class03_19_20

class03_19_20 - 1.017/1.010 Class 19 Analysis of Variance...

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Unformatted text preview: 1.017/1.010 Class 19 Analysis of Variance Concepts and Definitions Objective: Identify factors responsible for variability in observed data Specify one or more factors that could account for variability (e.g. location, time, etc.). Each factor is associated with a particular set of populations or treatments (e.g. particular sampling stations, sampling days, etc.). One-way analysis of variance (ANOVA) considers only a single factor. Suppose a random sample [ x i 1 , x i 2 , ..., x iJ ] is obtained for treatment i . There are i =1,..., I treatments (e.g. each treatment may correspond to a different sampling location). Arrange data in a table/array -- rows are treatments, columns are replicates: [ x 11 , x 12 , ..., x 1 J ] [ x 21 , x 22 , ..., x 2 J ] . . [ x I 1 , x I 2 , ..., x IJ ] Here we assume each treatment has same number of replicates J . The ANOVA procedure may be generalized to allow different number of replicates for each treatment. Each random sample has a CDF F xi ( x i ). The different F xi ( x i ) are assumed identical except for their means, which may differ. Classical ANOVA also assumes that all data are normally distributed....
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class03_19_20 - 1.017/1.010 Class 19 Analysis of Variance...

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