Answer:
Sum of Squares=50.5
Treatment Sum of Squares, 4.5
Error Mean Squares, 0.3
Treatment Mean Squares 0.9
Error Sum of Square = 3
Step-by-step explanation:
Given data
Observation A B C
1 8 7 10
2 7 7 11
3 6 6 10
4 7 6 9
5 8 7 10
6 6 6 10
A B C Row total (xr)
1 8 7 10 25
2 7 7 11 25
3 6 6 10 22
4 7 6 9 22
5 8 7 10 25
6 6 6 10 22
Col total (xc) 42 39 60 141
Using calculator for summarizing data
∑x²=1155 ⇒(A)
∑x²c/r=16(42²+39²+60²)
=1/6(1764+1521+3600)
=1/6(6885)
=1147.5⇒(B)
∑x²r/c=13(25²+25²+22²+22²+25²+22²)
=1/3(625+625+484+484+625+484)
=1/3(3327)
=1109⇒(C)
(∑x)²/n=(141)²/18
=19881/18
=1104.5⇒(D)
Sum of squares total
SST=∑x²-(∑x)²/n=(A)-(D)
=1155-1104.5
=50.5
Sum of squares between rows
SSR=∑x²r/c-(∑x)²/n=(C)-(D)
=1109-1104.5
=4.5
Sum of squares between columns
SSC=∑x²c/r-(∑x)²n=(B)-(D)
=1147.5-1104.5
=43
Sum of squares Error (residual)
SSE=SST-SSR-SSC
=50.5-4.5-43
=3
ANOVA table
Source Sums Degrees of Mean Squares
of Variation of Squares freedom F- value
SS DF MS
Between Treatments SSR=4.5 r-1=5 MSR=0.9 3
Between Blocks SSC=43 c-1=2 MS =21.5 71.6667
Error (residual) SSE=3 (r-1)(c-1)=10 MSE=0.3
Total SST=50.5 rc-1=17
