An experiment has been conducted for four treatments with ei

An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to 2 decimals, if necessary). Use aplha = .05 to test for any significant differences. The rho-value is What is your conclusion?

Solution

Sum of Squares of Error = Total - Sum of Squares (Treatment + Blocks)

= 1900 - (1100 + 400) = 400

DF treatments = No of treatment - 1 = 4 - 1 = 3

DF Blocks = No of blocks - 1 = 8 - 1 = 7

n = 4*8 = 32 (no of blocks * treatments)

DF Error = 32 - 4 - 8 + 1 = 21

DF Total = 21 + 7 + 3 = 31

Mean Square Treatment = Sum of Squares of Treatment / DF Treatment = 1100/3 = 366.67

Mean Square Blocks = Sum of Squares of Blocks / DF Blocks = 400/7 = 57.14

Mean Square Error = Sum of Squares of Error / DF Error = 400/21 = 19.05

F Treatment = MS treatment / MS Error = 366.67/19.05 = 19.25

p value = 0.000004

The test is significant and we can reject the null hypothesis