Question

Consider an experiment with six groups, with two values in each. For the ANOVA summary table shown to the right, fill in all the missing results.

Source    Degrees of Freedom    Sum of Squares    Mean Square (Variance) F

Among groups    c−1=? SSA=?    MSA=2424 FSTAT=?

Within groups    n−c=? SSW=7272    MSW=?   

Total n−1=? SST=?

Complete the ANOVA summary table.

Answer 1

Here c denote the number of groups, n is total treatments

we have 6 groups and 2 values in each group

so, c = 6 and total treatments = n = 6*2 = 12

df(among groups) = c-1 = 6-1 = 5

df(within groups) = n-c = 12 - 6 = 6

df(total) = n-1 = 12 - 1 = 11

we know that SSA = MSA*df(among groups)

where MSA = 24 and df(among groups) = 5

so, SSA = 24*5 = 120

we know that SST = SSA + SSW = 120 + 72 = 192

we know that MSW = SSW/df(within groups)

where SSW = 72 and df(within groups) = 6

so, MSW = 72/6 = 12

We know that Fstat = (MSA/MSW)

where MSA = 24 and MSW = 12

so, Fstat = (24/12) = 2