We investigated the eight decision rules for a same-different task, as summarized in Petrov (Psychonomic Bulletin & Review, 16(6), 1011–1025, 2009). These rules, including the differencing (DF) rule and the optimal independence rule, are all based on the standard model in signal detection theory. Each rule receives two stimulus values as inputs and uses one or two decision criteria. We proved that the false alarm rate p(F) ≤ 1/2 for four of the rules. We also conducted a same-different rating experiment on motion discrimination (n = 54), with 4^∘ or 8^∘ directional difference. We found that the human receiver operating characteristic (ROC) spanned its full range [0,1] in p(F), thus rejecting these four rules. The slope of the human Z-ROC was also < 1, further confirming that the independence rule was not used. We subsequently fitted in the four-dimensional (p_AA, p_AB, p_BA, p_BB) space the human data to the remaining four rules—DF and likelihood ratio rules, each with one or two criteria, where p_XY = p(responding “different” given stimulus sequence XY). We found that, using residual distribution analysis, only the two criteria DF rule (DF2) could account for the human data.

我们研究了针对相同不同任务的 8 条决策规则，如 Petrov ( Psychonomic Bulletin & Review, 16 (6), 1011–1025, 2009) 中总结的那样。这些规则，包括差分（DF）规则和最优独立规则，都是基于信号检测理论中的标准模型。每个规则接收两个刺激值作为输入并使用一个或两个决策标准。我们证明了四个规则的误报率p ( F ) ≤ 1/2。我们还对运动判别 ( n = 54)进行了相同不同的评级实验，具有 4 ^∘或 8 ^∘方向差异。我们发现人类接收器操作特性 (ROC) 跨越了其全范围 [0,1]p ( F )，从而拒绝这四个规则。人类Z -ROC的斜率也 < 1，进一步证实没有使用独立规则。我们随后在四维 ( p _{A A} , p _{A B} , p _{B A} , p _{B B} ) 空间中将人类数据拟合到其余四个规则——DF 和似然比规则，每个规则都有一个或两个标准，其中p _{X Y} = p（给定刺激序列X Y）。我们发现，使用残差分布分析，只有两个标准 DF 规则 (DF2) 可以解释人类数据。