Question

An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to 2 decimals, if necessary and p-value to 4 decimals). If your answer is zero enter "0".

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	700
Blocks	600
Error
Total	1,600

Use  = .05 to test for any significant differences.

Answer 1

Here we have 4 treatments, so a = 4, and 8 blocks, so b= 8 , so N = 8*4

So treatment df = a -1 = 4-1 =3 , blocks df = b-1 = 8-1 = 7

Error df = ( a -1 ) ( b-1) = 3*7 = 21 , Total df = N-1 = 32 - 1 = 31

Total sum of square = Treatment sum of square + Blocks sum of squares + Error sum of square

1600 = 700 + 600 + Error sum of square

So Error sum of square = 1600 - 700 - 600 = 300

Source of variation	Sum of square	Degrees of freedom	Mean Square	F	P value
Treatment	700	3	233.33	16.33	0
Blocks	600	7	85.71	6	0.0006
Error	300	21	14.29
Total	1600	31

Using excel formula, p value is given by,

P value for treatment = " =f.dist.rt(16.33,3,21)" = 0.0000

So here p value < ( 0.05) . Hence we reject null hypothesis.

Conclusion : Treatments are significant.

P value for Blocks = " =f.dist.rt(6,7,21)" = 0.0006

So here p value < ( 0.05) . Hence we reject null hypothesis.

Conclusion : Blocks are significant.