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In this chapter, I will discuss the use of randomization as a fundamental scientific tool in experiments where one wishes to make fair comparisons. I will begin with a brief discussion of the use of randomization in agricultural experiments many years ago, and how much later it became a prominent component of comparative clinical trials in medical research. To illustrate its usefulness and importance, I will describe a famous example of how randomization was used to obtain an unbiased comparison of two very different treatments for breast cancer that changed medical practice worldwide. An explanation of why randomization provides unbiased estimators of causal effects will be given. I will provide an example showing how a covariate effect can be mistaken for a treatment effect if one does not randomize, and instead relies on a conventional regression analysis of observational data. Reviews and illustrations will be given of statistical methods to correct for bias when analyzing observational data from non-randomized studies, including stratification, inverse probability weighting, and pair matching. Rubin’s (1978) Bayesian rationale for randomization will be described. A review will be given of two simulation studies of outcome-adaptive randomization, including potentially severe scientific flaws with this methodology that may not be apparent.