notes509fall11secanova

notes509fall11secanova - STAT 509 - Analysis of Variance...

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STAT 509 -- Analysis of Variance • The Analysis of Variance (ANOVA) is most simply a method for comparing the means of several populations. • It is commonly used to analyze experimental data arising from a Completely Randomized Design (CRD). • The experimental units are the individuals on which the response variable is observed or measured. • A specific experimental condition applied to the units is called a treatment . • This experimental condition may be based on one or more factors , each of which has multiple levels. Each combination of factor levels is a different treatment. Example: Plant growth study: Experimental Units : A sample of plants Response : Growth over one month Factors : • Fertilizer Brand (levels: A, B, C) • Environment (levels: Natural Sunlight, Artificial Lamp) There are how many treatments? (Could also have a quantitative factor…) If 5 plants are assigned to each treatment (5 replicates per treatment), there are how many observations in all?
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• A Completely Randomized Design is a design in which independent samples of experimental units are selected for each “treatment.” • That is, experimental units are assigned at random among the treatments. Three Principles of the Design of Experiments
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notes509fall11secanova - STAT 509 - Analysis of Variance...

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