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 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 - - -
1. See completed table above. Note the following
• MSamong is from multiplying F and MSwithin.
• dfamong is then SSamong divided by MSamong.
• dfwithin is then dftotal-dfamong.
• SSwithin is then MSwithin times dfwithin.
• SStotal is then SSamong + SSwithin.
• The p-value is from distrib(1.26,distrib="f",df1=3,df2=20,lower.tail=FALSE).
2. The number of groups = 3+1 = 4 (i.e., $dfamong+1). 3. The number of individuals = 23+1 = 24 (i.e.,$dftotal+1).
4. The variability among individuals within groups is sp2 = \$MSwithin = 4.56.
5. The variabilty among individuals ignoring groups is s>sup>2 = MStotal = $$\frac{108.45}{23}$$ = 4.72.
6. No there is not a difference among the group means because the p-value is greater than 0.05.