The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

Measures initially designed to be single-trait often yield data that are compatible with both an essentially unidimensional factor-analysis (FA) solution and a correlated-factors solution. For these cases, this article proposes an approach aimed at providing information for deciding which of the two solutions is the most appropriate and useful.…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

Much of the science reported in the media depends on correlation coefficients. But the size of correlation coefficients depends, in part, on the reliability with which the correlated variables are measured. Understanding this is a statistical literacy issue.

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

Intrinsic motivation to learn involves engaging in learning opportunities because they are seen as enjoyable, interesting, or relevant to meeting one's core psychological needs. As a result, intrinsic motivation is associated with high levels of effort and task performance. Students with greater levels of intrinsic motivation demonstrate strong…

Cronbach's coefficient alpha has been widely known and used in educational research. Many education research practitioners, however, may not be aware of the potential issues when the main assumptions for coefficient alpha are violated in research practice. This paper provides a brief discussion about two assumptions that may make the use and…

This paper presents a method for equating writing assessments using pairwise comparisons which does not depend upon conventional common-person or common-item equating designs. Pairwise comparisons have been successfully applied in the assessment of open-ended tasks in English and other areas such as visual art and philosophy. In this paper,…

Assuming item parameters on a test are known constants, the reliability coefficient for item response theory (IRT) ability estimates is defined for a population of examinees in two different ways: as (a) the product-moment correlation between ability estimates on two parallel forms of a test and (b) the squared correlation between the true…

In adolescence research, the treatment of measurement reliability is often fragmented, and it is not always clear how different reliability coefficients are related. We show that generalizability theory (G-theory) is a comprehensive framework of measurement reliability, encompassing all other reliability methods (e.g., Pearson "r,"…

This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach's alpha, are calculated using a Pearson…

This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error…

This article introduces new statistics for evaluating score consistency. Psychologists usually use correlations to measure the degree of linear relationship between 2 sets of scores, ignoring differences in means and standard deviations. In medicine, biology, chemistry, and physics, a more stringent criterion is often used: the extent to which…

According to the Simple View of Reading, reading ability can be divided into decoding and language comprehension. In the present study, decoding and comprehension's contribution to reading ability was studied both in children with reading difficulties and in children with typical reading ability. Decoding and comprehension was further divided into…

The rise in the prevalence of autism creates a need for a reliable and valid measure of attitudes towards autism. The current study describes the development of a brief 16-item measure of Societal Attitudes towards Autism (SATA) that exhibits sound psychometric properties and has a demonstrated ability to discriminate between expert and general…