Researchers often seek to synthesize results of multiple studies on the same topic to draw statistical or substantive conclusions and to estimate effect sizes that will inform power analyses for future research. The most popular synthesis approach is meta-analysis. There have been few discussions and applications of other synthesis approaches.…

Obtaining relevant data and conveying limitations of the results are two integral components to a successful statistical analysis. It is difficult for students to internalize a deep understanding of these components using only curated, textbook-style examples. Through hands-on data collection, this activity provides a channel for students to…

Students often believe that statistical significance is the only determinant of whether a quantitative result is "important." In this paper, I review traditional null hypothesis statistical testing to identify what questions inferential statistics can and cannot answer, including statistical significance, effect size and direction,…

Multimodal learning analytics (MMLA) has increasingly been a topic of discussion within the learning analytics community. The Society of Learning Analytics Research is home to the CrossMMLA Special Interest Group and regularly hosts workshops on MMLA during the Learning Analytics Summer Institute (LASI). In this paper, we articulate a set of 12…

Understanding human judgement and decision making during visual inspection of data is of both practical and theoretical interest. While visualizing data is a commonly employed mechanism to support complex cognitive processes such as inference, judgement, and decision making, the process of supporting and scaffolding cognition through effective…

The central purpose of this article is to provide an overview of the many ways in which special educators can generate and think about causal inference to inform policy and practice. Consideration of causality across different lenses can be carried out by engaging in multiple method and mixed methods ways of thinking about inference. This article…

Single case studies can provide vital contributions to theory-testing in social science studies. Particularly, by applying the process-tracing method, case studies can test theoretical frameworks through a rigorous research design that ensures substantial empirical leverage. While most scholarly contributions on process-tracing focus on either…

The purpose of this paper is to provide an easy template for the inclusion of the Bayes factor in reporting experimental results, particularly as a recommendation for articles in the "Journal of Problem Solving." The Bayes factor provides information with a similar purpose to the "p"-value--to allow the researcher to make…

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

In the wake of an increasing political commitment to evidence-based decision making and evidence-based educational reform that emerged with the No Child Left Behind effort, the question of what counts as evidence has become increasingly important in the field of science education. In current public discussions, academics, politicians, and other…

Confidence intervals (CIs) and effect sizes are essential to encourage meta-analytic thinking and to accumulate research findings. CIs provide a range of plausible values for population parameters with a degree of confidence that the parameter is in that particular interval. CIs also give information about how precise the estimates are. Comparison…

This paper proposes an argument framework for the teaching of null hypothesis statistical testing and its application in support of research. Elements of the Toulmin (1958) model of argument are used to illustrate the use of p values and Type I and Type II error rates in support of claims about statistical parameters and subject matter research…

Using Microsoft® Excel, several interactive, computerized learning modules are developed to illustrate the Central Limit Theorem's appropriateness for comparing the difference between the means of any two populations. These modules are used in the classroom to enhance the comprehension of this theorem as well as the concepts that provide the…

This paper provides a framework for developing sampling designs in mixed methods research. First, we present sampling schemes that have been associated with quantitative and qualitative research. Second, we discuss sample size considerations and provide sample size recommendations for each of the major research designs for quantitative and…

Describes the logic of statistical testing in the Fisher and Neyman-Pearson approaches. Reviews some common misinterpretations of basic concepts behind statistical tests. Analyzes the philosophical and psychological issues that can contribute to these misinterpretations. Suggests possible ways in which statistical education might contribute to the…