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Unformatted text preview: 61 ANOVA Analysis of Variance Oneway ANOVA is used to compare three or more means; i.e., k Ho = = 2 1 : . If the null hypothesis is rejected, then there is a difference somewhere; therefore, after rejecting the null hypothesis, follow the analysis with either the Scheffe Test or Tukey Test. ANOVA is a linear regression model. Assumptions: 1. Distributions are approximately normal (check for outliers and skewness). 2. The samples are independent. 3. The variances are homogeneous (check using the Ftest, pairwise). Test statistic: F = (between group variances)/(within group variances) with k 1 degrees of freedom in the numerator and N k degrees of freedom in the denominator. Recorded in the last column of the Table given below. Results are generally given in Table form: Source Sum of Squares df Mean Square F Between groups  = 2 ) ( x x n SS g g B k  1 1 2 = k SS S B B 2 2 W B S S Within groups  = 2 ) ( g W x x SS N  k k N SS S W W = 2 Total Add here N  1 Between groups source is the factor; within groups source is the error. If the results are significant, the Fvalue in the table is in the rejection region when compared to F(k  1, N  k), then the ANOVA should be followed with a comparison pairwise between means by using either Scheffe Test or the Tukey Test as follows: (1) Scheffe Test: o...
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This note was uploaded on 12/05/2011 for the course MATH 207 taught by Professor Bailey during the Spring '11 term at Emory.
 Spring '11
 Bailey
 Variance

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