When performing an F-test, if the means differ significantly, the between-group variance will be much smaller than the within-group variance. True False
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Step 2: Recall the F-statistic formula in ANOVA (which uses an F-test): $F = \frac{\text{Between-Group Variance (Mean Square Between)}}{\text{Within-Group Variance (Mean Square Within)}}$ Step 3: The F-test is used to determine if there are significant Show more…
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The F-test partitions the total variance into within-group variance and between-group variance. True False
Adi S.
Select the true statement below regarding the variances in ANOVA testing used to compare means of different groups (treatments). The F-statistic found in ANOVA testing is found by dividing the mean variation between groups by the mean variation within groups. When the mean variation that exists between groups increases, the ANOVA test will become more likely to result in the rejection of the null hypothesis. If variation between groups is large, the ANOVA test will conclude that there is a difference between the groups, regardless of the size of the variation within groups. When the mean variation within groups falls, the F-statistic will shrink. Only one of "variation between groups" and "variation within groups" needs to be considered in ANOVA testing.
In an ANOVA, if the null hypothesis is false, then the between-groups variance reflects the variation within the samples and the variation between the sample means. The within-group variance is significantly larger than the between-group variance. The variance within each sample is larger than if the null hypothesis were true. The variance between sample means is no greater than the variance within the sample with the largest variance.
Ana Carolina D.
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