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Jan 5, 2014 at 23:01 comment added Darren James See Kempthorne (1952) for theoretical details. Bias reduction through randomization can also be demonstrated by simulation.
Jan 5, 2014 at 22:08 comment added whuber I don't think I'm mistaken; I would propose instead that you are using "bias" in two slightly different senses. When samples are not randomized, how does one even begin assessing the bias of an estimator in the technical sense we have agreed on?
Jan 5, 2014 at 21:04 comment added Darren James Cochran, W. G. and G. M. Cox. 1957. Experimental Designs. New York: Wiley. Federer, W. T. 1955. Experimental Design. New York: Macmillan. Hinkelmann, K., and Kempthorne, O. 1994. Design and Analysis of Experiments. Wiley: New York. Kuehl, R. O. 2000. Design of Experiments: Statistical Principles of research design and analysis. Belmont, CA: Brooks/Cole.
Jan 5, 2014 at 21:04 comment added Darren James You are mistaken. The primary goal of randomization is to simulate the effect of independence. It does this by eliminating biases that arise through systematic assignment of treatments to subjects. These biases produce inaccurate estimates—most importantly, biased variance estimates—and loss of control over Types I and II error. Even confounding variables (which really amount to a lack of independence) are simply a case of omitted variable bias. But you need not take my word for this … If you are unconvinced by the Hurlburt paper above, here are some other resources to consult:
Jan 4, 2014 at 22:49 comment added whuber As far as I am aware, randomized sampling is not used to reduce bias, nor in many circumstances can it validly be claimed that it does reduce bias.
Jan 4, 2014 at 22:38 comment added Darren James I am referring to bias in a statistical sense. In statistics, “bias” is the difference between a statistic and the parameter it estimates. As you mention, the bias of an estimator is the difference between the estimator’s expected value and the true value of the parameter it is estimating. In my post, by “bias” I was referring to the difference between statistics calculated from the data and the parameters that they estimate—for example, between the sample mean (x bar) and the true mean (mu).
Jan 3, 2014 at 19:53 comment added whuber I enjoyed reading this, but am concerned that your use of "bias" in the penultimate paragraph might be misread because that term has a specific statistical meaning which would render your statement incorrect. Aren't you rather trying to say that randomization is intended to prevent confounding (a form of "bias" in a colloquial sense) rather than reduce bias (as a measure of inaccuracy of an estimator)?
S Jan 3, 2014 at 18:55 review Late answers
Jan 3, 2014 at 18:56
S Jan 3, 2014 at 18:55 review First posts
Jan 3, 2014 at 19:35
Jan 3, 2014 at 18:38 history answered Darren James CC BY-SA 3.0