Determine if the following statements are true or false. If the null hypothesis

Question

Determine if the following statements are true or false. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a significance level a 0.05, then... The standardized variability between the groups is higher than the standardized variability within the groups The appropriate modified significance level alpha^* to be used in pairwise comparisons of group means is 0.05/4 = 0.0125 because there are four groups. We can then conclude that all of the group means are different from one another.

Explanation / Answer

The test statistic F = MSB/ MSE

MSB = mean square between groups

MSE = mean square within groups

The null hypothesis is rejected which means F > critical value of F at alpha = 0.05

Which means F > 1 for sure

Which implies standardised variability between groups is more than within groups

First statement is true

Second statement is wrong, the level of significance remains same throughout

Third statement is false, when we reject the null hypothesis, which means atleast two means differ from each other

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