Evaluating scale comparability in international large-scale assessments depends on measurement invariance (MI). The root mean square deviation (RMSD) is a standard method for establishing MI in several programs, such as the Programme for International Student Assessment and the Programme for the International Assessment of Adult Competencies.…

Likert-type item is the most popular response format for collecting data in social, educational, and psychological studies through scales or questionnaires. However, there is no consensus on whether parametric or non-parametric tests should be preferred when analyzing Likert-type data. This study examined the statistical power of parametric and…

Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated.…

This article tackles the problem of what should be done with real textual data that are contaminated by errors of recording, particularly when the data contain words that are misspelt, unintentionally or otherwise. (Contains 5 tables and 2 figures.)

Purpose: The purpose of this study was to investigate the characteristics of missing physical activity (PA) data of children and youth. Method: PA data from the Chinese City Children and Youth Physical Activity Study ("N" = 2,758; 1,438 boys and 1,320 girls; aged 9-17 years old) were used for the study. After the data were sorted by the…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

This study serves as a teaching aid for teachers of introductory statistics. The aim of this study was limited to determining various sample sizes when estimating population proportion. Tables on sample sizes were generated using a C[superscript ++] program, which depends on population size, degree of precision or error level, and confidence…

Statistical modeling of school effectiveness data was originally motivated by the dissatisfaction with the analysis of (school-leaving) examination results that took no account of the background of the students or regarded each school as an isolated unit of analysis. The application of multilevel analysis was generally regarded as a breakthrough,…

This brief considers the problem of using value-added scores to compare teachers who work in different schools. The author focuses on whether such comparisons can be regarded as fair, or, in statistical language, "unbiased." An unbiased measure does not systematically favor teachers because of the backgrounds of the students they are…

This paper considers the model of school effectiveness (SE) currently dominant in research, policy and practice in England (although the concerns it raises are international). It shows, principally through consideration of initial and propagated error, that SE results cannot be relied upon. By considering the residual difference between the…

Secondary data analysis as a methodological approach is not without its critics. Indeed, three main objections to the use of secondary data analysis in social research stand out: first that because of the socially constructed nature of social data, the act of reducing it to a simple numeric form cannot fully encapsulate its complexity. Secondly,…

Several robust absolute deviation statistics have been developed recently. Two such correlation coefficients are developed and discussed, one for ranked data and another for interval level data. The standard error and range of the coefficients are given. The algebraic relationship between the coefficients and three widely used correlation…

Under the assumption of normalcy, a formula is derived for the reliability of the maximum score. It is shown that the maximum score is more reliable than each of the single observations but less reliable than their composite score. (Author/LMO)

Critiques H. W. Marsh and K.-T. Hau's (1996) assertion that parsimony is not always desirable when assessing model-fit on a particular counterexample drawn from Marsh's previous research. This counterexample is neither general nor valid enough to support such a thesis and it signals an oversight of extant, stochastic models justifying correlated…

In response to H. W. Marsh and K.-T. Hau's (1996) article on the potential for inferential errors when parsimony is rewarded in the evaluation of overall fit of structural equation models, a design-sensitive adjustment to the standard parsimony ratio is proposed. This ratio renders a more reasonable upper bound than does the standard parsimony…