The ANOVA test of the F distribution may be expressed as:

A) F = $\frac{\text{random error} + \text{possible treatment effects}} {\text{random error}}$

B) F = $\frac{\text{possible treatment effects } + \text{systematic error }} {\text{systematic error}}$

C) F = $\sum \frac{(\xi) \times(\text{Ψ})}{r^{2}}$

D) F = Ax + By + c

Question

The ANOVA test of the F distribution may be expressed as:

A) F = $\frac{\text{random error} + \text{possible treatment effects}} {\text{random error}}$

B) F = $\frac{\text{possible treatment effects } + \text{systematic error }} {\text{systematic error}}$

C) F = $\sum \frac{(\xi) \times(\text{Ψ})}{r^{2}}$

D) F = Ax + By + c

Quizplus · Accepted Answer

The ANOVA test of the F distribution compares the variance between groups to the variance within groups. This is expressed as the F-statistic, which is calculated as the ratio of the mean square between groups to the mean square within groups. Therefore, the correct formula for the F-statistic is F = between-group variation / within-group variation, which can be expressed as F = possible treatment effects + random error / random error.

The ANOVA Test of the F Distribution May Be Expressed random error+possible treatment effectsrandom error\frac{\text{random error} + \text{possible treatment effects}} {\text{random error}}random errorrandom error+possible treatment effects​

The ANOVA Test of the F Distribution May Be Expressed $\frac{\text{random error} + \text{possible treatment effects}} {\text{random error}}$