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,…

Suppose "X" and "Y" are binary exposure and outcome variables, and we have full knowledge of the distribution of "Y," given application of "X." We are interested in assessing whether an outcome in some case is due to the exposure. This "probability of causation" is of interest in comparative…

In any meta-analysis, it is critically important to report the dispersion in effects as well as the mean effect. If an intervention has a moderate clinical impact "on average" we also need to know if the impact is moderate for all relevant populations, or if it varies from trivial in some to major in others. Or indeed, if the…

As a measure of heterogeneity in meta-analysis, the coefficient of variation (CV) has been recently considered, providing researchers with a complement to the very popular I[superscript 2] measure. While I[superscript 2] measures the proportion of total variance that is due to variance of the random effects, the CV is the ratio of the standard…

A disadvantage to online clothes shopping is the inability to try on clothing to test the fit. A class project is discussed where students consult with the CEO of an online mensware clothing company to explore ways in which an online clothing customer can be assured of a superior fit by developing statistical models based on a shopper's height and…

Meta-analysis of proportions is conceptually simple: Faced with a binary outcome in multiple studies, we seek inference on some overall proportion of successes/failures. Under common effect models, exact inference has long been available, but is not when we more realistically allow for heterogeneity of the proportions. Instead a wide range of…

This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

While a dot plot depicts data on a quantitative variable without distortion, a boxplot shows only the five-number summary. For large data, to aid in counting, we propose an IVY plot as a companion to a dot plot. Also, for large data, if the variable is approximately normally distributed, as a companion to a boxplot, we propose a Gaussian interval…

The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

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…

Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to…

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian…

The present study evaluates the updating of long-term memory for duration. After learning a temporal discrimination associating one lever with a standard duration (4 sec) and another lever with both a shorter (1-sec) and a longer (16-sec) duration, rats underwent a single session for learning a new standard duration. The temporal generalization…

When playing card games, how many times should a deck be shuffled in order to achieve randomness? This article shows how card shuffling can be used as a classroom exercise to reinforce construction and interpretation of confidence intervals.

This article provides a conceptual framework for using fixed-interval praise delivery in the educational setting. Fixed-interval praise delivery can be conceptualized as an antecedent-based strategy that disrupts the natural behavior to contingency relationship in a four-term contingency model (Establishing…