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.