Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical…

For ease of instruction in the classroom, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. Likewise, the Kruskal-Wallis statistic may be rewritten in terms of pairwise differences in individual…

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…

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,…

Structural equation modeling is an ideal data analytical tool for testing complex relationships among many analytical variables. It can simultaneously test multiple mediating and moderating relationships, estimate latent variables on the basis of related measures, and address practical issues such as nonnormality and missing data. To test the…

The natural experiment proposed in this article extracts three stories from boxes of "100 paper clips". The activity requires students to apply three lessons from inferential statistics, starting with a hypothesis test and including confidence intervals as well as tolerance intervals.

Summary Employing a Wald confidence interval to test hypotheses about population proportions could lead to an increase in Type I or Type II errors unless the hypothesized value, p0, is used in computing its standard error rather than the sample proportion. Whereas the Wald confidence interval to estimate a population proportion uses the sample…

"p" values are commonly reported in quantitative research, but are often misunderstood and misinterpreted by research consumers. Our aim in this article is to provide special educators with guidance for appropriately interpreting "p" values, with the broader goal of improving research consumers' understanding and interpretation…

Reproducibility crises have arisen in psychology and other behavioral sciences, spurring efforts to ensure research findings are credible and replicable. Although reforms are occurring at professional levels in terms of new publication parameters and open science initiatives, the credibility and reproducibility of undergraduate research deserves…

For decades, instructional communication scholars have relied predominantly on cross-sectional survey methods to generate empirical associations between effective teaching and student learning. These studies typically correlate students' perceptions of their instructor's teaching behaviors with subjective self-report assessments of their own…

In the e-learning context, social network analysis (SNA) can be used to build understanding around the ways students participate and interact in online forums. This study contributes to the growing body of research that uses statistical methods to test hypotheses about structures in social networks. Specifically, we show how statistical analysis…

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

Data collected from surveys can result in hundreds of variables and thousands of respondents. This implies that time and energy must be devoted to (a) carefully entering the data into a database, (b) running preliminary analyses to identify any problems (e.g., missing data, potential outliers), (c) checking the reliability and validity of the…

Current practices in study design and data analysis have led to low reproducibility and replicability of findings in fields such as psychology, medicine, biology, and economics. Because gifted education research relies on the same underlying statistical and sociological paradigms, it is likely that it too suffers from these problems. This article…

Emerging professionals, particularly senior-level undergraduate and graduate students in kinesiology who have an interest in physical education for individuals with and without disabilities, should understand the basic assumptions of the quantitative research paradigm. Knowledge of basic assumptions is critical for conducting, analyzing, and…