In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomizationbased inference is especially important in experimental design and in survey sampling.
YouTube Encyclopedic

1/5Views:2 5189 834168 9415 905 00474 862

✪ Randomized Experiments: Causal Inference Bootcamp

✪ Randomized Experiments

✪ Types of Experimental Designs (3.3)

✪ 5 Experiments You Can Try At Home (Part 1)

✪ Observational Study vs Experiment
Transcription
[MUSIC] Last time, we talked about controlled experiments: we take two units that are identical in every variable, except you treat one and you don't treat the other. Today we're going to talk about randomized experiments. This is where you take a lot of units, and you randomly put some of them in a treatment group, some of them in a control group. And in the treatment group you treat everybody, and in the control group you don't treat everybody. So why would randomization help us learn about causality? Well, in a controlled experiment, you have your two units that are identical in everything, except one is treated and the other is not. In a randomized experiment, think about the time right after you've randomize everybody, but before you treat people. Well in that case, the two groups are identical, the control group and the treatment group. Because by the definition of randomization, you've arbitrarily split everybody up into these two groups. So there's no difference between the two, except that you're going to treat one and you're not going to treat the other. Well, what do I mean by there being no difference between the two groups? Well, suppose we picked one person from treatment group and another person from the control group. It's very unlikely that these two people are going to be exactly identical in every single variable. But, when we compare the average value of a variable in the treatment group with the average value of a variable in the control group, we're going to get the same number. And that's just because the distinction between these two groups is arbitrary. That's the definition of randomization. There's no systematic difference between the groups. Now, suppose that in practice we have our treatment group and our control group, and we looked and we saw there's a lot more women in the control group, for example. What that would then mean is that women were a lot more likely to be assigned to the control group than men. That's not possible with true random assignment. A different way of saying this, is that randomization produces balance in the variables across the two groups. Mathematically, you would say that the assignment of treatment is statistically independent of all the other variables, like gender. So, gender and whether they're assigned treatment or not, is uncorrelated, or independent. Now, it's helpful to remember that there are three kinds of variables that we're looking at. Our outcome variable, our treatment or policy variable, and our pretreatment variables, which are all variables that are happened before treatment. Randomization produces balance in the pretreatment variables like gender, but it doesn't produce balance in the treatment variable. That's the whole point. The treatment group gets treated, the control group doesn't. So now we can see what the main result of randomized experiment is. Because these two groups are identical in all of their pre treatment variables, the only thing that's different across the two groups is treatment, whether they are treated or not. Then any difference in the average outcomes between the two groups can be completely attributed to differences in the treatment status. So if we see the average outcomes in the treatment group are higher than average outcomes in the control group, we can say that's because treatment has a causal effect on outcomes. Now this argument requires there to be a large number of people in each group. Think about controlled experiments once again. That required us to have just two people. We could get causality with just two observations, and that's because we had two observations which were identical in every way except for their treatment status. But now in the randomized case, suppose we looked at a really extreme case, where we just had two people and we randomly assigned one to treatment and the other to control. Well I randomly assigning them, so can't I just look at the difference and learn causality? Well, no, not really, and that's because if you take those two people they are not going to be the same in all their variables, so you can't conclude that the only difference across the two groups is because of treatment. It's only once you start getting a very large number of people in each group that you can reasonably say that the groups are identical. And therefore the only difference between them is whether they are treated or not. This is one of the major differences between randomized experiments and controlled experiments. Now in practice, you're going to have to figure out just how many people do we need? And there's a whole body of techniques for doing that in statistics. We're not going to talk about that, you can go look it up. But basically the causality idea says you need a lot of people. And in statistical inference, under this statistical technique we'll quantify exactly how large you need. Now in practice, there’s a lot of benefits to doing randomization. One is that it makes data analysis very simple. Basically when you have randomized experiment, you're just going to have to compare the average outcome in the treatment group with average outcome of the control group, and the difference is going to be an average treatment effect. So it's going to tell you something about causality. And we are going to go through a lot of examples of how to analyze randomized experiments in the next few modules. [MUSIC].
