Tests for differences between several small proportions

Sensitivity of patch tests with rubber mixes: Results of the Information Network of Departments of Dermatology from 1990 to 1993*1

This study of the stability of teacher behavior over time is formulated through two major questions: (1) Is the behavior of an individual teacher consistent over time? and (2) Are individual differences among teachers consistent over time Regrettably, the first question has rarely been considered in previous investigations of the stability of teacher behavior, and empirical research on the second question has been marxed by considerable confusion. In this paper we develop statistical procedures for answering each of these questions. Approaches and methods of previous studies of temporal stability are reevaluated. In addition, methods for assessing the stability of teacher behavior across contexts are described. Observational data on classroom teachers are used throughout to illustrate our new approaches and methous for the stud:' of stability of behavior. ASSESSING THE STABILITY OF TEACHER BEHAVIOR' David Rogosa, Robert E. Floden, and John B. Willett 2 Questions About Stability Answers to the question, "Is teacher behavior stable?" have been sought by researchers for the past half-century. Despite the many extensive studies of teacher behavior, affirmative answers to this question have been rare. For example, Borich (1977) states, "The results of these studies suggest that teacher behavior may be unstable across long periods of time and content" (p. 300) 3 . Moreover, researchers lack confidence in the results of these research efforts; the conclusi.m of Shavelson and Dempsey-Atwood (1976) that "(a) most 'This research was supported primarily by a grant from the Program for Teaching and Instruction of the National Institute of Education, United States Department of Education. (Grant #NIE-G-81-0087) In addition, the work of the first and third authors was supported in part by grants from the Spencer Foundation; the work of the second author was supported in part by the Institute for Research on Teaching, College of Education, Michigan State University. 2 David Rogosa is an Assistant Professor at the Stanford University School of Education. Robert E. Floden is an IRT senior researcher and an MSU associate professor of teacher education and educational psychology. John B. Willett is a graduate student at the Stanford University School of Education. The authors wish to thank Donald Veldman of the University of Texas at Austin and Thomas Moon of California State College in Pennsylvania for providing them with the classroom observation data used in this paper. 3 The recent review by Darling-Hammond, Wise, and Pease (1983) summarizes the research on stability of teaching behavior as follows: "The bottom-line question is, Does a given teacher exhibit the same kinds of behavior at different points in time and within different teaching contexts? In general, the answer is 'no,' especially with regard to measures of specific, discrete teaching behaviors" (p. 299).

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Assessing the stability of teacher behavior

Three simple interval estimates for the risk ratio in inverse sampling are considered. The first two interval estimates are derived on the basis of Fieller's Theorem and the delta method with the logarithmic transformation, respectively. The third interval estimate is derived on the basis of an F-test statistic proposed by BENNETT (1981) for testing equal probabilities of a disease between two comparison groups when the disease is rare. To evaluate the performance of these three methods, a Monte Carlo simulation is used to compare the actual coverage probability with the nominal confidence level for each method and to estimate the expected length of the corresponding confidence interval in a variety of situations. On the basis of the results found in the simulation, we have concluded that the method with the logarithmic transformation is either equivalent to or better than the other two methods for all situations considered here.

Confidence intervals for the risk ratio in cohort studies under inverse sampling

The exact distribution of the maximum and minimum frequencies of Multinomial/Dirichlet and Multivariate Hypergeometric distributions of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact Multinomial/Dirichlet and Multivariate Hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

The exact distribution of the maximum, minimum and the range of Multinomial/Dirichlet and Multivariate Hypergeometric frequencies

The use of the negative binomial, or the method of inverse sampling (e.g. (1), (2)), is suggested for prospective studies. This method usually has the advantage of fostering an early decision on the statistical significance of some etiological factor in examining successive patient records. Several limiting situations for the distribution are discussed regarding the prevalence of a disease. An example illustrates the method.

On the Use of the Negative Binomial in Epidemiology

The negative binomial distribution (N.B.) was previously proposed (BENNETT, 1981) in the estimation of and tests of significance for the relative risk (ψ) in prospective studies in epidemiology. This paper discusses the application of the N.B. model in combining estimates of ψ from a series of prospective studies and in statistical tests of the equality of these estimates.

On Combining Estimates of Relative Risk Using the Negative Binomial Mode

This paper considers the exact distribution of the X2 index of dispersion and -2 log (likelihood ratio) tests for the hypothesis of homogeneity of c independent samples from a common binomial population. The exact significance levels and power of these tests under ‘logit’ alternatives are compared numerically for the cases: c = 3, 4, 5 and various sample sizes. n1 = 5,10 for i = 1,…, c.

Small Sample Distribution and Power of the Binomial Index of Dispersion and Log Likelihood Ratio Tests

The usual definitions of sensitivity, specificity and predictive value of a diagnostic test T refer only to the situation of the presence or absence of disease. There is then question of the appropriate extensions of these definitions in cases where there are more than two diagnostic categories, especially with ordered or graded responses. This paper deals with some aspects of this problem. An example with the data of BERGESON and STEINFELD (1974) on gradings of fever in children by palpation is analyzed, using the methods discussed in this paper.

On Generalized Indices of Diagnostic Efficiency

Categorical data on n patients are classified according to the results on an initial clinical test T, and also with respect to a subsequent and definitive diagnosis D. In this paper the sensitivity (=), specificity (=) and predictive values (=v) are discussed with reference to the tetrachoric correlation model based on the bivariate normal density (e.g. PEARSON, 1901; KENDALL and STUART, 1972, II, p. 317). The result of HAMDAN (1970) concerning the equivalence of the tetrachoric rt and the maximum likelihood estimate of the correlation coefficient is utilized in this paper to obtain a test of significance concerning rt, and also the relation between the tetrachoric function w and the relative risk ψ for the 2X2 table.

Use of the tetrachoric correlation model in assessing clinical tests

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