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Measurement reliability is a fundamental concept in psychology. It is traditionally considered a stable property of a questionnaire, measurement device, or experimental task. Although intraclass correlation coefficients (ICC) are often used to assess reliability in repeated measure designs, their descriptive nature depends upon the assumption of a common within-person variance. This work focuses on the presumption that each individual is adequately described by the average within-person variance in hierarchical models. And thus whether reliability generalizes to the individual level, which leads directly into the notion of individually varying ICCs. In particular, we introduce a novel approach, using the Bayes factor, wherein a researcher can directly test for homogeneous within-person variance in hierarchical models. Additionally, we introduce a membership model that allows for classifying which (and how many) individuals belong to the common variance model. The utility of our methodology is demonstrated on cognitive inhibition tasks. We find that heterogeneous within-person variance is a defining feature of these tasks, and in one case, the ratio between the largest to smallest within-person variance exceeded 20. This translates into a tenfold difference in person-specific reliability! We also find that few individuals belong to the common variance model, and thus traditional reliability indices are potentially masking important individual variation. We discuss the implications of our findings and possible future directions. The methods are implemented in the R package vICC

A common way to form scores from multiple-item scales is to sum responses of all items. Though sum scoring is often contrasted with factor analysis as a competing method, we review how factor analysis and sum scoring both fall under the larger umbrella of latent variable models, with sum scoring being a constrained version of a factor analysis. Despite similarities, reporting of psychometric properties for sum scored or factor analyzed scales are quite different. Further, if researchers use factor analysis to validate a scale but subsequently sum score the scale, this employs a model that differs from validation model. By framing sum scoring within a latent variable framework, our goal is to raise awareness that (a) sum scoring requires rather strict constraints, (b) imposing these constraints requires the same type of justification as any other latent variable model, and (c) sum scoring corresponds to a statistical model and is not a model-free arithmetic calculation. We discuss how unjustified sum scoring can have adverse effects on validity, reliability, and qualitative classification from sum score cut-offs. We also discuss considerations for how to use scale scores in subsequent analyses and how these choices can alter conclusions. The general goal is to encourage researchers to more critically evaluate how they obtain, justify, and use multiple-item scale scores.

An important tool in the advancement of cognitive science are quantitative models that represent different cognitive variables in terms of model parameters. To evaluate such models, their parameters are typically tested for relationships with behavioral and physiological variables that are thought to reflect specific cognitive processes. However, many models do not come equipped with the statistical framework needed to relate model parameters to covariates. Instead, researchers often revert to classifying participants into groups depending on their values on the covariates, and subsequently comparing the estimated model parameters between these groups. Here we develop a comprehensive solution to the covariate problem in the form of a Bayesian regression framework. Our framework can be easily added to existing cognitive models and allows researchers to quantify the evidential support for relationships between covariates and model parameters using Bayes factors. Moreover, we present a simulation study that demonstrates the superiority of the Bayesian regression framework to the conventional classification-based approach.

The Cognitive Reflection Test, measuring intuition inhibition and cognitive reflection, has become extremely popular because it reliably predicts reasoning performance, decision-making, and beliefs. Across studies, the response format of CRT items sometimes differs, based on the assumed construct equivalence of tests with open-ended versus multiple-choice items (the equivalence hypothesis). Evidence and theoretical reasons, however, suggest that the cognitive processes measured by these response formats and their associated performances might differ (the nonequivalence hypothesis). We tested the two hypotheses experimentally by assessing the performance in tests with different response formats and by comparing their predictive and construct validity. In a between-subjects experiment (n = 452), participants answered stem-equivalent CRT items in an open-ended, a two-option, or a four-option response format and then completed tasks on belief bias, denominator neglect, and paranormal beliefs (benchmark indicators of predictive validity), as well as on actively open-minded thinking and numeracy (benchmark indicators of construct validity). We found no significant differences between the three response formats in the numbers of correct responses, the numbers of intuitive responses (with the exception of the two-option version, which had a higher number than the other tests), and the correlational patterns of the indicators of predictive and construct validity. All three test versions were similarly reliable, but the multiple-choice formats were completed more quickly. We speculate that the specific nature of the CRT items helps build construct equivalence among the different response formats. We recommend using the validated multiple-choice version of the CRT presented here, particularly the four-option CRT, for practical and methodological reasons. Supplementary materials and data are available at https://osf.io/mzhyc/ .

The internet-based assessment of response time (RT) and error rate (ERR) has recently become a well-validated alternative to traditional laboratory-based assessment, because methodological research has provided evidence for negligible setting- and setup-related differences in RT and ERR measures of central tendency. However, corresponding data on potential differences in the variability of such performance measures are still lacking, to date. Hence, the aim of this study was to conduct internet-based mental chronometry in both poorly standardized domestic and highly standardized laboratory environments and to compare the variabilities of the corresponding performance measures. Using the Millisecond Inquisit4Web software, 127 men and women completed three different RT-based cognitive paradigms (i.e., go/no-go, two-back, and number-letter). Each participant completed all paradigms in two environments (i.e., at home and in the laboratory), with a time lag of seven days and in a counterbalanced order. Mixed-effects modeling was employed to estimate the between-setting variability across a comprehensive set of performance measures, including conventional measures of central tendency (i.e., mean RT and ERR) and further measures characterizing the joint distribution of RT/ERR. The latter measures were estimated using the diffusion model. The results suggested negligible differences between the domestic and laboratory settings. Thus, this study provides novel evidence suggesting that the statistical power of internet-based mental chronometry is commonly not compromised by increased environmental variance. The within- and between-session reliabilities were in a satisfactory range-that is, comparable to performance measures collected offline in laboratory settings. In consequence, our results support the broad applicability, robustness, and cost efficiency of mental chronometry assessment using the internet.