MIE360 21 Too Many Comparisons!

# MIE360 21 Too Many Comparisons! - MIE360 Computer Modeling...

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MIE360 Computer Modeling and Simulation Lecture Notes Daniel Frances © 2010 1 Lecture 21 – Too Many Comparisons! Earlier we mentioned that to consider 4 different types of additional resources in a model, two possible levels for each resource, you need to simulate 2 4 = 16 scenarios. Using the multiple comparison approach we need to perform 120 2 16 = comparisons. Based on n Bonferroni’s inequality we derived that the level of confidence required for the pairwise comparisons is the overall required level of confidence divided by the number of comparisons. Thus if we require 90% confidence, i.e. α =.1, then for each of 10 pairwise comparisons we need α = .01, i.e. 99% confidence. As the number of comparisons grows this approach becomes impractical. The subject of Design of Experiments (DE) tries to deal both with the problem of “too many comparisons” as well as “too many alternatives”. The material covered here, Factorial Design, addresses both problems. It provides an alternate approach for deciding on the appropriate follow-up to a set o f simulation t r ia ls fo r all possible scenarios. More advanced topics in DE such as Fractional Factorial Design try to reduce the number of scenarios that need to be simulated. It turns out this problem is very similar to that faced by scientists having to perform experiments to learn how various factors affect responses. Statisticians have then stepped into the breach to help them Design their Experiments. In our case the

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## This note was uploaded on 09/20/2011 for the course MIE 360 taught by Professor D.frances during the Fall '10 term at University of Toronto.

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MIE360 21 Too Many Comparisons! - MIE360 Computer Modeling...

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