卡方统计量的计算公式为 $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$，其中 $O_i$ 是观察频数，$E_i$ 是期望频数 [^3]。以下给出不同语言实现卡方统计量的代码示例： ### MATLAB 实现 ```matlab %% 计算交叉列联表的卡方统计量 clear clc %% 填充数据 A=[45 42; 105 78]; %% 计算过程 sum_A=sum(sum(A)); [r, c] = size(A); e=zeros(r,c);%观察频数 x_=zeros(r,c);%待求和的卡方分量 for i =1:r for j =1:c e(i,j)=sum(A(i,:)*sum(A(:,j)/sum_A)); x_(i,j)=(A(i,j)-e(i,j))^2/e(i,j); end end X = sum(sum(x_)); fprintf('χ2=%f\n',X); % 输出结果 ``` ### Python 实现 ```python import numpy as np # 填充数据 A = np.array([[45, 42], [105, 78]]) # 计算总和 sum_A = np.sum(A) # 获取行数和列数 r, c = A.shape # 初始化期望频数和卡方分量数组 e = np.zeros((r, c)) x_ = np.zeros((r, c)) # 计算期望频数和卡方分量 for i in range(r): for j in range(c): e[i, j] = np.sum(A[i, :]) * np.sum(A[:, j]) / sum_A x_[i, j] = (A[i, j] - e[i, j]) ** 2 / e[i, j] # 计算卡方统计量 X = np.sum(x_) print(f'χ2={X}') ``` ### C++ 实现 ```cpp #include <iostream> #include <vector> double chiSquareStatistic(const std::vector<std::vector<int>>& observed) { int r = observed.size(); int c = observed[0].size(); // 计算总和 int sum_A = 0; for (const auto& row : observed) { for (int val : row) { sum_A += val; } } // 计算期望频数和卡方统计量 double chi_square = 0.0; for (int i = 0; i < r; ++i) { int row_sum = 0; for (int val : observed[i]) { row_sum += val; } for (int j = 0; j < c; ++j) { int col_sum = 0; for (const auto& row : observed) { col_sum += row[j]; } double expected = static_cast<double>(row_sum * col_sum) / sum_A; double diff = observed[i][j] - expected; chi_square += (diff * diff) / expected; } } return chi_square; } int main() { std::vector<std::vector<int>> observed = { {45, 42}, {105, 78} }; double X = chiSquareStatistic(observed); std::cout << "χ2=" << X << std::endl; return 0; } ```