One of the most fundamental questions in astronomy is how the Universe evolved to become the highly structured system of stars and galaxies that we see today. The answer to this question can be largely uncovered in a relatively unexplored period in the history of the Universe known as the Epoch of Reionization (EoR), where radiation from the first generation of stars and galaxies ionized the neutral hydrogen gas in the intergalactic medium. The reionization process created "bubbles" of ionized regions around radiating sources that perturbed the matter density distribution and influenced the subsequent formation of stars and galaxies. Exactly how and when reionization occurred are currently up for debate. However, by studying this transformative period we hope to unravel the underlying astrophysics that governs the formation and evolution of the first stars and galaxies.

The most promising method to study reionization is 21 cm tomography, which aims to map the 3D distribution of the neutral hydrogen gas using the 21 cm emission lines from the spin-flip transition of neutral hydrogen atoms. Several radio interferometers operating at frequencies below 200 MHz are conducting these experiments, but direct images of the observed fields are limited due to contamination from astrophysical foreground sources and other systematics, forcing current and upcoming analyses to be statistical.

In this dissertation, I studied one-point statistics of the 21 cm brightness temperature intensity fluctuations, focusing on how measurements from observations would be biased by different contaminations and instrumental systematics and how to mitigate them. I develop simulation tools to generate realistic mock 21 cm observations of the Hydrogen Epoch of Reionization Array (HERA), a new interferometer being constructed in the Karoo desert in South Africa, and perform sensitivity analysis of the telescope to one-point statistics using the mock observations. I show that HERA will be able to measure 21 cm one-point statistics with sufficient sensitivity if foreground contaminations can be sufficiently mitigated. In the presence of foreground, I develop a rolling foreground avoidance filter technique and demonstrate that it can be used to obtain noise-limited measurements with HERA. To assess these techniques on real data, I obtain measurements from the legacy data from the first season observation of the Murchison Widefield Array (MWA) and perform additional high-precision radio interferometric simulations for comparison. Through these works, I have developed new statistical tools that are complementary to the power spectrum method that is currently the central focus of the majority of analyses. In addition to confirming power spectrum detections, one-point statistics offer additional information on the distribution of the 21 cm fluctuations, which is directly linked to the astrophysics of structure formation.