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.