Question

Block
Treatment	1	2	3	4	Treatment Mean
Tr1	2	1	2	3	2
Tr2	4	4	1	1	2.5
Tr3	3	4	3	2	3
Block Mean	2	3	3	2	overall mean = 2.5

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the value of the F statistic for blocks?

Answer 1

	Block 1	Block 2	Block 3	Block 4	Sum
Tr1	2	1	2	3	P1 =	8	N =	12
Tr2	4	4	1	1	P2 =	10	n =	3
Tr3	3	4	3	2	P3 =	12	k =	4
							G = ΣX =	30
							ΣX² =	90
Sum	T1 =	T2 =	T3 =	T4 =
	9	9	6	6
	SS1 =	SS2 =	SS3 =	SS4 =
	2	6	2	2

SSTotal = ΣX² - (ΣX)²/N = 90 - (30)²/12 = 15

SSBetween = Σ((ΣTᵢ)²)*(1/n) - (ΣX)²/N = (9² + 9² + 6² + 6²)*(1/3) - (30)²/12 = 3

SSSubject = Σ((ΣPⱼ)²)*(1/k) - (ΣX)²/N = (8² + 10²+ 12²)*(1/4) - (30)²/12 = 2

SSError = SSTotal - SSBetween - SSSubject = 15 - 3 - 2 = 10

dfBetween = k-1 = 3

dfSubject = n-1 = 2

dfError = (k-1)*(n-1) = 6

dfTotal = N-1 = 11

MSBetween = 3/3 = 1

MSSubject = 2/2 = 1

MSError = 10/6 = 1.66667

F for Block = MSBetween/ MSError = 1/1.6667 = 0.6

Source	SS	df	MS	F
Block	3	3	1	0.6
Treatment	2	2	1	0.6
Error	10	6	1.6667
Total	15	11