In psychology, researchers are often interested in testing hypotheses about mediation, such as testing the presence of a mediation effect of a treatment (e.g., intervention assignment) on an outcome via a mediator. An increasingly popular approach to testing hypotheses is the Bayesian testing approach with Bayes factors (BFs). Despite the growing…

The purpose of the current study is to examine the performance of four information criteria (Akaike's information criterion [AIC], corrected AIC [AICC] Bayesian information criterion [BIC], sample-size adjusted BIC [SABIC]) for detecting the correct number of latent classes in the mixture Rasch model through simulations. The simulation study…

Experimentation is the foundation of science and an important process for students to understand and experience. However, it can be difficult to teach some aspects of experimentation within the time and resource constraints of an academic semester. Interactive models can be a useful tool in bridging this gap. This freely accessible simulation…

Researchers occasionally have to work with an extremely small sample size, defined herein as "N" less than or equal to 5. Some methodologists have cautioned against using the "t"-test when the sample size is extremely small, whereas others have suggested that using the "t"-test is feasible in such a case. The present…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

Planned missing data designs allow researchers to increase the amount and quality of data collected in a single study. Unfortunately, the effect of planned missing data designs on power is not straightforward. Under certain conditions using a planned missing design will increase power, whereas in other situations using a planned missing design…

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…

A primary concern with testing differential item functioning (DIF) using a traditional point-null hypothesis is that a statistically significant result does not imply that the magnitude of DIF is of practical interest. Similarly, for a given sample size, a non-significant result does not allow the researcher to conclude the item is free of DIF. To…

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty,…

Derived a confidence interval for a ratio of correlated mean absolute deviations. Simulation results show that it performs well in small sample sizes across realistically nonnormal distributions and that it is almost as powerful as the most powerful test examined by R. Wilcox (1990). (SLD)

Type I error rates for the Johansen test were estimated using simulated data for a variety of conditions. Results indicate that Type I error rates for the Johansen test depend heavily on the number of groups and the ratio of the smallest sample size to the number of dependent variables. Sample size guidelines are presented. (SLD)

Whether one should use null hypothesis testing, confidence intervals, and/or effect sizes is a source of continuing controversy in educational research. An alternative to testing for statistical significance, known as equivalence testing, is little used in educational research. Equivalence testing is useful in situations where the researcher…

Five methods for testing the hypothesis of independence between two sets of variates were compared through simulation. Results indicate that two new methods, based on robust measures reflecting the linear association between two random variables, provide reasonably accurate control over Type I errors. Drawbacks to rank-based methods are discussed.…

This study developed and investigated an empirical sampling distribution of the congruence coefficient. The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model and…

Differential item functioning (DIF) continues to receive attention both in applied and methodological studies. Because DIF can be an indicator of irrelevant variance that can influence test scores, continuing to evaluate and improve the accuracy of detection methods is an essential step in gathering score validity evidence. Methods for detecting…