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There are three different warning stimuli (CSs) in this experiment (symbolized by red, horizontal lines, and vertical lines, and designated A, B and X) Two and only two of these CSs are presented together (“in compound”) on every training trial--either AX or BX.Thus, one CS (X) occurs on every trial, while the other two (A & B) occur each occurs on a random half of the trials together with (in compound with) X. A random half of the training trials terminate in reinforcement (shock or food depending on the version of the experiment). The only difference between the groups is how the reinforced trials are distributed relative to the AX and BX trials. For one group, the reinforcement occurs on half the AX trials and half the BX trials. For the other, it occurs only on the BX trials. Note that for both groups X is paired with reinforcement on half the trials. If temporal pairing were all the mattered, the conditioning (learned responding) to X should be the same in both groups. But it is not. Subjects in the AX(1/2), BX(1/2) Group respond almost exclusively to X, while subjects in the AX(+), BX(-) Group do not respond to X at all; they respond almost exclusively to A. In statistical terminology, X accounts for most of the variance in the first group (is the best predictor of reinforcement) and A accounts for most of the variance in the second group. Moreover, X in the first group and A in the second group account for all the variance that can be accounted for. That is, it is not possible to improve on the prediction of reinforcement by considering other CSs in addition to them. Thus, the subjects behave like sophisticated statisticians.