Question

Fifteen people are randomly assigned, so that 5 people exercise in the morning, afternoon, or night. After 8 weeks, their weight loss is measured in pounds. Compute the F ratio.

Morning	Afternoon	Night
10	8	6
8	8	7
7	9	5
5	7	4
9	7	5

Answer 1

Applying one way ANOVA:

	Morning	Afternoon	Night
	10	8	6
	8	8	7
	7	9	5
	5	7	4
	9	7	5
count ni=	5	5	5
Average==ΣXi/ni=	7.8000	7.8000	5.4000
Total=ΣX2i   =	319.000	307.0000	151.0000
SS=ΣX2i -(Σxi)2/ni=	14.800	2.8000	5.2000
Grand average Xgrand =∑xi/N =		105/10=	7.0000

i	ni	x̅i	ni*(Xi-Xgrand)2	SS=(ni-1)*s2
Morning	5	7.8000	3.200	14.8
Afternoon	5	7.8000	3.200	2.8
Night	5	5.4000	12.800	5.2
Total	15		19.200	22.8000
			SSTr	SSE
df treatments =	number of treatments-1=			2
df error =	N-k=	15-3=		12
df total=	N-1=	15-1=		14
MS(treatment) =SSTr/df(Tr)=19.2/2=			9.60000
MS(error) =SSE/df(error)=22.8/12=			1.90000
test statistic F ratio =MSTr/MSE =9.6/1.9=			5.0526