Testing equality of correlated proportions with incomplete data on both responses

Two test statistics are proposed for testing the equality of two correlated proportions when some observations are missing on both responses. The performance of these tests in terms of size and power is compared with other tests by means of Monte Carlo simulations. The proposed tests are easily computed and compare favorably with other tests.     

Tests for equality of several alpha coefficients when their sample estimates are dependent

In a variety of measurement situations, the researcher may wish to compare the reliabilities of several instruments administered to the same sample of subjects. This paper presents eleven statistical procedures which test the equality ofm coefficient alphas when the sample alpha coefficients are dependent. Several of the procedures are derived in detail, and numerical examples are given for two. Since all of the procedures depend on approximate asymptotic results, Monte Carlo methods are used to assess the accuracy of the procedures for sample sizes of 50, 100, and 200. Both control of Type I error and power are evaluated by computer simulation. Two of the procedures are unable to control Type I errors satisfactorily. The remaining nine procedures perform properly, but three are somewhat superior in power and Type I error control.A more detailed version of this paper is also available.     

An alternative test for multisample sphericity

A test for multisample sphericity based on the efficient scores criterion is obtained as an alternative to the likelihood ratio test developed by Mendoza.     

The derivation of some tests for the rasch model from the multinomial distribution

The present paper is concerned with testing the fit of the Rasch model. It is shown that this can be achieved by constructing functions of the data, on which model tests can be based that have power against specific model violations. It is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product-multinomial models. The model tests are presented in two versions: one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation.I am indebted to Norman Verhelst and Niels Veldhuijzen for their helpful comments. Requests for reprints should be sent to Cees A. W. Glas, Cito, PO Box 1034, 6801 MG Arnhem, THE NETHERLANDS.     

Use of an ambiguous-sample procedure to establish a cue to forget in pigeons

Pigeons were trained on a variation of the matching-to-sample task in which on double-sample trials two samples, one associated with each of the comparison stimuli, were presented successively. Responding to the comparison associated with the first sample was reinforced on half the double-sample trials, and responding to the comparison associated with the second sample was reinforced on the remaining half. One of two postsample stimuli was presented following the termination of each colored sample. A vertical line was presented after a correct or target sample, and a horizontal line was presented after an incorrect or interfering sample. With extended training, each bird demonstrated above-chance accuracy on double-sample trials, providing prima facie evidence that one or both of the postsample stimuli exerted control over matching behavior. Experiment 2 provided evidence that the horizontal line functioned as a cue to forget the code activated by the preceding sample stimulus. It was concluded that a condition sufficient to establish a postsample stimulus as a cue to forget is that the postsample immediately follow presentation of a sample that, if it were to control test responding, would lead to nonreinforcement.     

Short-term memory for responses: the "choose-small" effect

Pigeons' short-term memory for fixed-ratio requirements was assessed using a delayed symbolic matching-to-sample procedure. Different choices were reinforced after fixed-ratio 10 and fixed-ratio 40 requirements, and delays of 0, 5, or 20 s were sometimes placed between sample ratios and choice. All birds made disproportionate numbers of responses to the small-ratio choice alternative when delays were interposed between ratios and choice, and this bias increased as a function of delay. Preference for the small fixed-ratio alternative was also observed on "no-sample" trials, during which the choice alternatives were presented without a prior sample ratio. This "choose-small" bias is analogous to results obtained by Spetch and Wilkie (1983) with event duration as the discriminative stimulus. The choose-small bias was attenuated when the houselight was turned on during delays, but overall accuracy was not influenced systematically by the houselight manipulation.     

Extensions of the partial credit model

The partial credit model, developed by Masters (1982), is a unidimensional latent trait model for responses scored in two or more ordered categories. In the present paper some extensions of the model are presented. First, a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters. Secondly, two statistical tests for evaluating model fit are presented: the former test has power against violation of the assumption about the ability distribution, the latter test offers the possibility of identifying specific items that do not fit the model.The authors are indepted to professor Wim van der Linden and Huub Verstralen for their helpful comments.     

Comparing the variances of dependent groups

Recently several new attempts have been made to find a robust method for comparing the variances ofJ dependent random variables. However, empirical studies have shown that all of these procedures can give unsatisfactory results. This paper examines several new procedures that are derived heuristically. One of these procedures was found to perform better than all of the robust procedures studied here, and so it is recommended for general use.The author would like to thank the reviewers for their very helpful comments on an earlier draft of this paper.     

Effects of delayed reinforcement on infant vocalization rate.

Three previous studies have failed to demonstrate conditioning in infants using a 3-s delay of reinforcement. The effects of a delayed reinforcement schedule on vocalization rates therefore were explored in a single-subject repeated-reversal experimental design for 3 4- to 6-month-old normally developing infants. Each infant received delayed social reinforcement from his or her parent for vocalizing. The comparison condition was a schedule of differential reinforcement of behavior other than vocalizations to control for elicitation by social stimulation. An operant level of infant vocalizations was the initial condition, after which the differential reinforcement schedule was implemented in an across-subjects multiple baseline design. Infants' vocalization rates increased above levels measured during differential reinforcement following onset of the delayed reinforcement condition. Also, vocalization rates decreased during differential reinforcement compared to operant levels. The successful use of delayed reinforcement schedules with infants in this study, as opposed to others, is discussed in terms of procedural differences among them.     

Directed forgetting of elements in compound samples.

Pigeons were trained in a delayed matching-to-sample procedure in which the sample stimuli consisted of a compound of color (red or green) and spatial location (left or right). A postsample cue (houselight on or off) signaled whether color matching or location matching would be required following the delay. In Experiment 1, the reduction in performance on probe trials (in which the houselight condition was reversed relative to that on regular trials) was greater for location matching than for color matching. The birds showed overt mediational behavior during the delays on location-matching trials. On color-matching trials, the birds exhibited behavior during delays that might have interfered with that mediational behavior. In Experiment 2, the houselight condition was changed shortly before presentation of the comparison stimuli on probe trials. Accuracy of location matching was reduced when the cue initially signaled color matching and was then changed to signal location matching, whereas matching accuracy was not reduced by a change in the opposite direction. Accuracy of color matching was reduced by a change in illumination level from dark to light, regardless of type of the relevant dimension signaled by houselight illumination. Discussion of these findings focuses on the variables critical to establishment of an effective cue to forget.