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How to use this table: There are two tables here. The first one gives critical values of F at the p = 0.05 level of significance. The second table gives critical values of F at the p = 0.01 level of significance. Obtain your F-ratio.
F Distribution • The F distribution is the ratio of two independent χ random variables. • The test statistic F* follows the distribution – F* ~ F(1,n-2)
Chapter 7 Analysis of Variance (Anova) 7.3 One way (factor) anova In general, one way anova techniques can be used to study the effect of k()>2 levels of a single factor. To determine if different levels of the factor affect measured observations differently, the following hypotheses are tested. H 0: µi =µall i=1, 2, K, k H 1
Calculating Fisher’s F-ratio is a key step in a number of statistical procedures involving null hypothesis significance testing. This is particularly so in the case of ANOVA (analysis of variance) in its several forms, but even multiple regression includes a test of significance of the overall model which employs an F-ratio.
The F statistic = MSG/MSE If the null hypothesis is true, the F statistic has an F distribution with k 1 and n k degrees of freedom in the numerator/denominator respectively. If the alternate hypothesis is true, then F tends to be large. We reject H0 in favor of Ha if the F statistic is sufciently large.
Critical Values of the F Distribution (α = .01) df between df within 1 2 3 4 5 6 7 8 12 24 ∞ 5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 9.89
ANOVA Examples STAT 314 1. If we define s = MSE, then of which parameter is s an estimate? If we define s = MSE, then s i s a n e s t i m a t e o f t h e common population standard deviation, σ, of the populations under consideration. (This presumes, of course, that the equal-standard-deviations assumption holds.) 2.
