This study compared three methods of selecting the best discriminating test items and the resultant test reliability of mastery/nonmastery classifications. These three methods were (a) the agreement approach, (b) the phi coefficient approach, and (c) the random selection approach. Test responses from 1,836 students on a 50-item physical science test were used, from which 90 distinct data sets were generated for analysis. These 90 data sets contained 10 replications of the combination of three different sample sizes (75, 150, and 300) and three different numbers of test items (15, 25, and 35). The results of this study indicated that the agreement approach was an appropriate method to be used for selecting criterion-referenced test items at the classroom level, while the phi coefficient approach was an appropriate method to be used at the district and/or state levels. The random selection method did not have similar characteristics in selecting test items and produced the lowest reliabilities, when compared with the agreement and the phi coefficient approaches.

The odds ratio is one of the most widely used measures of association for 2 × 2 tables. A generalized Yule coefficient transforms the odds ratio into a correlation-like scale with a range from -1 to 1. Yule's Y, Yule's Q, Digby's H, and a new coefficient are special cases of a generalized Yule coefficient. The new coefficient is shown to be similar in value to the phi coefficient. A confidence interval and sample size formula for a generalized Yule coefficient are proposed. The proposed confidence interval is shown to perform much better than the Wald intervals that are implemented in statistical packages.

There are two principal definitions of response-reinforcer contingency in the current literature which Scott and Piatt (1985) have labeled the phi coefficient and Rescorla index. For both definitions, contingencies are sensitive to two conditional probabilities of reinforcement, that given the occurrence and that given the non-occurrence of the criterion response. However, phi coefficient is sensitive also to the probability of the criterion response. In order to examine the relationship between children's perceived contingencies of teacher reinforcements, as defined by the phi coefficient and Rescorla index, and the children's perceptions of competence and measures of their academic performances, 119 5th grade children (54 boys and 65 girls) were studied. Two variables derived specifically from the phi coefficient, the probability of children's responses and the probability of teacher reinforcements, were also examined in their relationship to perceived contingencies and academic performance. In general, children's perceptions of teachers as both contingently rewarding and punishing, as defined by the phi coefficient and Rescorla index, were predictive of good academic performance by the children and teachers rating them as academically competent. Childrens' perceptions of their academic competence were also predictive of their academic performances and teacher ratings. The children's perceptions of academic competence were related to their reporting themselves as likely to produce positive achievement behavior but unlikely to produce negative achievement behavior. No significant relationship was found between the children's perceived contingencies of teacher reinforcements and their perceptions of their own academic competence. These results were discussed as supporting Bandura's self-efficacy theory. Thus, expectations of reinforcement contingency and expectations of personal competence jointly determine actual competence. The contingency findings support the utility of the Children's Perceived Contingencies of Reinforcements Questionnaire as a measure of contingency in the applied setting.

No description available.