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//Caption: Completely Randomized Design
//Example4.2
//Page78
clear;
clc;
Yij = [80,70,65,90;90,60,50,89;96,55,58,85;85,85,55,95;70,90,40,80];
disp(Yij,'Yij=')
[m,n] = size(Yij);
Y = sum(Yij(:,:));
disp(Y,'Y=')
Y1 = sum(Yij(:,1));
disp(Y1,'Y1=')
Y2 = sum(Yij(:,2));
disp(Y2,'Y2=')
Y3 = sum(Yij(:,3));
disp(Y3,'Y3=')
Y4 = sum(Yij(:,4));
disp(Y4,'Y4=')
SS_total = sum(Yij(:,:).^2)-(Y^2)/(m*n);
disp(SS_total,'SS_total=')
SS_treatments = ((Y1^2)/m)+((Y2^2)/m)+((Y3^2)/m)+((Y4^2)/m)-(Y^2)/(m*n);
disp(SS_treatments,'SS_treatments=')
SS_error = SS_total-SS_treatments;
disp(SS_error,'SS_error=')
Bet_Treat_DOF = n-1;
disp(Bet_Treat_DOF,'Degrees of freedom Between treatments=')
Within_Treat_DOF = m*n-n;
disp(Within_Treat_DOF,'Degrees of freedom With in treatments=')
MSS = [SS_treatments/Bet_Treat_DOF,SS_error/Within_Treat_DOF];
disp(MSS,'Mean Sum of Squares =');
F_ratio = MSS(1)/MSS(2);
disp(F_ratio,'Calculated F ratio =')
Ftable = 3.24;
disp(Ftable,'Tablw F ratio for the significance level =0.05 7 degrees of freedom (3,16)=')
if (F_ratio<Ftable) then
disp('Null Hypothesis should be accepted')
else
disp('Reject Null Hypothesis')
end
//Result
//Yij=
//
// 80. 70. 65. 90.
// 90. 60. 50. 89.
// 96. 55. 58. 85.
// 85. 85. 55. 95.
// 70. 90. 40. 80.
//
// Y=
//
// 1488.
//
// Y1=
//
// 421.
//
// Y2=
//
// 360.
//
// Y3=
//
// 268.
//
// Y4=
//
// 439.
//
// SS_total=
//
// 5368.8
//
// SS_treatments=
//
// 3570.
//
// SS_error=
//
// 1798.8
//
// Degrees of freedom Between treatments=
//
// 3.
//
// Degrees of freedom With in treatments=
//
// 16.
//
// Mean Sum of Squares =
//
// 1190. 112.425
//
// Calculated F ratio =
//
// 10.584834
//
// Tablw F ratio for the significance level =0.05 7 degrees of freedom (3,16)=
//
// 3.24
//
// Reject Null Hypothesis
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