Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

This research project applied Projective Reflection (PR) as a theoretical and methodological framework to "facilitate" learning as identity exploration. PR was used to iteratively design and implement three versions of "Virtual City Planning," an augmenting virtual learning environment (AVLE) course in a science museum…

We build on identity-based motivation theory to integrate research on in-person and virtual learning environments so that we can articulate which features of virtual learning environments are likely to support or impede learning and identity exploration. Although students experience their identities as stable anchors for meaning-making and action,…

Despite increasing calls for science education that utilizes immersive technologies and authentically model scientific inquiry, little is known about how well curricula leveraging these technologies impact students' science identity. This paper presents a mixed-methods study of identity exploration in 7th grade science students using a three-week…

This paper discusses the role of Multi-User Virtual Environments (MUVEs) in the development of epistemic learner identity. MUVEs might help educators create the types of tasks and intellectual open spaces helping students with learner identity development in the information age. MUVEs can create new possibilities for dissemination and sharing of…

This article discusses the sample size requirements for the interaction, row, and column effects, respectively, by forming a linear contrast for a 2×2 factorial design for fixed-effects heterogeneous analysis of variance. The proposed method uses the Welch t test and its corresponding degrees of freedom to calculate the final sample size in a…

This study investigated changes in elementary school students' (n = 140) situational interest as a function of achievement goal orientation profiles and task characteristics. The authors repeatedly measured situational interest during a simulated science learning task in 2 task conditions that differed in the concreteness of the task elements. The…

Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…

Formulas to determine the necessary sample sizes for parametric tests of group comparisons are available from several sources and appropriate when population distributions are normal. However, in the context of nonnormal population distributions, researchers recommend Yuen's trimmed mean test, but formulas to determine sample sizes have not been…

In this study, the authors assess several strategies created on the basis of the Mantel-Haenszel (MH) procedure for conducting differential item functioning (DIF) analysis with small samples. One of the analytical strategies is a loss function (LF) that uses empirical Bayes Mantel-Haenszel estimators, whereas the other strategies use the classical…

Uses computer simulation to study the effects on parametric and nonparametric statistical tests when assumptions of normality and homogeneity of variance are violated. Results reveal that nonparametric methods are not always acceptable substitutes for parametric methods in research studies when parametric assumptions are not satisfied. (SLD)

Evaluated the use of Mallow's C(p) and Wherry's adjusted R squared (R. Wherry, 1931) statistics to select a final model from a pool of model solutions using computer generated data. Neither statistic identified the underlying regression model any better than, and usually less well than, the stepwise selection method, which itself was poor for…

Used Johnson's transformation (N. Johnson, 1978) with approximate test statistics to test the homogeneity of simple linear regression slopes in the presence of nonnormality and Type I, Type II or complete heteroscedasticity. Computer simulations show that the proposed techniques can control Type I error under various circumstances. (SLD)

Simulated population data were used to compare relative performances of the modification index and C. Chou and P. M. Bentler's Lagrange multiplier test (a multivariate generalization of a modification index) for four levels of model misspecification. Both indices failed to recover the true model except at the lowest level of misspecification. (SLD)

The power functions of Student t tests performed on initial scores, ordinary ranks, 3 kinds of modular ranks, and dichotomies were investigated for 1 normal and 3 nonnormal distributions using 2 samples of 26 simulated scores each. Advantages of extending the rank transformation concept are discussed. (SLD)