The asymptotic power of the Cramer-von Mises test when parameters are estimated from the data is studied under certain local (contiguous) alternatives. Notion of (asymptotic) direction and distance from the null hypothesis of alternatives is introduced, and it is shown that there exist directions with maximum, minimum, and arbitrary intermediate…

A FORTRAN program is provided for calculating the power of statistical tests based on the chi-square distribution. The program produces approximations to the exact probabilities obtained from the noncentral chi-square distribution. The calculation of the noncentrality parameter is discussed for tests of independence and goodness of fit.…

An alternative to Fisher's exact test and the chi-square test for homogeneity in two-by-two tables is developed. The method provides for Type I error rates which are closer to the stated alpha level than either of the alternatives. (JKS)

The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950's, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers. ( Author/JKS)

This paper presents an index of goodness-of-fit for comparing m models over n trials. The index allows for differentiated weighting of the trials as to their importance in the comparison of the models. Several possible weighting schemes are suggested and the conditions on the weights which assure asymptotic normality of the index distribution are…

The Chi-Square Test for Hierarchical Dependency (THD) is presented. The THD tests the hypothesis that all members of a population who possess a certain skill are a subset of the members who possess another skill. This hypothesis is basic to the writings of several prominent theorists, such as Gagne and Piaget. The THD is designed as an improvement…

The relative power of three possible experimental designs under the condition that data is to be analyzed by nonparametric techniques; the comparison of the power of each nonparametric technique to its parametric analogue; and the comparison of relative powers using nonparametric and parametric techniques are discussed. The three nonparametric…

A Monte Carlo technique was used to investigate the small sample goodness of fit and statistical power of several nonparametric tests and their parametric analogues when applied to data which violate parametric assumptions. The motivation was to facilitate choice among three designs, simple random assignment with and without a concomitant variable…

When repeated measures are obtained on the same subjects, interobservation dependencies frequently are generated. The major ways in which these dependencies can arise are illustrated and it is shown how these dependencies may invalidate the use of analysis of variance (ANOVA) and its extension, trend analysis, as methods of evaluating the data of…

This paper reports on a project which has developed the general latent class model as a framework for representation of item responses. This framework can be used to represent data in applications such as mastery tests and other kinds of achievement tests, where there is reason to believe that current foundations are deficient. Methods of…