People’s placement of numbers on number lines sometimes shows linear and sometimes compressive scaling. We investigated whether people’s placement of numbers was affected by their range and distribution, as indicated by Parducci’s (Psychological Review, 72, 407–418, 1965) range-frequency theory. Experiment 1 found large compressive effects when the endpoints were 1 and 10¹⁶. Experiment 2 showed compression when 14 logarithmically distributed numbers were placed on a line marked 1–1,000 and close to linear scaling when the numbers were linearly distributed. Thus, we found both range and frequency effects on compression. Where compression arose, it was not as pronounced as that predicted by logarithmic scaling, but analyses of the results from Experiments 1 and 2 indicate this was not explained by participants switching between linear and logarithmic scaling.

人们在数字线上的数字放置有时显示线性比例，有时显示压缩比例。我们调查了人们的数字位置是否受到其范围和分布的影响，正如Parducci的（Psychological Review，72，407-418，1965）范围频率理论所表明的那样。实验1发现端点为1和10 ¹⁶时有较大的压缩效果。实验2显示了将14个对数分布的数字放在标记为1–1,000的直线上时的压缩，当数字呈线性分布时接近线性比例。因此，我们发现范围和频率对压缩的影响。在出现压缩的地方，它不如对数缩放所预测的那样明显，但是对实验1和2的结果的分析表明，参与者没有在线性和对数缩放之间切换来解释这一点。