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Use the following ANOVA table to calculate the F value.

\begin{tabular}{|l|l|l|l|}
\hline & \begin{tabular}{l}
degrees of \\
freedom
\end{tabular} & sum of squares & mean squared \\
\hline within & 116 & 580 & 5 \\
\hline between & 5 & 7195 & 1439 \\
\hline
\end{tabular}

[tex]\[
F = \frac{\text{mean squared between}}{\text{mean squared within}}
\][/tex]

Sagot :

GinnyAnsweridn
To calculate the F value from the given ANOVA table, follow these steps:

1. Identify the relevant components from the ANOVA table:
- For the [tex]\(\text{Within groups}\)[/tex]:
- Degrees of freedom (df_within) = 116
- Sum of squares (SS_within) = 580
- Mean squared (MS_within) = 5
- For the [tex]\(\text{Between groups}\)[/tex]:
- Degrees of freedom (df_between) = 5
- Sum of squares (SS_between) = 7195
- Mean squared (MS_between) = 1439

2. Understand the formula for calculating the F value:
[tex]\[ F = \frac{\text{Mean Square Between (MS_between)}}{\text{Mean Square Within (MS_within)}} \][/tex]

3. Substitute the given values into the formula:
- Mean Square Between ([tex]\(\text{MS}_{\text{between}}\)[/tex]) = 1439
- Mean Square Within ([tex]\(\text{MS}_{\text{within}}\)[/tex]) = 5

So the F value is calculated as follows:
[tex]\[ F = \frac{1439}{5} \][/tex]

4. Perform the division:
[tex]\[ F = 287.8 \][/tex]

Therefore, the F value is 287.8.
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