Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

A formula is derived for the asymptotic standard error of a true-score equating by item response theory (IRT). The equating method is applicable when the two tests to be equated are administered to different groups along with an "anchor test." Numerical standard errors are shown for an actual equating 1) comparing the standard errors of…

Reliability coefficients of linear combinations of observed scores have anomalous properties which have led to difficulties in the investigation of difference scores and gain scores in test theory. Discrepancies between classical results and correct results obtained from more general formulas, which allow for correlated errors, are examined…

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)

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…

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…

This report provides the statistical tools necessary to measure the extent of error that exists in organizational record data and group survey data. It is felt that traditional methods of measuring error are inappropriate or incomplete when applied to organizational groups, especially in studies of organizational change when the same variables are…