Question

2) An ANOVA is computed for the effects of five different diets on the energy level of test animals. Eight animals are given each of the diets for a total of 40 animals. The f summary table below is partially completed. Fill in the remaining parts of the table and evaluate the F value for statistical significance. Make sure to indicate the critical value that you are using in your evaluation.

Source                   SS                   df                    MS                       F

Between  

                             

Within                 380                

Total                    557

Answer 1

Solution:

k = 5

Each treatment has 8 observations.

n = 8

Total number of observations N = 8 * 5 = 40

df(Between) = k - 1 = 5 - 1 = 4

df(within) = N - k = 40 - 5 = 35

df(Total) = N - 1 = 40 - 1 = 39

Now ,

SS(total) = SS(Between) + SS(Within)

557 = SS(Between) + 380

SS(Between) = 177

Now , MS = SS/df

So ,

MS(between) = 177/4 = 44.25

MS(within) = 380/35 = 10.8571428571

Now ,

F = MS(between)/MS(within) = 44.25/10.8571428571 = 4.0757

	SS	DF	MS	F
BETWEEN	177	4	44.25	4.0757
WITHIN	380	35	10.8571
TOTAL	557	39