Question

Suppose that the overall F-test obtained from performing a one-way ANOVA resulted in a p-value that was not statistically significant. Which of the following CANNOT be true?

		The variability within the groups is very large compared to between-group variability.
		The variability between the groups is very large compared to within-group variability.
		The ratio of the between and within variability was not sufficiently large.
		The F-statistic was not larger than the critical value obtained from the F-distribution.

Answer 1

option A is correct and it is possiblle because variation within group is large as compared to between groups, this means that we will get a smaller F statistic, which will be insignificant.

option B is incorrect and it is impossiblle because when variation between groups is very large compared to within group variation, then this means that the F statistic must be significant because the variation in numerator is greater than the denominator.

option C is correct and it is possiblle because variation within group is not sufficiently large than between groups, this means that we will get a smaller F statistic, which will be insignificant.

option D is correct and it is possiblle because the result is insignificant when the F statistic is smaller than F critical value

so, option B is answer