Question

ANOVA summary table. A partially completed ANOVA tale for a competely randomized design is shown here.

Source	df	SS	MS	F
Treatments Error	4 -	24.7
Total	34	62.4

(a) Complete the ANOVA table.

(b) How many treatments are involved in the experiment?

(c) Do the data provide sufficient evidence to indicate a difference among the treatment means? Test using α = .10.

Answer 1

(A) df(error) = df(total)-df(treatments) = 34-4 = 30

ss(error) = ss(total)-ss(treatments) = 62.4 - 24.7 = 37.7

MS(error) = ss(error)/df(error) = 37.7/30 = 1.26

MS(treatment) = ss(treatment)/df(treatment) = 24.7/4 = 6.18

F = MS(treatment)/MS(error)= 6.18/1.26 = 4.90

(B) Number of treatments = df(treatments) + 1

= 4 + 1

= 5

(C) Using F distribution to find the p value corresponding F statistics, we get

p value = 0.0037

p value is less than 0.10 level of significance, rejecting the null hypothesis.

We can conclude that there is sufficient evidence to indicate a difference among the treatment means