Quantitative results from empirical studies are common in the field of Scholarship of Teaching and Learning (SoTL), but it is important to remain aware of what the results from our studies can, and cannot, tell us. Oftentimes studies conducted to examine teaching and learning are constrained by class size. Small sample sizes negatively influence…

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

A common mistake in analysis of cluster randomized experiments is to ignore the effect of clustering and analyze the data as if each treatment group were a simple random sample. This typically leads to an overstatement of the precision of results and anticonservative conclusions about precision and statistical significance of treatment effects.…

Very little explanatory power is required in order for regressions to exhibit statistical significance. This article discusses some of the causes and implications. (Contains 2 tables.)

We are grateful to the commentators for providing many stimulating and valuable observations. The main point of our article was to call attention to the overestimation of individual differences correlations in a subset of neuroimaging papers. To structure our discussion of these comments, we list the main points from our paper, note where…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

An alternative analysis of the two-group single response variable design is proposed. It involves the classification of experimental units to populations represented by the two groups. Three real data sets are provided to illustrate the utility of the classification analysis. A table of sample sizes required for the analysis is presented.…

The normative implications of applying significance tests in evaluation research are examined. The authors conclude that evaluators often make normative decisions, based on the traditional .05 significance level in studies with small samples. Additional reporting of the magnitude of impact, the significance level, and the power of the test is…

Two stage multiple-comparison procedures give an exact solution to problems of power and Type I errors, but require equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes. (Author/BW)

The effects of some restraints not included in the classical assumptions of the F- and H-Test (e.g., correlation of mean and sample size) were examined in a simulation design. Also simulated was a situation in which two assumptions were not met simultaneously. (Author/BW)

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…

Power is an indicator of the ability of a statistical analysis to detect a phenomenon that does in fact exist. The issue of power is crucial for social science research because sample size, effects, and relationships studied tend to be small and the power of a study relates directly to the size of the effect of interest and the sample size.…

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.…

The method of unweighted means in the multivariate analysis of variance with unequal sample sizes was investigated. By approximating the distribution of the hypothesis sums-of-squares-and-cross-products with a Wishart distribution, multivariate test statistics were derived. Monte Carlo methods and a numerical example illustrate the technique.…

This paper discusses the sample size problem and four factors affecting its solution: significance level, statistical power, analysis procedure, and effect size. The interrelationship between these factors is discussed and demonstrated by calculating minimal sample size requirements for a variety of research conditions. (Author)