The height + width rule seems solid: Reply to Bogartz

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The conclusion that 5-yr-olds judge rectangle area by a height + width rule, as determined by the authors (see record 1980-22999-001), is counterintuitive, and R. Bogartz's (see record 1980-23005-001) concern over it is understandable. Fortunately, his question about sufficient statistical power is readily answered. A power calculation based on the rectangle design common to Exps II, III, V, and VI shows that if the physicalistic, height × width rule had been operative, it would have been detected with probability greater than .99. But little or no hint of the height × width pattern was seen in any of the variety of conditions in the authors' 8 experiments; instead the visible pattern in the data is that of the height + width rule. These results point to a general-purpose adding rule in young children's judgments of quantity. Important support for this concept of a general-purpose adding rule comes from extensive work by the 2nd author showing that judgments of numerosity follow a length + density rule. (14 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved)

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