This dissertation studies statistical inference in randomized experiments, extending important covariate-adaptive randomization tools to three commonly used experimental designs. Each chapter addresses a distinct experimental design, contributing to the broader field of design and analysis of experiments.

Chapter 1 investigates inference in randomized controlled trials with multiple treatments, specifically under a ``matched tuples'' design. Here, units are grouped into homogeneous blocks, and each treatment is randomly assigned within these blocks. The study establishes conditions for the asymptotic normality of a sample analogue estimator and constructs a consistent estimator of its asymptotic variance. It also compares the asymptotic properties of the fully-blocked $2^K$ factorial design with stratified factorial designs, demonstrating the efficiency of the former. Simulation studies and empirical applications highlight the practical implications of these results.

Chapter 2 explores inference in cluster randomized trials using a ``matched pairs'' design, where clusters are paired based on baseline covariates and one cluster in each pair is randomly assigned to treatment. This chapter presents the large-sample behavior of a weighted difference-in-means estimator and proposes a unified variance estimator consistent under different matching regimes. It also evaluates common $t$-tests and a randomization test within this framework, establishing their validity. Additionally, a covariate-adjusted estimator is proposed, showing precision improvements under certain conditions. Theoretical findings are supported by a simulation study.

Chapter 3 addresses inference in two-stage randomized experiments under covariate-adaptive randomization. In this design, clusters are first stratified and assigned to treatment or control, followed by a second stage where units within treated clusters are further randomized. The chapter develops difference-in-``average of averages'' estimators for primary and spillover effects, proving their consistency and asymptotic normality. It also demonstrates the efficiency of using covariate information in the design stage and the pitfalls of ignoring it. Finally, it studies optimal use of covariate information under covariate-adaptive randomization in large samples. The theoretical results are validated through simulations and an empirical application.

Together, these chapters advance the understanding of statistical inference in complex experimental designs, offering robust methods for empirical researchers dealing with stratified experiments.