# An Empirical Comparison of Parametric and Permutation Tests for Regression Analysis of Randomized Experiments

## TL;DR

This paper compares parametric ANCOVA and permutation tests in randomized experiments, showing permutation tests maintain power under assumption violations and can serve as robust alternatives in clinical trial analysis.

## Contribution

It provides an empirical comparison demonstrating permutation tests' robustness and effectiveness relative to ANCOVA when assumptions are violated in regression analysis.

## Key findings

- Permutation tests maintain power comparable to ANCOVA under assumption violations.
- Permutation tests offer a robust alternative for analyzing randomized experiments.
- Using permutation tests can serve as a robustness check in clinical trial analysis.

## Abstract

Hypothesis tests based on linear models are widely accepted by organizations that regulate clinical trials. These tests are derived using strong assumptions about the data-generating process so that the resulting inference can be based on parametric distributions. Because these methods are well understood and robust, they are sometimes applied to data that depart from assumptions, such as ordinal integer scores. Permutation tests are a nonparametric alternative that require minimal assumptions which are often guaranteed by the randomization that was conducted. We compare analysis of covariance (ANCOVA), a special case of linear regression that incorporates stratification, to several permutation tests based on linear models that control for pretreatment covariates. In simulations of randomized experiments using models which violate some of the parametric regression assumptions, the permutation tests maintain power comparable to ANCOVA. We illustrate the use of these permutation tests alongside ANCOVA using data from a clinical trial comparing the effectiveness of two treatments for gastroesophageal reflux disease. Given the considerable costs and scientific importance of clinical trials, an additional nonparametric method, such as a linear model permutation test, may serve as a robustness check on the statistical inference for the main study endpoints.