The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the…

Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…

Errors in oral reading tests result from inaccuracies that tend to creep in because children are not totally consistent while taking a test and from inaccuracies caused when the examiner does not catch a word recognition error, giving credit for an answer that is more wrong than right or vice versa. Every test contains a standard error of…

In all latent trait models there is an equation which describes the probabilistic outcome of the interaction of a person with a known ability and an item with a known difficulty. This modeled outcome can be compared to the observed outcome, and the residuals can be summed over the items to assess the fit of the person to the model. Various…

Stockton Unified School District's successful strategy of using a locally developed, non-normed achievement test to implement the norm referenced model of the Title I Evaluation and Reporting System (Model A2) is described. Documented are the procedures involved in the development of a curriculum guide and test items, and the administration of…

Beginning with the planning stages of the National Assessment of Educational Progress (NAEP), careful attention has been given to the design of efficient probability sampling methods for the selection of class-age respondents and the assignment of test packages. With these methods, it is possible for NAEP researchers to make relatively precise…

The reliability and validity of measurement is analyzed by a sampling model based on generalizability theory. A model for the relationship between a measurement procedure and an attribute is developed from an analysis of how measurements are used and interpreted in science. The model provides a basis for analyzing the concept of an error of…

Procedures are presented for equating simultaneously several tests which have been calibrated by the Rasch Model. Three multiple test equating designs are described. A Full Matrix Design equates each test to all others. A Chain Design links tests sequentially. A Vector Design equates one test to each of the other tests. For each design, the Rasch…

Empirical results are presented as regards the implementation of a latent-trait psychometric model by means of conditional maximum likelihood estimation. Items are scored polychotomously into varying numbers of nominal categories and the test and item characteristic curves and information functions are examined. It is concluded that scoring items…

Five-hundred dichotomously scored response patterns were generated with sequentially independent (SI) items and 500 with dependent (SD) items for each of thirty-six combinations of sampling parameters (i.e., three test lengths, three sample sizes, and four item difficulty distributions). KR-20, KR-21, and Split-Half (S-H) reliabilities were…

This paper, a revision of the original document, "Correcting Partial, Multiple, and Canonical Correlations for Attenuation" (see TM 000 535), presents the formula for correcting coefficients of partial correlation for attenuation due to errors of measurement. In addition, the correction for attenuation formulas for multiple and cannonical…

The correction for attenuation formulas for partial, multiple, and canonical correlation coefficients are discussed and the effects of measurement errors on these statistics are explored. The notation is standardized and the derivation extended where appropriate. It is shown that as the reliabilities of the predictors become more disparate, the…

In this paper problems caused by the existence of errors of measurement are identified for factor analysis, regression analysis, ANOVA, and ANCOVA. At least one detrimental effect is shown to exist for each type of analysis. When a researcher's interest is with infallible variables, he runs the risk of biased results from all of the procedures…

A stochastic disturbance term appears to be essential for structural models in the social sciences. The analysis of such models is considered from the perspective of Joreskog's (1970) general model for the analysis of covariance structure. (For related document, see TM 002 301.) (Author)

We are concerned with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a linear relation. A statistical test of this hypothesis is derived…