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Analysis of Variance (or ANOVA): A hypothesis-testing procedure that is…
Analysis of Variance (or ANOVA): A hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations).
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Testwise Alpha Level - The risk of a Type I error, or alpha level, for an individual hypothesis test.
Experimentwise Alpha Level - The total probability of a Type I error that is accumulated from all of the individual tests in the experiment. Typically, the experimentwise alpha level is substantially greater than the value of alpha used for any one of the individual tests.
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Distribution of F-ratios
The exact shape of the F distribution depends on the degrees of freedom for the two variances in the F-ratio. The precision of a sample variance depends on the number of scores or the degrees of freedom. In general, the variance for a large sample (large df) provides a more accurate estimate of the population variance. Because the precision of the MS values depends on df, the shape of the F distribution also depends on the df values for the numerator and denominator of the F-ratio. With very large df values, nearly all the F-ratios are clustered very near to 1.00. With the smaller df values, the F distribution is more spread out.
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ANOVA summary table
ANOVA tables show the source of variability (between treatments, within treatments, and total variability): SS, df, MS, and the final F-ratio.
Post hoc tests / Post-tests - Additional hypothesis tests that are done after an ANOVA to determine exactly which mean differences are significant and which are not.
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Components
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Total Degrees of Freedom, (dftotal)
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Pairwise Comparisons
Post-testing enables you to go back through the data and compare the individual treatments two at a time.