Question

The anova from a randomized complete block experiment output is shown below. source df ss ms f p treatment 4 1010.56 ? 29.84 ? block ? ? 64.765 ? ? error 20 169.33 ? total 29 1503.71 (a) fill in the blanks. you may give bounds on the p-value. (b) how many blocks were used in this experiment? (c) what conclusions can you draw?

Answer 1

Source DF SS MS F PTreatment 4 1010.56 252.64 29.84 3.545E-08Block 5 323.825 64.765 7.649 0.00037Error 20 169.33 8.467 Total 29 1503.71


d.f. for blocks =b-1= 29-(20+4)= 29-24=5Hence here b=6 blocks were used. MS for treatment Ms for error = So SS for Blocks = MS * df =64.765*5 = 323.825F for block = p value for treatment using excel : 'fdist(29.84,4,20)' = 3.545E-08p value for block : 'fdist(7.649,5,20)' = 0.00037Here p value for treatment ( 0.0000000354) < ( 0.05 )Hence we reject null hypothesis.Also p value for block (0.00037 ) < ( 0.05 )Hence we reject null hypothesisConclusion : There is difference between treatment means as well as block means.