Note:
• MSTotal 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 MSAmong. Variances ignoring groups uses the simple model and will thus be MSTotal.

## 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 - - -
1. See completed table above. Note the following
• dfamong and SSamong came from subtracting within values from total values.
• MSamong came from SSamong divided by dfamong.
• F is then MSamong divided by MSwithin.
• The p-value came from distrib(3.5,distrib="f",df1=7,df2=24,lower.tail=FALSE).
2. The number of groups = 7+1 = 8 (i.e., dfamong+1).
3. The number of individuals = 31+1 = 32 (i.e., dftotal+1).
4. The variability among individuals within groups is sp2 = MSwithin = 1462.
5. The variability among individuals ignoring groups is s2 = MStotal = $$\frac{70907}{31}$$ = 2287.3.
6. Yes, there is a difference among the group means because the p-value is less than 0.05.