Note:
- MS_{Total} is not usually shown in an ANOVA table but it is an important value (i.e., the overall variance ignoring the groups).
- When you see a question about a “variance” then it will be answered with an “MS”. Questions about variance of individuals will NOT be MS_{Among}. Variances ignoring groups uses the simple model and will thus be MS_{Total}.
ANOVA Table 1
Source | df | SS | MS | F | p-value |
---|---|---|---|---|---|
Among | 7 | 35819 | 5117 | 3.5 | 0.010 |
Within | 24 | 35088 | 1462 | - | - |
Total | 31 | 70907 | - | - | - |
- See completed table above. Note the following
- df_{among} and SS_{among} came from subtracting within values from total values.
- MS_{among} came from SS_{among} divided by df_{among}.
- F is then MS_{among} divided by MS_{within}.
- The p-value came from
distrib(3.5,distrib="f",df1=7,df2=24,lower.tail=FALSE)
.
- The number of groups = 7+1 = 8 (i.e., df_{among}+1).
- The number of individuals = 31+1 = 32 (i.e., df_{total}+1).
- The variability among individuals within groups is s_{p}^{2} = MS_{within} = 1462.
- The variability among individuals ignoring groups is s^{2} = MS_{total} = \(\frac{70907}{31}\) = 2287.3.
- Yes, there is a difference among the group means because the p-value is less than 0.05.