Institute of Cognitive Neuroscience, University College London, London, England.
J Exp Psychol Gen. 2011 Nov;140(4):693-706. doi: 10.1037/a0024255.
Previous investigations on the subjective scale of numerical representations assumed that the scale type can be inferred directly from stimulus-response mapping. This is not a valid assumption, as mapping from the subjective scale into behavior may be nonlinear and/or distorted by response bias. Here we present a method for differentiating between logarithmic and linear hypotheses robust to the effect of distorting processes. The method exploits the idea that a scale is defined by transformational rules and that combinatorial operations with stimulus magnitudes should be closed under admissible transformations on the subjective scale. The method was implemented with novel variants of the number line task. In the line-marking task, participants marked the position of an Arabic numeral within an interval defined by various starting numbers and lengths. In the line construction task, participants constructed an interval given its part. Two alternative approaches to the data analysis, numerical and analytical, were used to evaluate the linear and log components. Our results are consistent with the linear hypothesis about the subjective scale with responses affected by a bias to overestimate small magnitudes and underestimate large magnitudes. We also observed that in the line-marking task, participants tended to overestimate as the interval start increased, and in the line construction task, they tended to overconstruct as the interval length increased. This finding suggests that magnitudes were encoded differently in the 2 tasks: in terms of their absolute magnitudes in the line-marking task and in terms of numerical differences in the line construction task.
先前关于数字表示主观量表的研究假设，量表类型可以直接从刺激-反应映射中推断出来。这不是一个有效的假设，因为从主观量表到行为的映射可能是非线性的，并且可能会受到反应偏差的扭曲。在这里，我们提出了一种方法，可以区分对数和线性假设，并且对扭曲过程的影响具有鲁棒性。该方法利用了量表是由变换规则定义的这一思想，并且刺激幅度的组合运算应该在主观量表的可接受变换下封闭。该方法使用新型数字线任务变体实现。在线标记任务中，参与者在由各种起始数字和长度定义的区间内标记阿拉伯数字的位置。在线构建任务中，参与者给定部分来构建区间。使用数值和分析两种替代数据分析方法来评估线性和对数分量。我们的结果与主观量表的线性假设一致，响应受到对小幅度高估和对大幅度低估的偏差的影响。我们还观察到，在线标记任务中，随着区间起始的增加，参与者倾向于高估，在线构建任务中，随着区间长度的增加，他们倾向于过度构建。这一发现表明，在这两个任务中，幅度被以不同的方式编码：在线标记任务中是根据其绝对值，在线构建任务中是根据数值差异。
