About twenty years ago, Dehaene et al. (1993) asked participants to perform a parity task twice, each time with a different mapping of response hand to parity value. The participants responded with a keypress and latency served as the dependent variable. The two mappings are depicted in Panel (A) of Figure 1. The yellow background cells correspond to one mapping of parity to the possible responses: the odd (red) numbers are responded to by a left key-press and the even (blue) numbers are responded to by a right key-press. The green background cells correspond to the alternative mapping: the even (blue) numbers are responded to by the left key-press and the odd (red) numbers are responded to by a right key-press.
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Tzelgov et al. (2013) studied this question.
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