# Accuracy in parameter estimation and simulation approaches for sample-size planning accounting for item effects

## TL;DR

This paper explains how to plan sample sizes using accuracy in parameter estimation and simulations, especially for studies without clear hypotheses.

## Contribution

It introduces combining AIPE and simulation methods to handle studies with multiple items and no specific hypothesis.

## Key findings

- Combining AIPE and simulation allows flexible sample size planning for studies without specific hypotheses.
- Sample sizes can be planned to measure multiple items accurately and precisely.
- The paper provides code examples and package tools for researchers to adapt.

## Abstract

The planning of sample size for research studies often focuses on obtaining a significant result given a specified level of power, significance, and an anticipated effect size. This planning requires prior knowledge of the study design and a statistical analysis to calculate the proposed sample size. However, there may not be one specific testable analysis from which to derive power (Silberzahn et al., Advances in Methods and Practices in Psychological Science, 1(3), 337356, 2018) or a hypothesis to test for the project (e.g., creation of a stimuli database). Modern power and sample size planning suggestions include accuracy in parameter estimation (AIPE, Kelley, Behavior Research Methods, 39(4), 755–766, 2007; Maxell et al., Annual Review of Psychology, 59, 537–563, 2008) and simulation of proposed analyses (Chalmers & Adkins, The Quantitative Methods for Psychology, 16(4), 248–280, 2020). These toolkits offer flexibility in traditional power analyses that focus on the if-this, then-that approach. However, both AIPE and simulation require either a specific parameter (e.g., mean, effect size, etc.) or a statistical test for planning sample size. In this tutorial, we explore how AIPE and simulation approaches can be combined to accommodate studies that may not have a specific hypothesis test or wish to account for the potential of a multiverse of analyses. Specifically, we focus on studies that use multiple items and suggest that sample sizes can be planned to measure those items adequately and precisely, regardless of the statistical test. This tutorial also provides multiple code vignettes and package functionality that researchers can adapt and apply to their own measures.