Highly Confident but Slightly Uncertain: A Long Overdue Reinvention of the School Scientific Method, Uncertainty and Error - Volume 3

Authors

• Stephen DeMeo, CUNY Hunter CollegeFollow

Document Type

Book

Publication Date

Summer 7-2026

Abstract

Volume 3 explores the essential roles of uncertainty and error in scientific experimentation. It distinguishes between scientific error and scientific uncertainty: Scientific error refers to the difference between an experimental value and an accepted literature value, as well as the difference between data points in an x-y scatter plot and a predicted trendline. Scientific uncertainty, on the other hand, is associated with doubt arising from instrument limitations, variability within a data set, and psychological factors. Human error is set apart as mistakes or blunders, not to be conflated with scientific error.

Of utmost importance to the scientific investigator is the resolution and minimization of uncertainty and error, recognizing that some level of doubt will always be present in experimental results. Minimization can be achieved in a variety of ways, including conducting additional trials, drawing on a larger sample, using more precise instrumentation, eliminating procedural steps, and controlling environmental variables more rigorously.

I discuss the quantitative aspects of uncertainty and error in detail, using age-appropriate mathematics and statistics (e.g., differences, percentages, and average deviations) and visualizations (e.g., error and uncertainty bars in bar charts and x-y scatter plots).

Within this volume’s focus on scientific uncertainty and error, a Confidence–Uncertainty/Error Interval expression is introduced, discussed, and, as an expression of a confident result plus/minus an uncertainty or error range, it underscores the probabilistic nature of scientific knowledge. Numerous determinations of uncertainty and error, and their use in the Interval expression, are provided in experimental contexts that are appropriate for a wide range of science students.

Two key relationships between confidence-building and uncertainty/error developed in this volume are the conceptual and quantitative associations between precision and uncertainty, and accuracy and error. These associations provide students with a learning bridge to better understand the concepts of uncertainty and error.

I also discuss in this volume systematic and random bias and the limits of quantifying all sources of uncertainty, ultimately positioning uncertainty and error as essential for clarifying results, preventing false conclusions, increasing the motivation for better experiments, supporting decision-making, fostering transparency, and promoting a realistic, rigorous, and nuanced understanding of science.

It is my position that uncertainty and error are not signs of weak science but are integral to improving the scientific process and quality of results.