What is the mean square for within-group variance (MS_WG)? A) 75.31 B) 3.81 C) 122.81 D) 160.11

Question

Quizplus · Accepted Answer

The MSS1U1B1WGS1U1B0 value can be calculated by dividing the sum of squares for within-group variance (SS1U1B1WGS1U1B0) by the degrees of freedom for within-group variance (df1U1B1WGS1U1B0). The given ANOVA table does not provide the actual values of SS1U1B1WGS1U1B0 or df1U1B1WGS1U1B0, but we can use the F-ratio and total degrees of freedom (dfT) to determine df1U1B1WGS1U1B0.

First, calculate the F-ratio by dividing the mean square for between-group variance (MSS1U1B1) by the mean square for within-group variance (MSS1U1B1WGS1U1B0):

F = MSS1U1B1 / MSS1U1B1WGS1U1B0

The ANOVA table gives us MSS1U1B1 = 153.25 and MSS1U1B1WGS1U1B0 = 40.25, so:

F = 153.25 / 40.25
F = 3.8079208

Next, calculate df1U1B1WGS1U1B0 using the total degrees of freedom (dfT = 30) and the degrees of freedom for between-group variance (df1U1B1 = 1):

df1U1B1WGS1U1B0 = dfT - df1U1B1
df1U1B1WGS1U1B0 = 30 - 1
df1U1B1WGS1U1B0 = 29

Finally, calculate MSS1U1B1WGS1U1B0:

MSS1U1B1WGS1U1B0 = SS1U1B1WGS1U1B0 / df1U1B1WGS1U1B0

We do not have the value for SS1U1B1WGS1U1B0, but it does not matter - we only need to compare the mean square for within-group variance (MSS1U1B1WGS1U1B0) to the answer choices.

Plugging in the given answer choices, we can see that only choice (B) results in a mean square close to the F-ratio we calculated:

(A) 75.31: F / 75.31 = 0.0505 - too small
(B) 3.81: F / 3.81 = 1.0000 - just right
(C) 122.81: F / 122.81 = 0.0310 - too small
(D) 160.11: F / 160.11 = 0.0238 - too small

Therefore, the best choice is (B), with an explanation that the other choices either produce mean squares that are too large or too small compared to the F-ratio calculated from the given ANOVA table.

What Is the Mean Square for Within-Group Variance (MSWG)

What Is the Mean Square for Within-Group Variance (MS_WG)