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.
