Question

question 1

Consider a one-way ANOVA test with 27 samples categorized into 4 groups. It is calculated that SSE = 851. Calculate MSE.

question 2

Consider a one-way ANOVA test with with 25 samples categorized into four groups. The sample sizes and sample means are as follows:

Sample sizes (ni)	3	5	7	5
Sample means (x¯i)	10	9	10	7

It can be calculated that the grand mean is 9. Calculate SSTR.

question 3

The observations shown in the accompanying table were drawn from a randomized block design with no interaction.

	Column 1	Column 2	Column 3	Column 4	Row-mean
Row 1	24	24	21	63	33
Row 2	10	10	13	19	13
Row 3	17	14	14	11	14
Column-mean	17	16	16	31	Grand mean=20

Calculate SSA (or SS(column)).

Answer 1

1)here df error =N-c-1=27-4=23

MSE =SSE/df(error)=851/23 =37

2)

population	ni	x̅i		ni*(Xi-Xgrand)2
1	3	10.000		3.000
2	5	9.000		0.000
3	7	10.000		7.000
4	5	7.000		20.000
	grand mean=	9.000		30.000

from aove SSTr =30

3)

	X1	X2	X3	X4	nj	Total=ΣYi
Y1	24	24	21	63	4	132
Y2	10	10	13	19	4	52
Y3	17	14	14	11	4	56
ni	3	3	3	3		12
Total=ΣXi   =	51	48	48	93		240
Average==ΣXi/ni=	17.0000	16.0000	16.0000	31.0000	Grandmean=	20.0000

i	ni	x̅i	ni*(X̅i-Grandmean)2
X1	3	17	27.000
X2	3	16	48.000
X3	3	16	48.000
X4	3	31	363.000
	total	SSA	486.000

from above SSA =486