- Question 3

Fill in the missing values for this ANOVA summary table:
\begin{tabular}{|c|c|c|c|c|}
\hline & S.S. & d.f. & M.S. & $F$ \\
\hline Between & & & 408.777 & \\
\hline Within & 7743 & & & \\
\hline TOTAL & 11421.993 & 96 & & \\
\hline
\end{tabular}

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Step 1 ：Given values are: Total Sum of Squares (S.S.) = 11421.993, Within S.S. = 7743, Total degrees of freedom (d.f.) = 96, Between Mean Square (M.S.) = 408.777

Step 2 ：Calculate the Between S.S. by subtracting Within S.S. from Total S.S., i.e., Between S.S. = Total S.S. - Within S.S. = 11421.993 - 7743 = 3678.993

Step 3 ：Assume that the Within d.f. is Total d.f. - 1, which is a common assumption in ANOVA. So, Within d.f. = 96 - 1 = 95

Step 4 ：Calculate the Between d.f. by subtracting Within d.f. from Total d.f., i.e., Between d.f. = Total d.f. - Within d.f. = 96 - 95 = 1

Step 5 ：Calculate the Within M.S. by dividing Within S.S. by Within d.f., i.e., Within M.S. = Within S.S. / Within d.f. = 7743 / 95 = 81.505

Step 6 ：Calculate the F-statistic by dividing Between M.S. by Within M.S., i.e., F-statistic = Between M.S. / Within M.S. = 408.777 / 81.505 = 5.015

Step 7 ：The missing values for the ANOVA summary table are: Between S.S. = 3678.993, Between d.f. = 1, Within M.S. = 81.505, and F-statistic = 5.015