import numpy as np from scipy.stats import f, t # 数据集 datas = [ [29.6, 24.3, 28.5, 32.0], [27.3, 32.6, 30.8, 34.8], [5.8, 6.2, 11.0, 8.3], [21.6, 17.4, 18.3, 19.0], [29.2, 32.8, 25.0, 24.2] ] alpha = 0.05 def calculate_mean_and_variance(data): """计算数据集的均值和方差""" return np.mean(data), np.var(data, ddof=1) def calculate_total_square_sum(data): """计算总体平方和""" data_mean, _ = calculate_mean_and_variance(data) return (data - data_mean).sum() ** 2 def calculate_group_square_sum(data_all, datas): """计算组间平方和""" data_all_mean, _ = calculate_mean_and_variance(data_all) group_square_sum = 0 for group in datas: group_mean, _ = calculate_mean_and_variance(group) group_square_sum += len(group) * (group_mean - data_all_mean) ** 2 return group_square_sum def calculate_error_square_sum(data_all, datas): """计算误差平方和""" error_square_sum = 0 data_all_mean, _ = calculate_mean_and_variance(data_all) for group in datas: group_mean, _ = calculate_mean_and_variance(group) for value in group: error_square_sum += (value - group_mean) ** 2 return error_square_sum def calculate_f_statistics(group_square_sum, error_square_sum, s, n): """计算F统计量""" A_mean_square_sum = group_square_sum / (s - 1) E_mean_square_sum = error_square_sum / (n - s) return A_mean_square_sum / E_mean_square_sum def print_analysis_results(group_square_sum, error_square_sum, total_square_sum, s, n): """打印分析结果""" print("| 方差来源 | 平方和 | *度 | 均方和 |") print(f"| 因素A | {group_square_sum} | {s-1} | {group_square_sum/(s-1):.4f} |") print(f"| 误差E | {error_square_sum} | {n-s} | {error_square_sum/(n-s):.4f} |") print(f"| 总体T | {total_square_sum} | {n-1} | {total_square_sum/(n-1):.4f} |") def get_confidence_interval(data, alpha=0.05): """计算均值的置信区间""" n = len(data) mean, var = calculate_mean_and_variance(data) t_threshold = t.isf(alpha / 2, df=n - 1) std_err = np.sqrt(var) * t_threshold / np.sqrt(n) return mean - std_err, mean + std_err def get_difference_confidence_interval(data_x, data_y, n, r, Q_e, alpha=0.05): """计算两个均值差的置信区间""" n_x, n_y = len(data_x), len(data_y) x_mean, x_var = calculate_mean_and_variance(data_x) y_mean, y_var = calculate_mean_and_variance(data_y) t_threshold = t.isf(alpha / 2, df=n - r) Q_e_mean = Q_e / (n - r) std_err = np.sqrt((1/n_x + 1/n_y) * Q_e_mean) * t_threshold return (x_mean - y_mean) - std_err, (x_mean - y_mean) + std_err def main(datas, alpha): # 计算总样本量 n_total = sum(len(group) for group in datas) s = len(datas) # 计算总体数据 data_all = np.concatenate(datas) total_square_sum = calculate_total_square_sum(data_all) # 计算组间和误差平方和 group_square_sum = calculate_group_square_sum(data_all, datas) error_square_sum = calculate_error_square_sum(data_all, datas) # 计算F统计量和临界F值 F_value = calculate_f_statistics(group_square_sum, error_square_sum, s, n_total) F_threshold = f.isf(q=alpha, dfn=s-1, dfd=n_total-s) # 打印分析结果 print_analysis_results(group_square_sum, error_square_sum, total_square_sum, s, n_total) # 打印F值和临界F值 print(f"\na值: {alpha}") print(f"临界F值---F_{alpha}({s-1},{n_total-s}): {F_threshold}") # 根据F值判断显著性 if F_value > F_threshold: print('拒绝原假设，不同处理之间存在显著差异') else: print('接受原假设，不同处理之间不存在显著差异') # 计算每个组均值的置信区间 for i, group in enumerate(datas): interval = get_confidence_interval(group, alpha) print(f'第{i+1}组数据均值的置信区间为: {interval}') # 计算每两个组之间均值差的置信区间 for i in range(len(datas)): for j in range(i+1, len(datas)): interval = get_difference_confidence_interval(datas[i], datas[j], n_total, s, error_square_sum, alpha) print(f'第{i+1}组数据与第{j+1}组数据的均值差的置信区间为: {interval}') if __name__ == "__main__": main(datas, alpha)