Question

The null hypothesis in ANOVA is that all means of all groups are the same. The alternative is that at least one pair of means is different. We compute an F-statistic to explore sources of variability in our data to conduct the omnibus ANOVA. Question: what do you expect to happen when the null hypothesis is true?
A. More between group variability
B. Less between group variability

Answer 1

Answer:

Correct option: B. Less between group variability

Step-by-step explanation:

The Analysis of Variance (ANOVA) test is performed to determine whether there is a significant difference between the different group mean.

The hypothesis is defined as:

H₀: There is no difference between the group means, i.e. μ₁ = μ₂ = ... = μₙ

Hₐ: At least one of the mean is different from the others, i.e. μ$_{i}$ ≠ 0.

The test statistic is defined as:

$F=\frac{SS_{between}}{SS_{within}}$

If the null hypothesis is true then the test statistic will be small and if it is false then the test statistic will be large.

In this case it is provided that the null hypothesis is true.

This implies that:

$SS_{between}$

Implying that the sum of squares for between group variability is less than within group variability.

Thus, if the null hypothesis is true there will be less between group variability.