Are mice right-handed or left-handed? In a study of this question, 320 mice of a highly inbred strain were tested for paw preference by observing which forepaw-right or left -they used to retrieve food from a narrow tube. Each animal was tested 50 times, for a total of 320 × 50 = 16.000 observations. The results were as follows42:

Suppose we assign an expected frequency of 8,000 to each category and perform a goodness-of-fit test; we find that X2s = 4.16, so at a = 0.05 we would reject the hypothesis of a 1:1 ratio and find that there is sufficient evidence to conclude that mice of this strain are (slightly) biased toward use of the left paw. This analysis contains a fatal flaw. What is it?

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Right Left Number of observations 78718.129