The Practice of Statistics Daniel S. Yates The Practice of Statistics Third Edition Chapter 5: Producing Data 5.2 Designing Experiments Copyright © 2008 by W. H. Freeman & Company

Essential Questions What are the three basic principles of experimental design? What is completely randomized design? What is the purpose of randomization and blocking in an eperimental design? What are blocking, matched-pair, blind, double-blind experimental designs?

Terminology The individuals on which the experiment is done are the experimental units. When the units are human beings, they are called subjects. A specific experimental condition applied to the units is called the treatment.

Experiments Units Treatment Observe Response

More terminology The explanatory variables in an experiment are often called factors. Each treatment is formed by combining a specific value (often called a level) of each of the factors.

Two Explanatory variables: Factor A and Factor B. Factor A has two levels and Factor B has three levels.

Example Describe the units, factors, treatments and response variable. The ability to grow in shade may help pines found in the dry forests of Arizona to resist drought., How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light or light reduced to 5% of normal by shade cloth. At the end of the study, they dried the young trees and weighed them.

Other Variables Lurking variable – A variable that has an important effect and yet is not included amongst the predictor variables under consideration. Perhaps its existence is unknown or its effect unsuspected http://www.stat.berkeley.edu/users/brill/Stat215a/nov13.pdf Confounded varibles – Two possible influences on an observed outcome are confounded if they are mixed together in a way that makes it impossible to separate their effects on the response. (Statistics in Action Understanding a World of Data. Page 246.)

The Placebo Effect The patients’ response may have been due the placebo effect. A placebo is a dummy treatment. Many patients respond favorably to any treatment, even a placebo. This may be due to trust in the doctor and expectations of a cure, or simply to the fact that medical conditions often improve without treatment.

Principles of Experimental Design Control: We control sources of variation (lurking and confounded variables) other than the factors we are testing by random assignment and ensuring that conditions are similar as possible for all treatment groups. Randomization: The use of chance to assign units to treatments allows us to equalize the effects of unknown or uncontrolled sources of variation. Replication: Use enough subjects to reduce chance variation. We would like to see units in a treatment group responding similarly to one another and hopefully different from other treatment groups. (Systematic difference in response.)