Contents
Overview
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 modelbased statistical inference, especially Bayesian or likelihoodbased. 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 hardtochange 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.
Online randomized controlled experiments
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.^{[clarification needed]}
 Ability to rampup experiments from low percentages to higher percentages.
 Speed / performance has significant impact on key metrics.^{[3]}^{[6]}
 Ability to use the preexperiment 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 eighteenhundreds, 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.
Statistical interpretation
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 ttest, regression analysis, or a similar statistical test.
Empirical evidence that randomization makes a difference
Empirically differences between randomized and nonrandomized studies,^{[14]} 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
 ^ Schulz KF, Altman DG, Moher D; for the CONSORT Group (2010). "CONSORT 2010 Statement: updated guidelines for reporting parallel group randomised trials". BMJ. 340: c332. doi:10.1136/bmj.c332. PMC 2844940. PMID 20332509.CS1 maint: Multiple names: authors list (link)
 ^ Kohavi, Ron; Longbotham, Roger (2015). "Online Controlled Experiments and A/B Tests" (PDF). In Sammut, Claude; Webb, Geoff (eds.). Encyclopedia of Machine Learning and Data Mining. Springer. pp. to appear.
 ^ ^{a} ^{b} ^{c} Kohavi, Ron; Longbotham, Roger; Sommerfield, Dan; Henne, Randal M. (2009). "Controlled experiments on the web: survey and practical guide". Data Mining and Knowledge Discovery. 18 (1): 140–181. doi:10.1007/s1061800801141. ISSN 13845810.
 ^ Kohavi, Ron; Deng, Alex; Frasca, Brian; Longbotham, Roger; Walker, Toby; Xu Ya (2012). "Trustworthy Online Controlled Experiments: Five Puzzling Outcomes Explained". Proceedings of the 18th ACM SIGKDD Conference on Knowledge Discovery and Data Mining.
 ^ Kohavi, Ron; Deng Alex; Frasca Brian; Walker Toby; Xu Ya; Nils Pohlmann (2013). Online Controlled Experiments at Large Scale. Proceedings of the 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 19. Chicago, Illinois, USA: ACM. pp. 1168–1176. doi:10.1145/2487575.2488217.
 ^ Kohavi, Ron; Deng Alex; Longbotham Roger; Xu Ya (2014). Seven Rules of Thumb for Web Site Experimenters. Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 20. New York, New York, USA: ACM. pp. 1857–1866. doi:10.1145/2623330.2623341.
 ^ Deng, Alex; Xu, Ya; Kohavi, Ron; Walker, Toby (2013). "Improving the Sensitivity of Online Controlled Experiments by Utilizing PreExperiment Data". WSDM 2013: Sixth ACM International Conference on Web Search and Data Mining.
 ^ Neuhauser, D; Diaz, M (2004). "Daniel: using the Bible to teach quality improvement methods". Quality and Safety in Health Care. 13 (2): 153–155. doi:10.1136/qshc.2003.009480. PMC 1743807. PMID 15069225.
 ^ Angrist, Joshua; Pischke JörnSteffen (2014). Mastering 'Metrics: The Path from Cause to Effect. Princeton University Press. p. 31.
 ^ Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences. 3: 73–83. http://psychclassics.yorku.ca/Peirce/smalldiffs.htm
 ^ Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design". Isis. 79 (3): 427–451. doi:10.1086/354775. JSTOR 234674. MR 1013489.
 ^ Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology and Educational Research". American Journal of Education. 101 (1): 60–70. doi:10.1086/444032.
 ^ Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design". Isis. 88 (4): 653–673. doi:10.1086/383850. PMID 9519574.
 ^ Anglemyer A, Horvath HT, Bero L (April 2014). "Healthcare outcomes assessed with observational study designs compared with those assessed in randomized trials". Cochrane Database Syst Rev. 4 (4): MR000034. doi:10.1002/14651858.MR000034.pub2. PMID 24782322.
 ^ OdgaardJensen J, Vist G, et al. (April 2011). "Randomisation to protect against selection bias in healthcare trials". Cochrane Database Syst Rev (4): MR000012. doi:10.1002/14651858.MR000012.pub3. PMID 21491415.
 ^ Howick J, Mebius A (2014). "In search of justification for the unpredictability paradox". Trials. 15: 480. doi:10.1186/1745621515480. PMC 4295227. PMID 25490908.
 Caliński, Tadeusz & Kageyama, Sanpei (2000). Block designs: A Randomization approach, Volume I: Analysis. Lecture Notes in Statistics. 150. New York: SpringerVerlag. ISBN 9780387985787.
 Caliński, Tadeusz & Kageyama, Sanpei (2003). Block designs: A Randomization approach, Volume II: Design. Lecture Notes in Statistics. 170. New York: SpringerVerlag. ISBN 9780387954707.
 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 9780471727569. 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 9780940600249. MR 1194407.