Generation of all randomizations using circuits

After a rich history in medicine, randomized control trials (RCTs), both simple and complex, are in increasing use in other areas, such as web-based A/B testing and planning and design of decisions. A main objective of RCTs is to be able to measure parameters, and contrasts in particular, while guarding against biases from hidden confounders. After careful definitions of classical entities such as contrasts, an algebraic method based on circuits is introduced which gives a wide choice of randomization schemes.