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//Caption: Randomized Complete Block Design
//Example4.4
//Page86
clear;
clc;
Yij = [40,30,55,25,35;45,60,10,22,33;38,55,40,55,28;30,27,32,56,17;45,34,20,34,37];
disp(Yij,'Yij=')
[m,n] = size(Yij);
Y = sum(Yij(:,:));
disp(Y,'Y=')
Yi1 = sum(Yij(:,1));
disp(Yi1,'Yi1=')
Yi2 = sum(Yij(:,2));
disp(Yi2,'Yi2=')
Yi3 = sum(Yij(:,3));
disp(Yi3,'Yi3=')
Yi4 = sum(Yij(:,4));
disp(Yi4,'Yi4=')
Yi5 = sum(Yij(:,5));
disp(Yi5,'Yi5=')
Y1j = sum(Yij(1,:));
disp(Y1j,'Y1j=')
Y2j = sum(Yij(2,:));
disp(Y2j,'Y2j=')
Y3j = sum(Yij(3,:));
disp(Y3j,'Y3j=')
Y4j = sum(Yij(4,:));
disp(Y4j,'Y4j=')
Y5j = sum(Yij(5,:));
disp(Y5j,'Y5j=');
SS_total = sum(Yij(:,:).^2)-(Y^2)/(m*n);
disp(SS_total,'SS_total=')
SS_team = ((Y1j^2)/n)+((Y2j^2)/n)+((Y3j^2)/n)+((Y4j^2)/n)+((Y5j^2)/n)-(Y^2)/(m*n);
disp(SS_team,'SS_team_leader=')
SS_team_leader = ((Yi1^2)/m)+((Yi2^2)/m)+((Yi3^2)/m)+((Yi4^2)/m)+((Yi5^2)/m)-(Y^2)/(m*n);
disp(SS_team,'SS_team=')
SS_error = SS_total-SS_team_leader-SS_team;
Bet_Treat_DOF = n-1;
disp(Bet_Treat_DOF,'Degrees of freedom Between treatments=')
Bet_Blocks = m-1;
disp(Bet_Blocks,'Degrees of freedom Between Blocks=')
Error = m*n-n-m+1;
disp(Error,'Degrees of freedom With in treatments=')
MSS = [SS_team_leader/Bet_Treat_DOF,SS_team/Bet_Blocks,SS_error/Error];
disp(MSS,'Mean Sum of Squares =');
F_ratio1 = MSS(1)/MSS(3);
F_ratio2 = MSS(2)/MSS(3);
disp(F_ratio1,'Calculated F ratio1 for component treatment- team leader=')
disp(F_ratio2,'Calculated F ratio2 for component block=')
Ftable = 3.01;
disp(Ftable,'Tablw F ratio for the significance level =0.05 and degrees of freedom (4,16)=')
if (F_ratio1 <Ftable) then
disp('Null Hypothesis should be accepted')
disp('This means that there is no significant difference in terms of net worth between the team leaders')
else
disp('Reject Null Hypothesis')
end
if (F_ratio2 <Ftable) then
disp('Null Hypothesis should be accepted')
disp('This means that there is no significant difference in terms of net worth between different teams')
else
disp('Reject Null Hypothesis')
end
//Result
// Yij=
//
// 40. 30. 55. 25. 35.
// 45. 60. 10. 22. 33.
// 38. 55. 40. 55. 28.
// 30. 27. 32. 56. 17.
// 45. 34. 20. 34. 37.
//
// Y=
//
// 903.
//
// Yi1=
//
// 198.
//
// Yi2=
//
// 206.
//
// Yi3=
//
// 157.
//
// Yi4=
//
// 192.
//
// Yi5=
//
// 150.
//
// Y1j=
//
// 185.
//
// Y2j=
//
// 170.
//
// Y3j=
//
// 216.
//
// Y4j=
//
// 162.
//
// Y5j=
//
// 170.
//
// SS_total=
//
// 4118.64
//
// SS_team_leader=
//
// 368.64
//
// SS_team=
//
// 368.64
//
// Degrees of freedom Between treatments=
//
// 4.
//
// Degrees of freedom Between Blocks=
//
// 4.
//
// Degrees of freedom With in treatments=
//
// 16.
//
// Mean Sum of Squares =
//
// 128.56 92.16 202.235
//
// Calculated F ratio1 for component treatment- team leader=
//
// 0.6356961
//
// Calculated F ratio2 for component block=
//
// 0.4557075
//
// Tablw F ratio for the significance level =0.05 7 degrees of freedom (3,9)=
//
// 3.86
//
// Null Hypothesis should be accepted
//
// This means that there is no significant difference in terms of net worth between the team leaders
//
// Null Hypothesis should be accepted
//
// This means that there is no significant difference in terms of net worth between different teams
//
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