# Power contours: optimising sample size and precision in experimental psychology and human neuroscience

## TL;DR

This paper introduces a two-dimensional power contour visualization to optimize sample size and number of trials in experimental psychology and neuroscience, emphasizing the importance of trial count when within-participant variance is high.

## Contribution

It develops a novel power contour method considering both trials and participants, with empirical data across multiple paradigms, and provides an online tool for study design optimization.

## Key findings

- Within-participant variance exceeds between-participant variance in studied paradigms.
- Number of trials significantly affects statistical power when within-participant variance is large.
- Power contour plots help determine optimal trial and participant numbers for future studies.

## Abstract

When designing experimental studies with human participants, experimenters must decide how many trials each participant will complete, as well as how many participants to test. Most discussion of statistical power (the ability of a study design to detect an effect) has focussed on sample size, and assumed sufficient trials. Here we explore the influence of both factors on statistical power, represented as a two-dimensional plot on which iso-power contours can be visualised. We demonstrate the conditions under which the number of trials is particularly important, i.e. when the within-participant variance is large relative to the between-participants variance. We then derive power contour plots using existing data sets for eight experimental paradigms and methodologies (including reaction times, sensory thresholds, fMRI, MEG, and EEG), and provide example code to calculate estimates of the within- and between-participant variance for each method. In all cases, the within-participant variance was larger than the between-participants variance, meaning that the number of trials has a meaningful influence on statistical power in commonly used paradigms. An online tool is provided (https://shiny.york.ac.uk/powercontours/) for generating power contours, from which the optimal combination of trials and participants can be calculated when designing future studies.