bility that the i-th independent variable, or set of independent variables, has a different effect on the post-TUCE in the two groups. If such is the case, Soper's multiple regression estimates reflect erroneous aggregation between groups demonstrating different post-TUCE eftects. The customary way to check for such aggregation or distribution coefficient biases is to use an Arnold Zellner unrelated regression testing procedure [9] or a Gregory Chow type coefficient stability testing procedure [2]. Although I have additional comments concerning the lack of error term specifications and analysis, I believe the comments above are sufficient to indicate major statistical weaknesses in Soper's contention that his quantitative evidence suggests that PI material can be used effectively in large-enrollment principles courses when used in combination with a set of optional, objective quizzes.
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John C. Soper (1976) studied this question.