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+//Caption:K-Samples Tests
+//K-samples Median Test
+//Example9.22
+//Page349
+//Ho: There is no significant difference between the ages of respondents in three regions
+//H1: There is significant difference between the ages of respondents in three regions
+clear;
+clc;
+X1 = [35,42,28,31,44,50,33,52,56];//Age of Respondents in Region-1
+X2 = [45,55,32,47,53,46,41,34,49];//Age of Respondents in Region-2
+X3 = [38,36,43,30,60,39,54,57,27];//Age of Respondents in Region-3
+n1 = length(X1);//size of the first sample
+n2 = length(X2);//size of the second sample
+n3 = length(X3);//size of the third sample
+N = n1+n2+n3;//size of the pooled observations
+alpha = 0.05;//significance level
+X = [X1,X2,X3];
+Xsort = gsort(X,'g','i');
+u = median(Xsort);
+disp(Xsort,'The pooled observations in the increasing order are:')
+disp(u,'The median of the pooled observations u =')
+p1 = 0;
+q1 = 0;
+for i = 1:length(X1)
+    if (X1(i)>u) then
+        p1 = p1+1;
+    elseif(X1(i)<=u)
+        q1 = q1+1;
+    end  
+end
+p2 = 0;
+q2 = 0;
+for i = 1:length(X2)
+    if (X2(i)>u) then
+        p2 = p2+1;
+    elseif(X2(i)<=u)
+        q2 = q2+1;
+    end
+end
+p3 = 0;
+q3 = 0;
+for i = 1:length(X3)
+    if (X3(i)>u) then
+        p3 = p3+1;
+    elseif(X3(i)<=u)
+        q3 = q3+1;
+    end
+end
+p = [p1,p2,p3;q1,q2,q3]
+disp(p,'Frequency of pooled observations');
+//v1 = factorial(n1)/((factorial(n1-p1))*(factorial(p1)));
+//v2 = factorial(n2)/((factorial(n2-p2))*(factorial(p2)));
+//v3 = factorial(n3)/((factorial(n3-p3))*(factorial(p3)));
+//v4 = factorial(N)/((factorial(N-(p1+p2+p3)))*(factorial(p1+p2+p3)));
+//P = (v1*v2*v3)/v4;
+//disp(P,'calculated Probability  value  =')
+[r,c] = size(p);
+for i = 1:r
+    for j = 1:c
+        Row_Tot(i) = sum(p(i,:));
+        Col_Tot(j) = sum(p(:,j)); 
+        e(i,j)     = (Row_Tot(i)* Col_Tot(j))/N;
+    end
+end
+disp(Row_Tot,'Row Total=')
+disp(Col_Tot','Column Total=')
+chi = 0;
+for i = 1:r
+    for j =1:c
+        chi= chi+(((p(i,j)-e(i,j))^2)/(e(i,j)));
+    end
+end
+disp(chi,'The Chi-square Statistic value =')
+Chi_stand = 5.991;//for 2 degrees of freedom and significance level = 0.05
+disp(Chi_stand,'The table Chi-Square statistic for 2 degrees of freedom & alpha =0.05')
+if (chi < Chi_stand) then
+    disp('Since the calculated Chi-square statistic is less than table value')
+    disp('Accept the Null Hypothesis')
+else
+    disp('Reject Null Hypothesis')
+end
+//Result
+ 
+// The pooled observations in the increasing order are:   
+// 
+// 
+//         column  1 to 17
+// 
+//    27.    28.    30.    31.    32.    33.    34.    35.    36.    38.    39.    41.    42.    43.    44.    45.    46.  
+// 
+//         column 18 to 27
+// 
+//    47.    49.    50.    52.    53.    54.    55.    56.    57.    60.  
+// 
+// The median of the pooled observations u =   
+// 
+//    43.  
+// 
+// Frequency of pooled observations   
+// 
+//    4.    6.    3.  
+//    5.    3.    6.  
+// 
+// Row Total=   
+// 
+//    13.  
+//    14.  
+// 
+// Column Total=   
+// 
+//    9.    9.    9.  
+// 
+// The Chi-square Statistic value =   
+// 
+//    2.0769231  
+// 
+// The table Chi-Square statistic for 2 degrees of freedom & alpha =0.05   
+// 
+//    5.991  
+// 
+// Since the calculated Chi-square statistic is less than table value   
+// 
+// Accept the Null Hypothesis   
+\ No newline at end of file