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//Caption:Kruskal-Wallis Test (H Test)
//Example9.23
//Page350
//Ho: There is no significant difference between the production volumes of units assmebled by the three operators
//H1: There is significant difference between the production volumes of units assmebled by the three operators
clear;
clc;
X1 = [29,34,34,20,32,45,42,24,35];//Operator-1:production volume of Units Assembled
X2 = [30,21,23,25,44,37,34,19,38];//Operator-2:production volume of Units Assembled
X3 = [26,36,41,48,27,39,28,46,15];//Operator-3:production volume of Units Assembled
n1 = length(X1);//number of shifts worked by operator-1
n2 = length(X2);//number of shifts worked by operator-2
n3 = length(X3);//number of shifts worked by operator-3
N = n1+n2+n3;//total number of shifts
X =[X1,X2,X3];
[X_sort,ind] = gsort(X,'g','i');
j = 1;
for i = 1:N
R(i)=i;
if (i~=N) then
if (X_sort(i)==X_sort(i+1)) then
K(j)=i;
j = j+1;
elseif (i>1)&(X_sort(i)==X_sort(i-1))
K(j)= i;
j = j+1;
end
end
end
disp(X_sort,'Observations of all samples=')
disp(R,'Ranks of all observations')
for i = 1:length(K)
R(K(i))= sum(K(:))/length(K);
end
for i =1:N
for j= 1:n1
if(X_sort(i)==X1(j))
R_S1(j) = R(i);
elseif (X_sort(i)==X2(j))
R_S2(j) = R(i);
elseif (X_sort(i)==X3(j))
R_S3(j) = R(i);
end
end
end
R_S1 = gsort(R_S1,'g','i');
disp(R_S1,'Ranks of Sample-1=');
R_S2 = gsort(R_S2,'g','i');
disp(R_S2,'Ranks of Sample-2=');
R_S3 = gsort(R_S3,'g','i');
disp(R_S3,'Ranks of Sample-3=');
Sum_R_S1 = sum(R_S1);
disp(Sum_R_S1,'The sum of the ranks of the sample-1')
Sum_R_S2 = sum(R_S2);
disp(Sum_R_S2,'The sum of the ranks of the sample-2')
Sum_R_S3 = sum(R_S3);
disp(Sum_R_S3,'The sum of the ranks of the sample-3')
H = (12/(N*(N+1)))*((Sum_R_S1^2/n1)+(Sum_R_S2^2/n2)+(Sum_R_S3^2/n3))-3*(N+1);
disp(H,'H~chi-square distribution with (K-1) degrees of freedom, where K is the total number of samples H=')
H_table = 5.991;//for 2 degrees of freedom & significance level = 0.05
disp(H_table,'H~chi-square table value for 2 degrees of freedom and significance level of 0.05=')
if(H<H_table)
disp('Since the calculated value of H is < the table chi-square table, accept the null hypothesis' )
else
disp('Reject null hypothesis')
end
//Result
// Observations of all samples=
//
//
// column 1 to 17
//
// 15. 19. 20. 21. 23. 24. 25. 26. 27. 28. 29. 30. 32. 34. 34. 34. 35.
//
// column 18 to 27
//
// 36. 37. 38. 39. 41. 42. 44. 45. 46. 48.
//
// Ranks of all observations
//
// 1.
// 2.
// 3.
// 4.
// 5.
// 6.
// 7.
// 8.
// 9.
// 10.
// 11.
// 12.
// 13.
// 14.
// 15.
// 16.
// 17.
// 18.
// 19.
// 20.
// 21.
// 22.
// 23.
// 24.
// 25.
// 26.
// 27.
//
// Ranks of Sample-1=
//
// 3.
// 6.
// 11.
// 13.
// 15.
// 15.
// 17.
// 23.
// 25.
//
// Ranks of Sample-2=
//
// 2.
// 4.
// 5.
// 7.
// 12.
// 15.
// 19.
// 20.
// 24.
//
// Ranks of Sample-3=
//
// 1.
// 8.
// 9.
// 10.
// 18.
// 21.
// 22.
// 26.
// 27.
//
// The sum of the ranks of the sample-1
//
// 128.
//
// The sum of the ranks of the sample-2
//
// 108.
//
// The sum of the ranks of the sample-3
//
// 142.
//
// H~chi-square distribution with (K-1) degrees of freedom, where K is the total number of samples H=
//
// 1.0299824
//
// H~chi-square table value for 2 degrees of freedom and significance level of 0.05=
//
// 5.991
//
// Since the calculated value of H is < the table chi-square table, accept the null hypothesis
//
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