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Lecture20standard - Statistics 511: Statistical Methods Dr....

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Lecture 19: One-way Analysis of Variance (ANOVA Devore: Section 10.1-10.3 Aug, 2010 Page 1

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Introduction The Analysis of Variance refers to a collection of experiments and statistical procedures for the analysis of responses from experimental units For now, we only study the single-factor ANOVA that involves analysis of data obtained from experiments in which more than two treatments have been used. The treatments are differentiated from each other by different levels of a single factor Example: studying the effects of ﬁve different brands of gas in automobile engine operating efﬁciency (mpg) or an experiment to decide whether the color density of fabric specimens depends on the amount of dye used Aug, 2010 Page 2
Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Single-factor ANOVA: notation I - the number of treatments μ 1 ,...,μ I - means of i th population, i = 1 ,...,I H 0 : μ 1 = ... = μ I vs. H a : at least two of the μ i s are different X i,j - the RV denoting the j th measurement taken from the i th population; x i,j is the observed value of X i,j It is assumed that X i,j are independent within each sample and the samples are independent of each other Aug, 2010 Page 3

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Example Several different types of boxes are compared with respect to compression strength (lb) Aug, 2010 Page 4
Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Aug, 2010 Page 5

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2010 Single-factor ANOVA: notation J is the number of observations in each sample I ; the data consists of IJ observations Sample means are ¯ X i. = J
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This note was uploaded on 02/20/2012 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University-West Lafayette.

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Lecture20standard - Statistics 511: Statistical Methods Dr....

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