Abstract: PURPOSE: We investigated the eight decision rules for a same-different task, as summarized in Petrov (Psychonomic Bulletin & Review, 16(6), 1011-1025, 2009).
METHODS: 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.
RESULTS: We proved that the false alarm rate p(F) ≤ 1/2 for four of the rules. We also conducted a samedifferent 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 ).
CONCLUSIONS: We found that, using residual distribution analysis, only the two criteria DF rule (DF2) could account for the human data.

Key words: Same-different, Motion discrimination, ROC, Signal detection theory.