Anova theoretical response practice

What is a theoretical F-distribution for a one-way ANOVA in the context of this research question?

If I ran a one-way ANOVA (comparing mean adherence to dietary recommendations across in-person, telehealth, and mobile map counseling) an infinite number of times, the F-values would form a right-skewed distribution ranging from zero to infinity.

Where does the null hypothesis fit within the F-distribution in this context?

If the null is true, the F ratio should be close to 1.0, meaning no differences in adherence between in-person, telehealth, and mobile map counseling.

What is the purpose of alpha in a theoretical F-distribution?

Alpha sets the cutoff point, separating 95% of F-values from the 5% in the extreme right tail.

What are the zones of rejection and fail to reject in this F-distribution?

If the F-ratio falls in the 95% zone, we fail to reject the null. no significant difference among counseling methods.

If it falls in the 5% extreme right tail, we reject the null. at least one counseling method differs significantly.

What is the p value in relation to the F-ratio in this context?

The p value is the probability of getting an F-ratio of 6.50 or more extreme if the null is true. Here, p = 0.003, which is less than alpha (0.05). So, we reject the null and conclude that at least one counseling method leads to different adherence levels.

What does a significant F-ratio say about between-group and within-group mean squares?

A significant F-ratio means the variance between groups (differences across counseling methods) is much larger than the variance within groups (differences among individuals in the same method), large enough to reject the null.