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STATS 2B03 (25)
Chapter 8

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Aaron Childs

Stats 2B03: Statistical Methods for Science Chapter 8: Analysis of Variance 8.2 The Completely Randomized Design - One-way ANOVA:  Only one source of variation is investigated - Hypothesis testing steps:  Description of data:  x ijthe ith observation resulting from the jth treatment (there are a total of k treatments)  i = 1, 2, …,jn j = 1, 2, …, k  T = ∑ = total of the jth treatment .j  = mean of the jth treatment  ∑ ∑ ∑ = total of all observations  ∑  Assumptions:  The model: symbolic representation of a typical value of a data set o o represents the mean of all the k population means and is called the gran mean o represents the difference between the mean of the jth population and the grand mean and is called the treatment effect o represents the amount by which an individual measurement differs from the mean of the population to which it belongs and is called the error term  Components of the model: composed of the grand mean, a treatment effect, and an error term representing the deviation of the observation from its group mean  Assumptions of the model: o The k sets of observed data constitute k independent random samples from the respective populations o Each of the populations from which the samples come is normally distributed with mean and variance o Each of the populations has the same variance. That is, o The are unknown constants and ∑ since the sum of all deviations of the from their mean , is zero o The have a mean of 0, since the mean of is o The have a variance equal to the variance of the , since the and differ only by a constant; that is, the error variance is equal to , the common variance specified in assumption c. o The are normally (and independently) distributed  Hypotheses:  H0: μ1=μ2=…=μ ok τ=0j  HA: not all j are equal or not aljτ=0  Test
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