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//Caption: Two-samples Medain Test (Large Samples)
//Example9.18
//Page340
clear;
clc;
S1 = [25,30,46,40,65,45,33,35,41,51,64,66,77,82,96,68];//sample 1:Catalyst X
S2 = [28,32,42,47,62,53,29,34,54,57,63,70,80,78,93];//sample 2: Catalyst Y
n1 = length(S1);//size of the first sample
n2 = length(S2);//size of the second sample
N = n1+n2;//size of the pooled obsrevations
alpha = 0.05;//significance level
X = [S1,S2];//increased warranty period & Increased price discount
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 =')
p = 0;
r = 0;
for i = 1:length(S1)
if (S1(i)>u) then
p = p+1;
elseif(S1(i)<=u)
r = r+1;
end
end
q = 0;
s = 0;
for i = 1:length(S2)
if (S2(i)>u) then
q = q+1;
elseif(S2(i)<=u)
s = s+1;
end
end
P = [p,q;r,s]
disp(P,'Table. Frequency of pooled observations')
chi_calc = (N*(abs(p*s-q*r)-(N/2))^2)/((p+q)*(r+s)*(p+r)*(q+s));
chi_table = 3.841;//chi-square value for 1 degree of freedom and alpha = 0.05
disp(chi_calc,'calculated chi-square value =')
disp(chi_table,'chi-square table value=')
if (chi_calc < chi_table) then
disp('Since the calculated chi-square value is less than the 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
//
// 25. 28. 29. 30. 32. 33. 34. 35. 40. 41. 42. 45. 46. 47. 51. 53. 54.
//
// column 18 to 31
//
// 57. 62. 63. 64. 65. 66. 68. 70. 77. 78. 80. 82. 93. 96.
//
// The median of the pooled observations u =
//
// 53.
//
// Table. Frequency of pooled observations
//
// 7. 8.
// 9. 7.
//
// calculated chi-square value =
//
// 0.0302734
//
// chi-square table value=
//
// 3.841
//
// Since the calculated chi-square value is less than the table value
//
// Accept the Null Hypothesis
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