ISyE2028C Example for ANOVA Contents

ISyE2028C Example for ANOVA Contents - ISyE2028C Example...

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ISyE2028C Example for ANOVA Contents I will use the regular ONE-WAY ANOVA to discuss the contents in the ANOVA that students need to know for Exam #3. Data: See textbook examples Data Model: Y ij = μ + α i + ε ij , where Y ij is the response (outcome) of the study with i = 1, 2, …, a (= #levels in the fixed-effect variable), j = 1, 2, …, n (=#replicates). Model Parameters: The parameter μ represents the average of the responses when there is no effect applied to the process, i.e., the variable is set at the nominal level. α i is the effect from changing the variable from the nominal level to a specific level of study, e.g., temperature changed from the nominal 300 degrees to 500 degrees for studying an impact of high temperature to some chemical products. There is one additional parameter in the error term, ε ij . A typical assumption in ANOVA is that ε ij ’s are random (i.i.d.) samples from a normal distribution with zero mean and σ 2 variance. The variance parameter σ 2 will be estimated by the MSE described below.
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