STAT368 Lecture : Mathematics of ANOVA.pdf
5 Apr 2014
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It is no accident that following technique is basic; learn it now. A more methodical and rigorous development of. Anova starts with a statistical model of the data, and goes on to derive procedures according to some optimality principle. In this case there are two popular models: In both cases we assume that the random er- are independently and normally distrib- rors uted, with common variance 2. 2 and we seek estimates of the parameters 1. The hypothesis that all treatments are equally ef- 51 must then = 0 on average, since a non-zero av- erage would be included in . Here we concentrate on the e ects model, and de- rive parameter estimates. A common and in certain senses optimal method of estimation is least squares, by which we minimize the total squared discrepancy between the observations and their means: We aim to nd estimates = ( 1. By calculus we get (show that p = 0. )
