STA 106 Study Guide - Final Guide: Analysis Of Variance, Random Variable, Independent And Identically Distributed Random Variables
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Recall anova model yij = [overall mean] + [group e ect] + [individual error] Let yij = numeric, xi = categorical variable with a categories. The basic model to expressing the relationship between x, y is. Ij population group mean for group i (constant) jth residual/erriror/individual variance for ith group = random variable: a random sample was taken from all groups = yij are independent. Anova assumptions: i groups are independent i [1, a] z, ij iid n (0, 2. The errors are independent and identically distributed normally with mean 0 and variance. I is a constant and ij is a random variable. E{yij} expectation of jth value from ith group. E[yij] = e[ i + ij] = e[ i] + e[ ij] = i + 0 = i. 2[yij] = 2[ i + ij] = 2[ ij] = 2.
