Showing papers on "Random effects model published in 1972"

A Combination of F-statistics

Abstract: This paper presents a statistic composed of independent F-statistics, testing the same hypothesis, combined in the manner in which Zelen (1957) combines intra and interblock information for incomplete block models with fixed treatment effects and random block effects. This work is applicable to certain two factor random effect models with interaction and unequal number of readings per cell. When the number of readings remains constant within groups of levels of one factor the data yields a number of similar but independent F-stastics, from intragroup and intergroup sources.

A Computer Program for Selecting Optimum Sample Size and Number of Levels in a one Way Random Effects Analysis of Variance

Abstract: effects, but in the variance of the population from which these effects were randomly selected. For example, suppose that a population of school teachers is available to teach reading to first grade pupils using a certain method. It is decided that the method will be adopted for use provided its success is not heavily dependent on the personalities of individual teachers. A random sample of teachers is drawn and randomly assigned to a random sample of classes of first grade pupils. The dependent variable (a standardized reading test) is selected and a one way analysis of variance, random effects model, is to be used to test the hypothesis that there are no significant differences among the teachers. Researchers faced with the preceding problem are often ignorant of how many teachers to select and the number of students to as-

Exact results for extensions of twofold nested anova for variance components

Abstract: Consider the standard twofold nested design for analysis of variance with random effects (a variance components model). The usual assumption of zero means and equal variances is made for each of the three types of random variables that occur in this balanced model, and the random variables are assumed to be mutually uncorrelated. The customary normality assumption is also made when tests or confidence regions are desired. This standard model is extended, in several ways, by adding one, two or three additional random terms (of an “error” nature) to the standard model. The extensions apply to very much more general situations than does the standard model. Exact procedures are obtained, however, for investigating all of the mean effect and the three types of variance components, and for investigating various subsets of these parameters. The generality level for an extended model depends on which of the parameters are investigated simultaneously, and is greater for a subset of a set of the parameters than for the set. Most of the investigation procedures are different from those customarily used for the standard model.

Estimation of the mean and variance components in some random effects models with composited samples

Abstract: A method is presented for estimating the mean, variance components , and their variances in a two-way crossed classification where the experimental units are composited. Estimates of the variance components are obtained using a procedure similar to Henderson's method I in which the sums of squares are computed using weighted or unweighted observations or cell means. Four estimation procedures were suggested and compared. The results show that any best estimation procedure depends on the relative sizes of the variance components. Conditions on the various design parameters were investigated to determine when exact tests of hypotheses on the variance components can be made. For all estimation procedures considered, the designs should be completely balanced if exact F-tests are required. Using some of the results from the two-way crossed classification, estimates of the mean, variance components and their variances in 2-and 3-stage nested designs were derived. These nested designs allowed for the experimental units to be composited in all but the last stage. Four estimation procedures were proposed and evaluated. For both the 2-and 3-staqe nested designs any best estimation procedure depends on the relative sizes of the variance components.