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+//Caption: Randomized Complete Block Design
+//Example4.3
+//Page82
+clear;
+clc;
+Yij = [23,30,25,28;34,20,29,34;45,30,45,40;34,20,35,40];
+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=')
+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=')
+SS_total = sum(Yij(:,:).^2)-(Y^2)/(m*n);
+disp(SS_total,'SS_total=')
+SS_Blocks = ((Y1j^2)/n)+((Y2j^2)/n)+((Y3j^2)/n)+((Y4j^2)/n)-(Y^2)/(m*n);
+disp(SS_Blocks,'SS_blocks=')
+SS_treatments = ((Yi1^2)/m)+((Yi2^2)/m)+((Yi3^2)/m)+((Yi4^2)/m)-(Y^2)/(m*n);
+disp(SS_treatments,'SS_treatments=')
+SS_error = SS_total-SS_treatments-SS_Blocks;
+disp(SS_error,'SS_error=')
+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=')
+Within_Treat_DOF = m*n-n-m+1;
+disp(Within_Treat_DOF,'Degrees of freedom With in treatments=')
+MSS = [SS_treatments/Bet_Treat_DOF,SS_Blocks/Bet_Blocks,SS_error/Within_Treat_DOF];
+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=')
+disp(F_ratio2,'Calculated F ratio2 for component block=')
+Ftable =  3.86;
+disp(Ftable,'Tablw F ratio for the significance level =0.05 7 degrees of freedom (3,9)=')
+if (F_ratio1 <Ftable) then
+    disp('Null Hypothesis should be accepted')
+    disp('There is no significant difference in terms of weekly sales made between the graduates of different business schools')
+else
+    disp('Reject Null Hypothesis')
+end
+if (F_ratio2 <Ftable) then
+    disp('Null Hypothesis should be accepted')
+    disp('There is no significant difference in terms of weekly sales made between different sections of the showroom')
+else
+    disp('Reject Null Hypothesis')
+    disp('There is significant difference in terms of weekly sales made between different sections of the showroom')
+end
+//Result
+//Yij=   
+// 
+//    23.    30.    25.    28.  
+//    34.    20.    29.    34.  
+//    45.    30.    45.    40.  
+//    34.    20.    35.    40.  
+// 
+// Y=   
+// 
+//    512.  
+// 
+// Yi1=   
+// 
+//    136.  
+// 
+// Yi2=   
+// 
+//    100.  
+// 
+// Yi3=   
+// 
+//    134.  
+// 
+// Yi4=   
+// 
+//    142.  
+// 
+// Y1j=   
+// 
+//    106.  
+// 
+// Y2j=   
+// 
+//    117.  
+// 
+// Y3j=   
+// 
+//    160.  
+// 
+// Y4j=   
+// 
+//    129.  
+// 
+// SS_total=   
+// 
+//    938.  
+// 
+// SS_blocks=   
+// 
+//    407.5  
+// 
+// SS_treatments=   
+// 
+//    270.  
+// 
+// SS_error=   
+// 
+//    260.5  
+// 
+// Degrees of freedom Between treatments=   
+// 
+//    3.  
+// 
+// Degrees of freedom Between Blocks=   
+// 
+//    3.  
+// 
+// Degrees of freedom With in treatments=   
+// 
+//    9.  
+// 
+// Mean Sum of Squares =   
+// 
+//    90.    135.83333    28.944444  
+// 
+// Calculated F ratio1 for component treatment=   
+// 
+//    3.109405  
+// 
+// Calculated F ratio2 for component block=   
+// 
+//    4.6928983  
+// 
+// Tablw F ratio for the significance level =0.05 7 degrees of freedom (3,9)=   
+// 
+//    3.86  
+// 
+// Null Hypothesis should be accepted   
+// 
+// There is no significant difference in terms of weekly sales made between the graduates of different business schools   
+// 
+// Reject Null Hypothesis   
+// 
+// There is significant difference in terms of weekly sales made between different sections of the showroom   
+// 
+\ No newline at end of file