This article advocates that introductory statistics be taught by basing all calculations on a single simple margin-of-error formula and deriving all of the standard introductory statistical concepts (confidence intervals, significance tests, comparisons of means and proportions, etc) from that one formula. It is argued that this approach will…

This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect' sizes. Using 1,000 simulations of randomised trials with up to 1,000 cases in each, the paper shows that both approaches are very similar in outcomes, and each…

The statistical power of a significance test is closely related to the length of the confidence interval (i.e. estimate precision). In the case of a "Z" test, the length of the confidence interval can be expressed as a function of the statistical power. (Contains 1 figure and 1 table.)

Recommendations made by major educational and psychological organizations (American Educational Research Association, 2006; American Psychological Association, 2001) call for researchers to regularly report confidence intervals. The purpose of the present paper is to provide support for the use of confidence intervals. To contextualize this…

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…

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.)

This paper offers a practical guide to use null hypotheses significance testing and its alternatives. The focus is on improving the quality of statistical inference in quantitative communication research. More consistent reporting of descriptive statistics, estimates of effect size, confidence intervals around effect sizes, and increasing the…

Confidence intervals are widely accepted as a preferred way to present study results. They encompass significance tests and provide an estimate of the magnitude of the effect. However, comparisons of correlations still rely heavily on significance testing. The persistence of this practice is caused primarily by the lack of simple yet accurate…

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

With great interest the author read the May 2002 editorial in the "Journal for Research in Mathematics Education (JRME)" (King, 2002) regarding changes to the 5th edition of the "Publication Manual of the American Psychological Association" (APA, 2001). Of special note to him, and of great import to the field of mathematics education research, are…

P. A. Frazier, A. P. Tix, and K. E. Barron (2004) highlighted a normal theory method popularized by R. M. Baron and D. A. Kenny (1986) for testing the statistical significance of indirect effects (i.e., mediator variables) in multiple regression contexts. However, simulation studies suggest that this method lacks statistical power relative to some…

If we let all students at Ithaca College be our population, then our Office of Institutional Research can provide us with various parameters about this population. For example, we can obtain parameters regarding SAT scores, birth month, and GPA. Each student samples from the population and we compare their results to the parameters. This allows us…