The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

There has been much controversy over the null hypothesis significance testing procedure, with much of the criticism centered on the problem of inverse inference. Specifically, p gives the probability of the finding (or one more extreme) given the null hypothesis, whereas the null hypothesis significance testing procedure involves drawing a…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

Latent transition analysis (LTA) was initially developed to provide a means of measuring change in dynamic latent variables. In this article, we illustrate the use of a cognitive diagnostic model, the DINA model, as the measurement model in a LTA, thereby demonstrating a means of analyzing change in cognitive skills over time. An example is…

This note is concerned with a latent variable modeling approach for the study of differential item functioning in a multigroup setting. A multiple-testing procedure that can be used to evaluate group differences in response probabilities on individual items is discussed. The method is readily employed when the aim is also to locate possible…

The use of confidence intervals (CIs) as an addition or as an alternative to null hypothesis significance testing (NHST) has been promoted as a means to make researchers more aware of the uncertainty that is inherent in statistical inference. Little is known, however, about whether presenting results via CIs affects how readers judge the…

Measurement invariance in the partial credit model (PCM) can be conceptualized in several different but compatible ways. In this article the authors distinguish between three forms of measurement invariance in the PCM: step invariance, item invariance, and threshold invariance. Approaches for modeling these three forms of invariance are proposed,…

An exact probability test for use with certain Likert-type scales is presented. The procedure assumes equally-spaced points, independence of subjects' responses, and that each point has an equal likelihood of response for each subject. Tables for critical values are presented. (Author/JKS)

Problems of type I errors associated with multiple comparisons in the same experiment are discussed. A table is provided for the rapid determination of experimentwise alpha level when a number of independent statistical tests are employed in the same experiment. Suggested applications and the rationale for this procedure are supplied. (Author/JKS)

A computer program for testing the association of two nominal variables using Fisher's exact probability test is described. Theoretical corrections according to recent literature are made. Various methods of discovering the source of association at the cellwise level are given. (Author/JKS)

When comparing k normal populations an investigator might want to know the probability that the population with the largest population mean will have the largest sample mean. This paper describes and illustrates methods of approximating this probability when the variances are unknown and possibly unequal. (Author/BW)

This paper provides a mathematical algorithm for Fisher's exact probability test which is adaptable to contingency tables greater than two by two, and which provides the user with an index of predictive association designed for crosstabulations of nominal level variables. (Author/JKS)

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

The controversy regarding the admissibility of one-tailed tests of hypotheses was examined. Rather than taking a stand with regard to whether the one-or the two-tailed test is the most seriously flawed, a procedure is developed which can capitalize on the advantages of each. (RC)