Randomized experiment

In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.

Randomized experimentation is not haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, the simplest design for comparing treatments is the "completely randomized design". Some "restriction on randomization" can occur with blocking and experiments that have hard-to-change factors; additional restrictions on randomization can occur when a full randomization is infeasible or when it is desirable to reduce the variance of estimators of selected effects.

Randomization of treatment in clinical trials pose ethical problems. In some cases, randomization reduces the therapeutic options for both physician and patient, and so randomization requires clinical equipoise regarding the treatments.

Web sites can run randomized controlled experiments [2] to create a feedback loop.[3] Key differences between offline experimentation and online experiments include:[3][4]

• Logging: user interactions can be logged reliably.
• Number of users: large sites, such as Amazon, Bing/Microsoft, and Google run experiments, each with over a million users.
• Number of concurrent experiments: large sites run tens of overlapping, or concurrent, experiments.[5]
• Robots, whether web crawlers from valid sources or malicious internet bots.
• Ability to ramp-up experiments from low percentages to higher percentages.
• Speed / performance has significant impact on key metrics.[3][6]

• Ability to use the pre-experiment period as an A/A test to reduce variance.[7]

A controlled experiment appears to have been suggested in the Old Testament's Book of Daniel. King Nebuchadnezzar proposed that some Israelites eat "a daily amount of food and wine from the king's table." Daniel preferred a vegetarian diet, but the official was concerned that the king would "see you looking worse than the other young men your age? The king would then have my head because of you." Daniel then proposed the following controlled experiment: "Test your servants for ten days. Give us nothing but vegetables to eat and water to drink. Then compare our appearance with that of the young men who eat the royal food, and treat your servants in accordance with what you see". (Daniel 1, 12– 13).[8][9]

Randomized experiments were institutionalized in psychology and education in the late eighteen-hundreds, following the invention of randomized experiments by C. S. Peirce.[10][11][12][13] Outside of psychology and education, randomized experiments were popularized by R.A. Fisher in his book Statistical Methods for Research Workers, which also introduced additional principles of experimental design.

The Rubin Causal Model provides a common way to describe a randomized experiment. While the Rubin Causal Model provides a framework for defining the causal parameters (i.e., the effects of a randomized treatment on an outcome), the analysis of experiments can take a number of forms. Most commonly, randomized experiments are analyzed using ANOVA, student's t-test, regression analysis, or a similar statistical test.

Empirically differences between randomized and non-randomized studies,[14] and between adequately and inadequately randomized trials have been difficult to detect.[15][16]

• A/B testing
• Allocation concealment
• Random assignment
• Randomized block design
• Randomized controlled trial

• Caliński, Tadeusz & Kageyama, Sanpei (2000). Block designs: A Randomization approach, Volume I: Analysis. Lecture Notes in Statistics. 150. New York: Springer-Verlag. ISBN 978-0-387-98578-7.
• Caliński, Tadeusz & Kageyama, Sanpei (2003). Block designs: A Randomization approach, Volume II: Design. Lecture Notes in Statistics. 170. New York: Springer-Verlag. ISBN 978-0-387-95470-7.
• Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design". Isis. 79 (3): 427–451. doi:10.1086/354775. JSTOR 234674. MR 1013489.
• Hinkelmann, Klaus; Kempthorne, Oscar (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (Second ed.). Wiley. ISBN 978-0-471-72756-9. MR 2363107.
• Kempthorne, Oscar (1992). "Intervention experiments, randomization and inference". In Malay Ghosh and Pramod K. Pathak (ed.). Current Issues in Statistical Inference—Essays in Honor of D. Basu. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Hayward, CA: Institute for Mathematical Statistics. pp. 13–31. doi:10.1214/lnms/1215458836. ISBN 978-0-940600-24-9. MR 1194407.