Chapter Ten

Chapter Ten - Lecture Notes Chapter Ten Analysis of...

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Lecture Notes Chapter Ten: Analysis of Variance Randall Miller 1 | Page 1. Elements of a Designed Experiment Definition 10.1 The response variable is the variable of interest to be measured in the experiment. We also refer to the response as the dependent variable . Definition 10.2 Factors are those variables whose effect on the response is of interest to the experimenter. Quantitative factors are measured on a numerical scale, whereas qualitative factors are not (naturally) measured on a numerical scale. Definition 10.3 Factor levels are the values of the factor utilized in the experiment. Definition 10.4 The treatments of an experiment are the factor-level combinations utilized. Definition 10.5 An experimental unit is the object on which the response and factors are observed or measured. Definition 10.6 A designed experiment is an experiment in which the analyst controls the specification of the treatments and the method of assigning the experimental units to each treatment. An observational experiment is an experiment in which the analyst simply observes the treatments and the response on a sample of experimental units.
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Lecture Notes Chapter Ten: Analysis of Variance Randall Miller 2 | Page 2. The Completely Randomized Design Definition 10.7 The completely randomized design is a design in which treatments are randomly assigned to the experimental units or in which independent random samples of experimental units are selected for each treatment. ANOVA F -test to Compare k Treatment Means: Completely Randomized Design 01 2 : ... : At least two treatment means differ. k a H H µµ µ = = = Test statistic : MST MSE F = Rejection region : FF α > where F is based on ( ) 1 1 k ν = numerator degrees of freedom (associated with MST) and ( ) 2 nk = denominator degrees of freedom (associated with MSE). Conditions required for a Valid ANOVA F -test: Completely Randomized Design 1. The samples are randomly selected in an independent manner from the k treatment populations. (This can be accomplished by randomly assigning the experimental units to the treatments.) 2. All k sampled populations have distributions that are approximately normal. 3. The k population variances are equal (i.e., 22 2 12 ... k σσ σ = = ). General ANOVA Summary Table for a Completely Randomized Design Source df SS MS F Treatments 1 k SST SST MST = 1 k MST MSE Error SSE SSE MSE = Total 1 n SS(Total) What Do You Do When the Assumptions are not Satisfied for the Analysis of Variance for a Completely Randomized Design? Answer : Use a nonparametric statistical method such as the Kruskal-Wallis H -test of section 14.5.
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Lecture Notes Chapter Ten: Analysis of Variance Randall Miller 3 | Page Steps for Conducting an ANOVA for a Completely Randomized Design 1. Make sure that the design is truly completely randomized, with independent random samples for each treatment.
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This note was uploaded on 07/23/2011 for the course STA 3123 taught by Professor Staff during the Fall '08 term at FIU.

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Chapter Ten - Lecture Notes Chapter Ten Analysis of...

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