Teaching: confidence, prediction and tolerance intervals in scientific practice: a tutorial on binary variables

Abstract

Background One of the emerging themes in epidemiology is the use of interval estimates. Currently, three interval estimates for confidence (CI), prediction (PI), and tolerance (TI) are at a researcher's disposal and are accessible within the open access framework in R. These three types of statistical intervals serve different purposes. Confidence intervals are designed to describe a parameter with some uncertainty due to sampling errors. Prediction intervals aim to predict future observation(s), including some uncertainty present in the actual and future samples. Tolerance intervals are constructed to capture a specified proportion of a population with a defined confidence. It is well known that interval estimates support a greater knowledge gain than point estimates. Thus, a good understanding and the use of CI, PI, and TI underlie good statistical practice. While CIs are taught in introductory statistical classes, PIs and TIs are less familiar. Results In this paper, we provide a concise tutorial on two-sided CI, PI and TI for binary variables. This hands-on tutorial is based on our teaching materials. It contains an overview of the meaning and applicability from both a classical and a Bayesian perspective. Based on a worked-out example from veterinary medicine, we provide guidance and code that can be directly applied in R. Conclusions This tutorial can be used by others for teaching, either in a class or for self-instruction of students and senior researchers.

Bayesian estimation in veterinary pharmacology: A conceptual and practical introduction

“…What oral dose would be required in goats, such that at least 90% of goats would be expected to have drug exposure () at least as large as an oral dose of 1 mg/kg in an average sheep? If we are to determine this from the information at hand, then we must simultaneously take into account our uncertainty about relevant pharmacokinetic parameters in goats, including between‐subject variation, and our uncertainty about pharmacokinetic parameters in sheep (Hartnack & Roos, 2021). For frequentist approaches this may be an intractable problem, making direct quantification of uncertainty difficult for secondary parameters or functions thereof, for example, in Bousquet‐Mélou et al.…”