A Primer on the Understanding, Use, and Calculation of Confidence Intervals that are Based on Central and Noncentral Distributions

TLDR

Reform of statistical practice in the social and behavioral sciences requires wider use of confidence intervals, effect size measures, and meta‑analysis, and broader use of CIs for standardized effect sizes should promote this desirable reform. The authors calculate confidence intervals for Cohen’s δ using noncentral t distributions, compare them to CIs for raw means, apply them to power and meta‑analysis, and provide the ESCI Excel software to illustrate the approach. They argue that confidence intervals are readily interpretable, linked to significance tests, encourage meta‑analytic thinking, and provide precision information.

Abstract

Reform of statistical practice in the social and behavioral sciences requires wider use of confidence intervals (CIs), effect size measures, and meta-analysis. The authors discuss four reasons for promoting use of CIs: They (a) are readily interpretable, (b) are linked to familiar statistical significance tests, (c) can encourage meta-analytic thinking, and (d) give information about precision. The authors discuss calculation of CIs for a basic standardized effect size measure, Cohen’s δ (also known as Cohen’s d), and contrast these with the familiar CIs for original score means. CIs for δ require use of noncentral t distributions, which the authors apply also to statistical power and simple meta-analysis of standardized effect sizes. They provide the ESCI graphical software, which runs under Microsoft Excel, to illustrate the discussion. Wider use of CIs for δ and other effect size measures should help promote highly desirable reform of statistical practice in the social sciences.