An analysis of variance produces $S S _ { \text {between } }$ = 40 and t $M S _ { \text {between } }$ = 20.In this analysis,how many treatment conditions are being compared?
A)2
B)3
C)4
D)20

Question

Quizplus · Accepted Answer

The formula for calculating the mean sum of squares between treatment conditions is:

$M S _ { \text {between } } = \frac { S S _ { \text {between } } } { d f _ { \text {between } } } $

where $df_{between}$ is the degrees of freedom between treatment conditions.

We can use the formula to solve for $df_{between}$:

$20 = \frac{40}{df_{between}}$

$df_{between} = 2$

Since we have 2 degrees of freedom between treatment conditions, we must have 3 treatment conditions (since the total degrees of freedom in an ANOVA is $df_{total} = df_{between} + df_{within} = k-1 + N-k = N-1$, where k is the number of treatment conditions and N is the total sample size). Therefore, the correct answer is B.

An Analysis of Variance Produces SSbetween S S _ { \text {between } }SSbetween ​

An Analysis of Variance Produces $S S _ { \text {between } }$