This analysis reveals potential issues in testing second order interactions in contingency tables, suggesting reconsideration of standard methods.
Summary The definition of second order interaction in a (2 × 2 × 2) table given by Bartlett is accepted, but it is shown by an example that the vanishing of this second order interaction does not necessarily justify the mechanical procedure of forming the three component 2 × 2 tables and testing each of these for significance by standard methods.
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Esther Simpson (1951) studied this question.
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