Question

If we run a one-way ANOVA on 4th graders, 5th graders, and 6th graders, which of these outcomes are possibly true?

		There is a significant difference between 4th and 5th graders, but not between 5th and 6th graders.
		There is a significant difference between 5th and 6th graders, but not between 4th and 5th graders.
		There are no significant differences among any of the grades.
		All of the above are possibly true outcomes.

Answer 1

Solution:

If we run a one-way ANOVA on 4th graders, 5th graders, and 6th graders, which of these outcomes are possibly true?

Answer: The possible outcome is:

There are no significant differences among any of the grades.

Explanation:

The null and alternative hypotheses for the one-way ANOVA is:

H0: There is no difference in the means for the various groups

Ha: At least one mean is different

The one-way ANOVA tests whether there is significant differences between various means or not. It does not tell us which of these groups are significantly different from the others. It just tells us if the difference exists or not. The options A and C are specifying particular graders are significant while others are not. These conditions cannot be tested by one-way ANOVA, instead, we need to run Posthoc analysis to reach such conclusions. Therefore, the correct answer is:

There are no significant differences among any of the grades.