POSSA: Power simulation for sequential analyses and multiple hypotheses

Abstract

Conventional experiment designs have a fixed sample size: observations are collected until the planned sample size is reached, and then the experiment is concluded. Alternatively however, sequential designs can also be used (e.g., Lakens, 2014). In that case, interim analyses can be performed during data collection, and whenever the analysis suggests sufficient evidence for the presence or absence of the given effect, the experiment can be concluded without further data collection. This can drastically reduce the required sample sizes, saving time, expenses, and effort. However, sequential analyses require adjustments for Type 1 error rate (i.e., the ratio of false significant findings) and affect statistical power (which is crucial to determine the required sample size, e.g., Cohen, 1988; Perugini et al., 2018). Furthermore, regardless of sequential analysis, in case of multiple hypotheses (multiple tests included in an analysis), for both Type 1 error rate and power, correction is necessary (e.g., Khandis & Gangestad, 2020). The present POSSA R package serves to perform, via a simulation framework, the necessary adjustments and calculate power for sequential analyses as well as for multiple hypotheses for practically any significance test.