In mixed methods approaches, statistical models are used to identify "nested" cases for intensive, small-n investigation for a range of purposes, including notably the examination of causal mechanisms. This article shows that under a commonsense interpretation of causal effects, large-n models allow no reliable conclusions about effect…

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

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…

The purpose of this document is to describe the methods RAND used to analyze achievement for 23 personalized learning (PL) schools for the 2012-13 through 2013-14 academic years. This work was performed at the request of the Bill & Melinda Gates Foundation (BMGF), as part of a multi-year evaluation contract. The 23 schools were selected from a…

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…

Undergraduate biology education is undergoing dramatic changes, emphasizing student training in the "tools and practices" of science, particularly quantitative and problem-solving skills. We redesigned a freshman ecology lab to emphasize the importance of scientific inquiry and quantitative reasoning in biology. This multi-week investigation uses…

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…

The reaction that occurs when Mentos are added to bottled soft drinks has become a staple demonstration in earth science courses to explain how volcanoes erupt. This paper presents how this engaging exercise can be used in a marketing research course to provide hands-on experience with problem formation, hypothesis testing, and causal research. A…

In this article, the authors address the practicalities of how data should be presented, summarized, and interpreted. There are no exact rules; indeed there are valid concerns that exact rules may be inappropriate and too prescriptive. New procedures evolve, and new methods may be needed to deal with new types of data, just as people know that new…

Personalized, online homework was used to supplement textbook homework, quizzes, and exams for one section of a course in material and energy balances. The objective of this study was to test the hypothesis that students using personalized, online homework earned better grades in the course. The online homework system asks the same questions of…

Statistics teaching should not be carried out in the same way for all kinds of university students. Instead, teaching statistics should take into account the different fields of study that students have chosen. For example, students of sciences or engineering have different interests and backgrounds compared to students of any social or juridical…

Studies that examine the impacts of education interventions on key student, teacher, and school outcomes typically collect data on large samples and on many outcomes. In analyzing these data, researchers typically conduct multiple hypothesis tests to address key impact evaluation questions. Tests are conducted to assess intervention effects for…

Methods to compare population means in the univariate case and population mean vectors in the multivariate case are presented in terms of hypotheses tested by various procedures. Tests relevant to each hypothesis are described and compared in terms of maximizing power while controlling Type I error rates over the widest variety of conditions. (SLD)

Contrasts or comparisons can be used to investigate specific differences between means. Contrasts, as explained by B. Thompson (1985, 1994) are coding vectors that mathematically express hypotheses. The most basic categories of contrasts are planned and unplanned. The purpose of this paper is to explain the relative advantages of using planned…

A particular strategy for investigating effects resulting from a multivariate analysis of variance (MANOVA) is proposed. The strategy involves multiple two-group multivariate analyses. The two groups result from considering multivariate pairwise group contrasts or multivariate complex group contrasts. Assuming a given two-group analysis yields…