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//Caption: Chi-Square Test for Checking Independence of categorized data
//Example8.35
//Page294
//Ho: pij = pi.pj; H1: pij>pi.pj
//ROR_LOT: Rate of return versus level of technology used
clear;
clc;
ROR_LOT =[20,50,30,10;50,70,75,35;10,20,70,60]';
disp('Level of technology used=')
disp('Low Medium High')
disp('___________________________')
disp(ROR_LOT)
disp('___________________________')
[m,n]= size(ROR_LOT);
for j = 1:n
oj(j)= sum(ROR_LOT(:,j));
end
oj = oj';
disp(oj,'Column total =')
for i = 1:m
oi(i) = sum(ROR_LOT(i,:));
end
disp(oi,'Row total =')
oij = sum(oj);
disp(oij,'Total number of observations in the entire table=')
for i = 1:m
for j = 1:n
eij(i,j) = (oi(i)*oj(j))/oij
end
end
disp(eij,'The expected frequencies for different combinations of rows and columns')
for i = 1:m
for j = 1:n
chi(i,j) = ((ROR_LOT(i,j)-eij(i,j))^2)/eij(i,j);
end
end
tot_chi = sum(chi(:,:));
disp(tot_chi,'The calculated chi-square statistic =')
alpha = 0.05;
chi_stand = 12.592//chi-square statistic form table chi-square value
disp(chi_stand,'The chi-square statistic form table chi-square value=')
if (tot_chi>chi_stand) then
disp('It falls in the Rejection Region')
disp('Then Null Hypothesis Ho should be Rejected')
else
disp('It falls in the Acceptance Region')
disp('Then Null Hypothesis Ho should be Accepted')
end
//Result
//Level of technology used=
//
// Low Medium High
//
// ___________________________
//
// 20. 50. 10.
// 50. 70. 20.
// 30. 75. 70.
// 10. 35. 60.
//
// ___________________________
//
// Column total =
//
// 110. 230. 160.
//
// Row total =
//
// 80.
// 140.
// 175.
// 105.
//
// Total number of observations in the entire table=
//
// 500.
//
// The expected frequencies for different combinations of rows and columns
//
// 17.6 36.8 25.6
// 30.8 64.4 44.8
// 38.5 80.5 56.
// 23.1 48.3 33.6
//
// The calculated chi-square statistic =
//
// 78.339245
//
// The chi-square statistic form table chi-square value=
//
// 12.592
//
// It falls in the Rejection Region
//
// Then Null Hypothesis Ho should be Rejected
//
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