产生的等级。结果突出显示了提供个人数据的重要性，并表明全局和局部数字环境会影响人们对数字的判断。刺激泛化可能是发生局部影响的一种机制。