Question

An experiment was performed where 7 treatments were randomly and equally assigned to 28 exper- imental units. The only information you obtain is that the sample variance among the responses in s2y = 12.3 and the MSE = 7.1. Construct the ANOVA table and test whether there is at least one treatment effect different from zero at the .05 level.

1. An experiment was performed where 7 treatments were randomly and equally assigned to 28 exper- imental units. The only information you obtain is that the sample variance among the responses in s.. 12.3 and the MSE = 7.1. Construct the ANOVA table and test whether there is at least one treatment effect different from zero at the .05 level

Answer 1

Ans:

Total number of subjects=28

Total df=28-1=27

df(treatments)=7-1=6

df(error)=28-7=21

Total SS=12.3*27=332.1

SS(error)=MS(error)*df=7.1*21=149.1

SS(treatments)=332.1-149.1=183

MS(treatments=183/6=30.5

F=30.5/7.1=4.30

ANOVA table:

Source	SS	df	MS	F
Between treatments	183	6	30.5	4.30
Error	149.1	21	7.1
Total	332.1	27

p-value=FDIST(4.30,6,21)=0.0056

Reject H₀,as p-value<0.05

There is sufficient evidence to conclude that there is atleast one treatment effect different from zero at the 0.05 level.