In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

During timing tasks, the brain learns the statistical distribution of target intervals and integrates this prior knowledge with sensory inputs to optimise task performance. Daily events can have different temporal statistics (e.g., fastball/slowball in baseball batting), making it important to learn and retain multiple priors. However, the rules…

A reference interval provides a basis for physicians to determine whether a measurement is typical of a healthy individual. It can be interpreted as a prediction interval for a new individual from the overall population. However, a reference interval based on a single study may not be representative of the broader population. Meta-analysis can…

Network meta-analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast-based meta-analysis models, but recent studies have revealed the resultant confidence intervals of average…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

Diagnostic accuracy studies often evaluate diagnostic tests at several threshold values, aiming to make recommendations on optimal thresholds for use in practice. Methods for meta-analysis of full receiver operating characteristic (ROC) curves have been proposed but still have deficiencies. We recently proposed a parametric approach that is based…

Systematic reviews and meta-analyses are the cornerstones of evidence-based medicine and inform treatment, diagnosis, or prevention of individual patients as well as policy decisions in health care. Statistical methods for the meta-analysis of intervention studies are well established today. Meta-analysis for diagnostic accuracy trials has also…

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

This paper introduces a dataset and associated analysis of the scores of National Football League (NFL) games over the 2012, 2013, and first five weeks of the 2014 season. In the face of current media attention to "lopsided" scores in Thursday night games in the early part of the 2014 season, t-test results indicate no statistically…

Research has shown that forest plots are a gold standard in the visualization of meta-analytic results. However, research on the general interpretation of forest plots and the role of researchers' meta-analysis experience and field of study is still unavailable. Additionally, the traditional display of effect sizes, confidence intervals, and…

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

In a recent study, G. Kuhn and Z. Dienes (2005) reported that participants previously exposed to a set of musical tunes generated by a biconditional grammar subsequently preferred new tunes that respected the grammar over new ungrammatical tunes. Because the study and test tunes did not share any chunks of adjacent intervals, this result may be…

Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we…

When taking mathematics courses, students will sometimes ask their recurring question, "When will I ever use this in real life?" Educators are often unable to provide a direct connection between what they are teaching in the classroom and a real-life application. However, when such an opportunity does arise, they should seize it and…