Huynh

Some approximate tests for repeated measurement designs

Four approximate tests are considered for repeated measurement designs in which observations are multivariate normal with arbitrary covariance matrices. In these tests traditional within-subject mean square ratios are compared with critical values derived fromF distributions with adjusted degrees of freedom. Two of them—the ∈ approximate and the improved general approximate (IGA) tests—behave adequately in terms of Type I error. Generally, the IGA test functions better than the ∈ approximate test, however the latter involves less computations. In regards to power, the IGA test may compete with one multivariate procedure when the assumptions of the latter are tenable.

Performance of traditional f tests in repeated measures designs under covariance heterogeneity

This study investigates the performance of two traditional F tests, one for main effects and the other for interaction in repeated measures designs under several conditions of covariance heterogeneity. Overall, the test for interaction is more vulnerable than the one for main effects. Distortion in the level of significance is less serious for the case of equal group size.

A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables

By use of an inequality of Marcus and Lopes for elementary symmetric functions, a new proof is presented for the following result by Ghurye and Wallace: Given that the independent random variablesXj are Bernoulli with success probabilitypj (θ) strictly between 0 and 1 and nondecreasing inθ, the sum ΣXj has monotone likelihood ratio.

Performance of Students with Disabilities under Regular and Oral Administrations of a High-Stakes Reading Examination.

This study examined the effect of oral administration accommodations on test structure and student performance on the Reading test of the South Carolina High School Exit Examination (HSEE). The examination was given at Grade 10 and was untimed; hence, students were permitted as much time as they needed to answer all the questions. Three groups of students were studied. The 1st group consisted of students with disabilities (SWD) who were given the test under oral administration. Students in the 2nd group were SWD who were given the regular forms without oral accommodations. The last group comprised students without disabilities who took the regular forms, also without accommodations. It was found that the internal (factorial) structure of the HSEE test remained stable across these students groups. In addition, it was found that, after controlling for major background variables, HSEE performance of SWD under oral administration accommodations was equal to that of SWD (presumably with milder disabilities) under regular administration. It was concluded that oral administration accommodation served to level the playing field for students whose disabilities were presumably severe enough to require oral accommodations.

A nonrandomized minimax solution for passing scores in the binomial error model

A nonrandomized minimax solution is presented for passing scores in the binomial error model. The computation does not require prior knowledge regarding an individual examinee or group test data for a population of examinees. The optimum passing score minimizes the maximum risk which would be incurred by misclassifications. A closed-form solution is provided for the case of constant losses, and tables are presented for a variety of situations including linear and quadratic losses. A scheme which allows for correction for guessing is also described.

Decomposition of a Rasch partial credit item into independent binary and indecomposable trinary items

For each Rasch (Masters) partial credit item, there exists a set of independent Rasch binary and indecomposable trinary items for which the sum of the scores and the partial credit score have identical probability density functions. If each indecomposable trinary item is further expressed as the sum of two binary items, then the binary items are positively dependent and cannot be both of the Rasch type.

On Score Locations of Binary and Partial Credit Items and Their Applications to Item Mapping and Criterion-Referenced Interpretation

A procedure is presented for locating on the latent trait scale the scores (or responses) of items that follow the three-parameter logistic (3PL) and monotone partial credit (MPC) models. The procedure is based on a Bayesian updating of the item information and is identical to locating the score at the latent trait value that maximizes the Bock score information. Applications are provided in terms of selecting items or score categories for criterion-referenced interpretation and mapping and analyzing score categories.

Two simple classes of mastery scores based on the beta-binomial model

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to posta priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.

On equivalence between a partial credit item and a set of independent Rasch binary items

Given a Masters partial credit item withn known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. The conditions are those for the existence ofn positive values with predetermined elementary symmetric functions and include the requirement that then step difficulties form an increasing sequence.

Statistical Inference for two Reliability Indices in Mastery Testing Based on the Beta-Binomial Model

In mastery testing the raw agreement index and the kappa index may be estimated via one test administration when the test scores follow beta-binomial distributions. This paper reports formulae, tables, and a computer program which facilitate the computation of the standard errors of the estimates. Illustrative applications are provided in the form of confidence intervals, hypothesis testing, and minimum sample sizes in reliability studies for mastery tests.