A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output. From the data below, calculate the test value.
Source
Sum of Squares d.f. Mean Square $F$
Between
$\begin{array} { l l l l } \text { Within (error) } & 174 & 43 & 4.05 \ \text { Total } & 230 & 47 & \end{array}$
A) F = 0.91
B) F = 3.46
C) F = 1.32
D) F = 2.39

Question

Quizplus · Accepted Answer

The F-value is calculated as the ratio of the Mean Square Between to the Mean Square Within. First, we need to find the Sum of Squares Between (SSB) and its degrees of freedom (dfB). The Total Sum of Squares (SST) is 230, and the Sum of Squares Within (SSW) is 174, so SSB = SST - SSW = 230 - 174 = 56. The total degrees of freedom (dfT) is 47, and the degrees of freedom Within (dfW) is 43, so dfB = dfT - dfW = 47 - 43 = 4. The Mean Square Between (MSB) is SSB / dfB = 56 / 4 = 14. The Mean Square Within (MSW) is given as 4.05. Therefore, the F-value is MSB / MSW = 14 / 4.05 ≈ 3.46.

A Researcher Calculated the ANOVA Summary Table for an Experiment FFF

A Researcher Calculated the ANOVA Summary Table for an Experiment $F$