STATS 2B03 Chapter Notes - Chapter 8: Analysis Of Variance, Statistical Hypothesis Testing, Test Statistic
19 Jun 2013
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Only one source of variation is investigated. Xij = the ith observation resulting from the jth treatment (there are a total of k treatments) i = 1, 2, , nj j = 1, 2, , k. 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. Ha: not all j are equal or not all j=0. The test statistic for one-way analysis of variance is a computed variance ratio. V. r. is distributed as the f distribution when h0 is true and the assumptions are met. Reject the null hypothesis if the computed value of v. r. is equal to or greater than the critical value of f for the chosen level. The term variation used in this context refers to the sum of squared deviations of observations from their mean, or sum of squares for short.
