Randomized experiment

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

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
  internet bots.^{[clarification needed}
  ]
• 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]

History

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

, which also introduced additional principles of experimental design.

Statistical interpretation

This section needs expansion. You can help by adding to it. (September 2012)

The

statistical test

. The model also accounts for potential confounding factors, which are factors that could affect both the treatment and the outcome. By controlling for these confounding factors, the model helps to ensure that any observed treatment effect is truly causal and not simply the result of other factors that are correlated with both the treatment and the outcome.

The Rubin Causal Model is a useful a framework for understanding how to estimate the causal effect of the treatment, even when there are confounding variables that may affect the outcome. This model specifies that the causal effect of the treatment is the difference in the outcomes that would have been observed for each individual if they had received the treatment and if they had not received the treatment. In practice, it is not possible to observe both potential outcomes for the same individual, so statistical methods are used to estimate the causal effect using data from the experiment.

Empirical evidence that randomization makes a difference

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

See also

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

References