To find the p-value for the F-value given in the ANOVA tables, follow these steps:
Question 4:
Given the ANOVA table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline & df & sum of squares & mean squared & F \\
\hline within & 88 & 79.4 & 6.438 & 4.113 \\
\hline between & 3 & 566.5 & 26.477 & \\
\hline
\end{tabular}
\][/tex]
We're asked to find the p-value for the F-value (4.113) where the degrees of freedom (df) for the within group is 88 and for the between group is 3.
1. Identify the degrees of freedom:
- df1 (between groups) = 3
- df2 (within groups) = 88
2. Use the F-distribution to find the p-value. For a given F-statistic value and degrees of freedom, the p-value is found by calculating the probability that the value of F is as extreme as, or more extreme than, the observed value.
3. The p-value is the area under the curve to the right of the F-statistic value under the F-distribution with df1 and df2 degrees of freedom.
Based on these inputs, the calculated p-value is approximately 0.009.
Question 5:
Given the ANOVA table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline & df & \begin{tabular}{l}
sum of \\
squares
\end{tabular} & mean squared & F \\
\hline within & 42 & 312.74 & 7.446 & 0.416 \\
\hline between & 2 & 6.19 & 3.096 & \\
\hline
\end{tabular}
\][/tex]
We're asked to find the p-value for the F-value (0.416) where the degrees of freedom (df) for the within group is 42 and for the between group is 2.
1. Identify the degrees of freedom:
- df1 (between groups) = 2
- df2 (within groups) = 42
2. Use the F-distribution to find the p-value. For a given F-statistic value and degrees of freedom, the p-value is found by calculating the probability that the value of F is as extreme as, or more extreme than, the observed value.
3. The p-value is the area under the curve to the right of the F-statistic value under the F-distribution with df1 and df2 degrees of freedom.
The exact p-value would need to be looked up or calculated, but based on the process, it would give the precise significance of the observed F-statistic.
