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 3
Source | df | SS | MS | F | p-value |
---|---|---|---|---|---|
Among | 3 | 17.25 | 5.75 | 1.26 | 0.315 |
Within | 20 | 91.20 | 4.56 | - | - |
Total | 23 | 108.45 | - | - | - |
- See completed table above. Note the following
- MS_{among} is from multiplying F and MS_{within}.
- df_{among} is then SS_{among} divided by MS_{among}.
- df_{within} is then df_{total}-df_{among}.
- SS_{within} is then MS_{within} times df_{within}.
- SS_{total} is then SS_{among} + SS_{within}.
- The p-value is from
distrib(1.26,distrib="f",df1=3,df2=20,lower.tail=FALSE)
.
- The number of groups = 3+1 = 4 (i.e., $df_{among}+1).
- The number of individuals = 23+1 = 24 (i.e., $df_{total}+1).
- The variability among individuals within groups is s_{p}^{2} = $MS_{within} = 4.56.
- The variabilty among individuals ignoring groups is s>sup>2 = MS_{total} = \(\frac{108.45}{23}\) = 4.72.
- No there is not a difference among the group means because the p-value is greater than 0.05.