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…

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…

Meta-analyses are often used to synthesize the findings of studies examining the correlational relationship between two continuous variables. When only dichotomous measurements are available for one of the two variables, the biserial correlation coefficient can be used to estimate the product-moment correlation between the two underlying…

A cordless mouse with an added reed switch is used as a wireless data logger to record every time the wheel of a trolley completes a revolution. The limitations of the system in terms of maximum clicking rate and spatial resolution are considered and data obtained from the descent of a trolley down a ramp at various different angles is analysed in…

This final article in the authors' series draws together some of the ideas they have addressed, and suggests important "ingredients" that make a paper palatable to the reviewer and the reader. These ingredients include: (1) Describe the methods; (2) Plan the analysis; (3) Design the study; (4) Use the correct experimental unit; and (5)…

The "radioactive dice" experiment is a commonly used classroom analogue to model the decay of radioactive nuclei. However, the value of the half-life obtained from this experiment differs significantly from that calculated for real nuclei decaying exponentially with the same decay constant. This article attempts to explain the discrepancy and…

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)

A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB…

Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue…

In this article, the authors address the practicalities of how data should be presented, summarized, and interpreted. There are no exact rules; indeed there are valid concerns that exact rules may be inappropriate and too prescriptive. New procedures evolve, and new methods may be needed to deal with new types of data, just as people know that new…

Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals…

It is no accident that the first use of computers in school systems was to arrange schedules for students and teachers. The proper use of the computer in the classroom is as a replacement for the clock and its strict temporal schedule. By conveying information through self-instructional content, the computer can schedule work for pupils in…

When two or more univariate population means are compared, the proportion of variation in the dependent variable accounted for by population group membership is eta-squared. This effect size can be generalized by using multivariate measures of association, based on the multivariate analysis of variance (MANOVA) statistics, to establish whether…

School districts are in the process of adopting the Response to Intervention (RTI) approach to identify and remediate academic and behavioral deficits. As an integral member of the school behavior team, school counselors must use data on individual interventions to contribute to the data-based decision making process in RTI. This article presents…