Analysis-of-Variance Models and their use in a Three-Way Design without Replication
THE TECHNIQUE of analysis of variance has enjoyed rapidly increasing popularity in the treat ment of data collected in educational experiments and surveys. Although the interpretation of the results of such analyses is closely dependent o n the assumption made about the model underlying the use of the technique, most textbooks have offered little or no guidance about the choice of models or their relationship to the conclusions to be drawn. As a result, some of the potential ities of the analysis of variance are not being realized, and the technique has on occasion been misused. It is the purpose of this paper to at tempt to state and illustrate as simply as possi ble the implications of the use of each of thr e e elementary analysis-of-variance models, using data gathered in a series of observ a t i o n s of classroom teachers. In the belief that the verbal behavior o f a teacher is a valid measure of the social emotional climate of her classroom, Withall (9) developed a technique for classifying statements made by a teacher during a typical class period into seven categories. Using this technique, Mitzel and Rabinowitz (6) made two series of four visits each to each of four classroom teachers at intervals of about one week and made tal 1 i e s of each teacher's remarks independently until approximately 100 had been reported. The pro portion of statements which fell into the learner centered category, when transformed to an an gle by the arc sine transformation (4), is known as the Climate Index. The 32 values of this In dex obtained by the two observers on four visits to the four teachers are shown in Table I. These are the data that will be used for illustrative pur poses in the discussion to follow.