Researchers often have hypotheses concerning the state of affairs in the population from which they sampled their data to compare group means. The classical frequentist approach provides one way of carrying out hypothesis testing using ANOVA to state the null hypothesis that there is no difference in the means and proceed with multiple comparisons…

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a robust inference for internal validity, that is, the PIV, as a robustness index…

There is a wealth of evidence that people's reasoning is influenced by explanatory considerations. Little is known, however, about the exact form this influence takes, for instance about whether the influence is unsystematic or because of people's following some rule. Three experiments investigate the descriptive adequacy of a precise proposal to…

Model evaluation -- the process of making inferences about the performance of predictive models -- is a critical component of predictive modelling research in learning analytics. We survey the state of the practice with respect to model evaluation in learning analytics, which overwhelmingly uses only naïve methods for model evaluation or…

This dissertation consists of three manuscripts. The manuscripts contribute to a budding "methodological reform" currently taking place in quantitative second-language (L2) research. In the first manuscript, the researcher describes an empirical investigation on the application of two well-known effect size estimators, eta-squared (eta…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

A few studies suggest that gifted children with dyslexia have better literacy skills than averagely intelligent children with dyslexia. This finding aligns with the hypothesis that giftedness-related factors provide compensation for poor reading. The present study investigated whether, as in the native language (NL), the level of foreign language…

One of the vexing problems in the analysis of SSD is in the assessment of the effect of intervention. Serial dependence notwithstanding, the linear model approach that has been advanced involves, in general, the fitting of regression lines (or curves) to the set of observations within each phase of the design and comparing the parameters of these…

This study investigated how gifted children with dyslexia might be able to mask literacy problems and the role of possible compensatory mechanisms. The sample consisted of 121 Dutch primary school children that were divided over four groups (typically developing [TD] children, children with dyslexia, gifted children, gifted children with…

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue…

A new process model of the interplay between memory and judgment processes was recently suggested, assuming that retrieval fluency--that is, the speed with which objects are recognized--will determine inferences concerning such objects in a single-cue fashion. This aspect of the fluency heuristic, an extension of the recognition heuristic, has…

Demonstrates the use of the well-known Bayes factor in the Bayesian literature for hypothesis testing and model comparison in general two-level structural equation models. Shows that the proposed method is flexible and can be applied to situations with a wide variety of nonnested models. (SLD)

Through Monte Carlo simulation, respective normative and intuitive strategies for covariation assessment and Bayesian inference are compared. Results indicate that better performance in both tasks results from considering alternative hypotheses, although not necessarily using a normative strategy. Conditions under which intuitive strategies may be…