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Find two way anova {{1,4,0,7 13,5,7,15 9,16,18,13},{15,6,10,13 6,18,9,15 14,7,6,13}} [ Calculator, Method and examples ]

Solution:
Your problem -> two way anova {{1,4,0,7 13,5,7,15 9,16,18,13},{15,6,10,13 6,18,9,15 14,7,6,13}}

Given problem
 Observation A B C 1 1, 4, 0, 7 13, 5, 7, 15 9, 16, 18, 13 2 15, 6, 10, 13 6, 18, 9, 15 14, 7, 6, 13

Row and column sums
 A B C Row total (x_(a)) 1 12 40 56 108 2 44 48 40 132 Col total (x_(b)) 56 88 96 240

sum x^2=1^2 + 4^2 + 0^2 + ... + 7^2 + 6^2 + 13^2=3010 ->(A)

(sum x_(b)^2)/(ra)=1/(4*2)(56^2+88^2+96^2)

=1/8(3136+7744+9216)

=1/8(20096)

=2512 ->(B)

(sum x_(a)^2)/(rb)=1/(4*3)(108^2+132^2)

=1/12(11664+17424)

=1/12(29088)

=2424 ->(C)

(sum sum x_(ab)^2)/r=1/4(12^2+40^2+56^2+44^2+48^2+40^2)

=1/4(144+1600+3136+1936+2304+1600)

=1/4(10720)

=2680 ->(C)

(sum x)^2/(rab)=(240)^2/(4*2*3)

=57600/24

=2400 ->(D)

Sum of squares total
SS_T=sum x^2 - (sum x)^2/(n)=(A)-(D)

=3010-2400

=610

Sum of squares between rows
SS_A=(sum x_(a)^2)/(rb) - (sum x)^2/(n)=(C)-(D)

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