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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
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