The surface form x problem size interaction in cognitive arithmetic: evidence against an encoding locus

Sixty-four university students received simple addition problems with operands presented as arabic digits (e.g. 2 + 3, 8 + 6) or as English number words (two + three, eight + six). Operands either were displayed simultaneously or sequentially with the left operand appearing 800 ms before the right operand. Consistent with previous findings, word problems were slower than digit problems and this word-format cost was larger for large- than small-number problems. The central question addressed by this experiment concerned whether this Format x Size interaction arises during problem encoding processes or in subsequent retrieval or production processes. In the simultaneous condition, both operands would contribute to format-related differences in encoding, whereas in the sequential condition encoding differences would arise only in connection with the second operand. Critically, however, the Format x Size interaction did not differ between the sequential and simultaneous conditions, although the experiment had ample power to detect such an effect. The results argue that the Format x Size interaction does not arise during encoding, but instead arises during calculation or production processes.