  Stratified factorial experiments are widely used in industrial engineering,
clinical trials, and social science to measure the joint effects of several
factors on an outcome. Researchers often use a linear model and analysis of
covariance to analyze experimental results; however, few studies have addressed
the validity and robustness of the resulting inferences because assumptions for
a linear model might not be justified by randomization. In this paper, we
establish the finite-population joint central limit theorem for usual
(unadjusted) factorial effect estimators in stratified $2^K$ factorial
experiments. Our theorem is obtained under randomization-based inference
framework, making use of an extension of the vector form of the
Wald--Wolfowitz--Hoeffding theorem for a linear rank statistic. It is robust to
model misspecification, arbitrary numbers of strata, stratum sizes, and
propensity scores across strata. To improve the estimation and inference
efficiency, we propose three covariate adjustment methods and show that under
mild conditions, the resulting covariate-adjusted factorial effect estimators
are consistent, jointly asymptotically normal, and generally more efficient
than the unadjusted estimator. In addition, we propose Neyman-type conservative
estimators for the asymptotic variances to facilitate valid inferences.
Simulation studies demonstrate the benefits of covariate adjustment methods.
Finally, we apply the proposed methods to analyze a real dataset from a
clinical trial to evaluate the effects of the addition of bevacizumab and/or
carboplatin on pathologic complete response rates in patients with stage II to
III triple-negative breast cancer.
