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# ANOVA - 61 ANOVA Analysis of Variance One-way ANOVA is used...

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61 ANOVA – Analysis of Variance One-way ANOVA is used to compare three or more means; i.e., k Ho μ μ μ = = 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 F-test, 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 F-value 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 pair-wise between means by using either Scheffe Test or the Tukey Test as follows:

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ANOVA - 61 ANOVA Analysis of Variance One-way ANOVA is used...

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