应用示例 (Examples) =================== 本文档提供了统计检验模块在实际场景中的综合应用示例，涵盖数据科学、商业分析、科学研究等多个领域。 .. contents:: 目录 :local: :depth: 2 数据科学场景 ------------ 机器学习模型评估 ~~~~~~~~~~~~~~~~ 在机器学习项目中，统计检验可以帮助评估模型性能的显著性差异。 .. code-block:: python from pywayne.statistics import LocationTests, NormalityTests import numpy as np from sklearn.model_selection import cross_val_score from sklearn.ensemble import RandomForestClassifier from sklearn.svm import SVC from sklearn.datasets import make_classification def model_comparison_analysis(): """比较不同机器学习模型的性能""" # 生成数据集 X, y = make_classification(n_samples=1000, n_features=20, n_informative=10, random_state=42) # 定义模型 models = { 'Random Forest': RandomForestClassifier(random_state=42), 'SVM': SVC(random_state=42) } # 交叉验证评估 cv_scores = {} for name, model in models.items(): scores = cross_val_score(model, X, y, cv=10, scoring='accuracy') cv_scores[name] = scores print(f"{name}: 均值={np.mean(scores):.4f}, 标准差={np.std(scores):.4f}") # 统计检验比较 lt = LocationTests() nt = NormalityTests() rf_scores = cv_scores['Random Forest'] svm_scores = cv_scores['SVM'] # 检验正态性 rf_norm = nt.shapiro_wilk(rf_scores) svm_norm = nt.shapiro_wilk(svm_scores) print(f"\n正态性检验:") print(f"Random Forest: p={rf_norm.p_value:.4f}, 正态={not rf_norm.reject_null}") print(f"SVM: p={svm_norm.p_value:.4f}, 正态={not svm_norm.reject_null}") # 配对t检验（交叉验证是配对的） paired_result = lt.paired_ttest(rf_scores, svm_scores) print(f"\n配对t检验结果:") print(f"t统计量: {paired_result.statistic:.4f}") print(f"p值: {paired_result.p_value:.4f}") print(f"模型性能差异显著: {paired_result.reject_null}") # 效应量计算 diff_mean = np.mean(rf_scores - svm_scores) diff_std = np.std(rf_scores - svm_scores, ddof=1) cohens_d = diff_mean / diff_std print(f"效应量 (Cohen's d): {cohens_d:.4f}") return paired_result A/B测试分析 ~~~~~~~~~~~ 在产品优化和营销活动中，A/B测试是常用的实验方法。 .. code-block:: python def ab_test_analysis(): """A/B测试完整分析流程""" # 模拟A/B测试数据 np.random.seed(42) # 控制组和实验组的转化率数据 control_conversions = np.random.binomial(1, 0.12, 5000) # 12%转化率 treatment_conversions = np.random.binomial(1, 0.14, 5000) # 14%转化率 # 转化率统计 control_rate = np.mean(control_conversions) treatment_rate = np.mean(treatment_conversions) print("A/B测试分析报告") print("=" * 40) print(f"控制组: n={len(control_conversions)}, 转化率={control_rate:.4f}") print(f"实验组: n={len(treatment_conversions)}, 转化率={treatment_rate:.4f}") print(f"提升幅度: {(treatment_rate - control_rate)/control_rate*100:.2f}%") # 统计检验 from scipy import stats # 双比例Z检验 count = np.array([np.sum(treatment_conversions), np.sum(control_conversions)]) nobs = np.array([len(treatment_conversions), len(control_conversions)]) from statsmodels.stats.proportion import proportions_ztest z_stat, p_value = proportions_ztest(count, nobs) print(f"\n双比例Z检验:") print(f"Z统计量: {z_stat:.4f}") print(f"p值: {p_value:.4f}") print(f"差异显著: {p_value < 0.05}") # 置信区间 from statsmodels.stats.proportion import proportion_confint ci_control = proportion_confint(np.sum(control_conversions), len(control_conversions), alpha=0.05) ci_treatment = proportion_confint(np.sum(treatment_conversions), len(treatment_conversions), alpha=0.05) print(f"\n95%置信区间:") print(f"控制组: [{ci_control[0]:.4f}, {ci_control[1]:.4f}]") print(f"实验组: [{ci_treatment[0]:.4f}, {ci_treatment[1]:.4f}]") 商业分析场景 ------------ 销售数据分析 ~~~~~~~~~~~~ 分析不同销售策略、区域或时间段的销售表现差异。 .. code-block:: python def sales_analysis(): """销售数据统计分析""" # 模拟销售数据 np.random.seed(42) # 三个销售区域的月销售额（万元） region_a = np.random.normal(150, 30, 24) # 24个月 region_b = np.random.normal(180, 35, 24) region_c = np.random.normal(165, 25, 24) lt = LocationTests() nt = NormalityTests() print("销售区域分析报告") print("=" * 40) # 描述性统计 regions = {'A区': region_a, 'B区': region_b, 'C区': region_c} for name, data in regions.items(): print(f"{name}: 均值={np.mean(data):.2f}万, 标准差={np.std(data, ddof=1):.2f}万") # 正态性检验 print(f"\n正态性检验:") for name, data in regions.items(): norm_result = nt.shapiro_wilk(data) print(f"{name}: p={norm_result.p_value:.4f}, 正态={not norm_result.reject_null}") # 方差齐性检验 from scipy.stats import levene levene_stat, levene_p = levene(region_a, region_b, region_c) print(f"\nLevene方差齐性检验: p={levene_p:.4f}, 方差齐={levene_p >= 0.05}") # 单因素方差分析 anova_result = lt.one_way_anova(region_a, region_b, region_c) print(f"\n单因素ANOVA:") print(f"F统计量: {anova_result.statistic:.4f}") print(f"p值: {anova_result.p_value:.4f}") print(f"区域间差异显著: {anova_result.reject_null}") # 两两比较（如果ANOVA显著） if anova_result.reject_null: print(f"\n两两比较(Bonferroni校正):") region_list = [region_a, region_b, region_c] region_names = ['A区', 'B区', 'C区'] alpha_corrected = 0.05 / 3 # Bonferroni校正 for i in range(len(region_list)): for j in range(i+1, len(region_list)): result = lt.two_sample_ttest(region_list[i], region_list[j]) significant = result.p_value < alpha_corrected print(f"{region_names[i]} vs {region_names[j]}: " f"p={result.p_value:.4f}, 显著={significant}") 质量控制分析 ~~~~~~~~~~~~ 在制造业中使用统计检验进行质量控制和过程改进。 .. code-block:: python def quality_control_analysis(): """质量控制统计分析""" # 模拟生产线质量数据 np.random.seed(42) # 改进前后的产品重量数据（目标：100g） before_improvement = np.random.normal(99.5, 2.5, 100) # 偏离目标 after_improvement = np.random.normal(100.1, 1.8, 100) # 接近目标 lt = LocationTests() nt = NormalityTests() print("质量控制分析报告") print("=" * 40) # 描述性统计 print(f"改进前: 均值={np.mean(before_improvement):.3f}g, " f"标准差={np.std(before_improvement, ddof=1):.3f}g") print(f"改进后: 均值={np.mean(after_improvement):.3f}g, " f"标准差={np.std(after_improvement, ddof=1):.3f}g") # 单样本t检验：检验是否达到目标值100g target_weight = 100.0 before_target_test = lt.one_sample_ttest(before_improvement, target_weight) after_target_test = lt.one_sample_ttest(after_improvement, target_weight) print(f"\n目标值检验 (100g):") print(f"改进前: t={before_target_test.statistic:.4f}, " f"p={before_target_test.p_value:.4f}, 达标={not before_target_test.reject_null}") print(f"改进后: t={after_target_test.statistic:.4f}, " f"p={after_target_test.p_value:.4f}, 达标={not after_target_test.reject_null}") # 配对比较：改进效果 # 注意：这里假设是相同条件下的对比 improvement_test = lt.two_sample_ttest(before_improvement, after_improvement) print(f"\n改进效果检验:") print(f"t统计量: {improvement_test.statistic:.4f}") print(f"p值: {improvement_test.p_value:.4f}") print(f"改进有效: {improvement_test.reject_null}") # 方差比较：一致性改善 from scipy.stats import bartlett variance_test_stat, variance_test_p = bartlett(before_improvement, after_improvement) print(f"\n方差齐性检验 (一致性):") print(f"统计量: {variance_test_stat:.4f}, p值: {variance_test_p:.4f}") print(f"方差显著不同: {variance_test_p < 0.05}") 科学研究场景 ------------ 临床试验分析 ~~~~~~~~~~~~ 医学研究中的临床试验数据分析。 .. code-block:: python def clinical_trial_analysis(): """临床试验统计分析""" # 模拟临床试验数据 np.random.seed(42) # 治疗前后的血压数据（mmHg） n_patients = 80 baseline_bp = np.random.normal(160, 20, n_patients) # 基线血压 # 治疗后血压（假设有治疗效果） treatment_effect = np.random.normal(-15, 8, n_patients) # 平均降低15mmHg follow_up_bp = baseline_bp + treatment_effect # 对照组（安慰剂） placebo_baseline = np.random.normal(158, 18, n_patients) placebo_effect = np.random.normal(-3, 6, n_patients) # 轻微安慰剂效应 placebo_follow_up = placebo_baseline + placebo_effect lt = LocationTests() ct = CorrelationTests() print("临床试验分析报告") print("=" * 40) # 基线比较 baseline_comparison = lt.two_sample_ttest(baseline_bp, placebo_baseline) print(f"基线血压比较:") print(f"治疗组: {np.mean(baseline_bp):.1f}±{np.std(baseline_bp, ddof=1):.1f} mmHg") print(f"对照组: {np.mean(placebo_baseline):.1f}±{np.std(placebo_baseline, ddof=1):.1f} mmHg") print(f"基线差异: p={baseline_comparison.p_value:.4f}, 平衡={not baseline_comparison.reject_null}") # 治疗效果分析 treatment_change = follow_up_bp - baseline_bp placebo_change = placebo_follow_up - placebo_baseline print(f"\n治疗效果:") print(f"治疗组变化: {np.mean(treatment_change):.1f}±{np.std(treatment_change, ddof=1):.1f} mmHg") print(f"对照组变化: {np.mean(placebo_change):.1f}±{np.std(placebo_change, ddof=1):.1f} mmHg") # 组间比较 effect_comparison = lt.two_sample_ttest(treatment_change, placebo_change) print(f"\n效果比较:") print(f"t统计量: {effect_comparison.statistic:.4f}") print(f"p值: {effect_comparison.p_value:.4f}") print(f"治疗有效: {effect_comparison.reject_null}") # 效应量 pooled_std = np.sqrt(((len(treatment_change)-1)*np.var(treatment_change, ddof=1) + (len(placebo_change)-1)*np.var(placebo_change, ddof=1)) / (len(treatment_change)+len(placebo_change)-2)) cohens_d = (np.mean(treatment_change) - np.mean(placebo_change)) / pooled_std print(f"效应量 (Cohen's d): {cohens_d:.3f}") 教育研究分析 ~~~~~~~~~~~~ 教育效果评估和学习方法比较。 .. code-block:: python def education_research_analysis(): """教育研究统计分析""" # 模拟教育实验数据 np.random.seed(42) # 三种教学方法的学生成绩 traditional = np.random.normal(75, 12, 50) # 传统教学 online = np.random.normal(78, 15, 48) # 在线教学 blended = np.random.normal(82, 10, 52) # 混合教学 # 学习时间与成绩的关系 study_hours = np.random.uniform(1, 8, 150) performance = 60 + 3 * study_hours + np.random.normal(0, 5, 150) lt = LocationTests() ct = CorrelationTests() print("教育研究分析报告") print("=" * 40) # 教学方法比较 print("1. 教学方法效果比较:") methods = {'传统': traditional, '在线': online, '混合': blended} for name, scores in methods.items(): print(f"{name}教学: n={len(scores)}, 均值={np.mean(scores):.2f}, " f"标准差={np.std(scores, ddof=1):.2f}") # 方差分析 anova_result = lt.one_way_anova(traditional, online, blended) print(f"\nANOVA结果:") print(f"F统计量: {anova_result.statistic:.4f}") print(f"p值: {anova_result.p_value:.4f}") print(f"教学方法差异显著: {anova_result.reject_null}") # 学习时间与成绩相关性 correlation_result = ct.pearson_correlation(study_hours, performance) print(f"\n2. 学习时间与成绩相关性:") print(f"Pearson相关系数: {correlation_result.statistic:.4f}") print(f"p值: {correlation_result.p_value:.4f}") print(f"相关显著: {correlation_result.reject_null}") # 回归分析预测 from sklearn.linear_model import LinearRegression from sklearn.metrics import r2_score lr = LinearRegression() X = study_hours.reshape(-1, 1) lr.fit(X, performance) print(f"\n简单线性回归:") print(f"回归方程: 成绩 = {lr.intercept_:.2f} + {lr.coef_[0]:.2f} × 学习时间") print(f"R²: {r2_score(performance, lr.predict(X)):.4f}") 金融数据分析 ------------ 时间序列和风险分析 ~~~~~~~~~~~~~~~~~~ 金融市场数据的统计分析。 .. code-block:: python def financial_analysis(): """金融时间序列分析""" # 模拟股票收益率数据 np.random.seed(42) n_days = 252 # 一年交易日 # 股票A：稳定型 returns_a = np.random.normal(0.0005, 0.015, n_days) # 日收益率 # 股票B：波动型（GARCH效应） returns_b = np.zeros(n_days) h = 0.015**2 # 初始方差 for i in range(n_days): h = 0.00001 + 0.85*h + 0.1*returns_b[i-1]**2 if i > 0 else h returns_b[i] = np.random.normal(0.0008, np.sqrt(h)) tst = TimeSeriesTests() lt = LocationTests() print("金融数据分析报告") print("=" * 40) # 描述性统计 print("1. 收益率统计:") print(f"股票A: 均值={np.mean(returns_a)*252:.3f} (年化), " f"波动率={np.std(returns_a, ddof=1)*np.sqrt(252):.3f} (年化)") print(f"股票B: 均值={np.mean(returns_b)*252:.3f} (年化), " f"波动率={np.std(returns_b, ddof=1)*np.sqrt(252):.3f} (年化)") # 收益率差异检验 returns_comparison = lt.two_sample_ttest(returns_a, returns_b) print(f"\n2. 收益率比较:") print(f"t统计量: {returns_comparison.statistic:.4f}") print(f"p值: {returns_comparison.p_value:.4f}") print(f"收益率差异显著: {returns_comparison.reject_null}") # ARCH效应检验 arch_a = tst.arch_test(returns_a, lags=5) arch_b = tst.arch_test(returns_b, lags=5) print(f"\n3. 波动率聚集检验 (ARCH):") print(f"股票A: LM统计量={arch_a.statistic:.4f}, p={arch_a.p_value:.4f}, " f"ARCH效应={arch_a.reject_null}") print(f"股票B: LM统计量={arch_b.statistic:.4f}, p={arch_b.p_value:.4f}, " f"ARCH效应={arch_b.reject_null}") # 风险度量 var_95_a = np.percentile(returns_a, 5) # 5% VaR var_95_b = np.percentile(returns_b, 5) print(f"\n4. 风险度量 (95% VaR):") print(f"股票A: {var_95_a:.4f} ({var_95_a*np.sqrt(252):.3f} 年化)") print(f"股票B: {var_95_b:.4f} ({var_95_b*np.sqrt(252):.3f} 年化)") 综合案例：电商平台分析 ---------------------- 综合运用多种统计检验方法分析电商平台数据。 .. code-block:: python def ecommerce_comprehensive_analysis(): """电商平台综合统计分析""" np.random.seed(42) # 模拟电商数据 n_users = 1000 # 用户特征 age = np.random.normal(35, 12, n_users) income = np.random.normal(50000, 15000, n_users) # 年收入 # 购买行为（受年龄和收入影响） purchase_prob = 0.1 + 0.003 * (age - 20) + 0.000008 * income purchase_prob = np.clip(purchase_prob, 0, 1) purchases = np.random.binomial(1, purchase_prob, n_users) # 购买金额（仅对购买用户） purchase_amounts = [] for i, purchased in enumerate(purchases): if purchased: base_amount = 100 + 2 * age[i] + 0.002 * income[i] amount = np.random.gamma(2, base_amount/2) purchase_amounts.append(amount) purchase_amounts = np.array(purchase_amounts) # 不同推荐算法的点击率 algo_a_clicks = np.random.binomial(1, 0.08, 500) # 传统算法 algo_b_clicks = np.random.binomial(1, 0.12, 500) # 新算法 # 分析开始 lt = LocationTests() ct = CorrelationTests() nt = NormalityTests() print("电商平台综合分析报告") print("=" * 50) # 1. 用户画像分析 print("1. 用户画像:") print(f" 总用户数: {n_users}") print(f" 平均年龄: {np.mean(age):.1f}岁") print(f" 平均收入: {np.mean(income)/1000:.1f}千元") print(f" 购买率: {np.mean(purchases):.3f}") print(f" 平均购买金额: {np.mean(purchase_amounts):.2f}元") # 2. 年龄与购买行为关系 purchase_ages = age[purchases == 1] non_purchase_ages = age[purchases == 0] age_purchase_test = lt.two_sample_ttest(purchase_ages, non_purchase_ages) print(f"\n2. 年龄与购买行为:") print(f" 购买用户平均年龄: {np.mean(purchase_ages):.1f}岁") print(f" 未购买用户平均年龄: {np.mean(non_purchase_ages):.1f}岁") print(f" 差异显著: {age_purchase_test.reject_null} (p={age_purchase_test.p_value:.4f})") # 3. 收入与购买金额相关性 purchase_incomes = income[purchases == 1] correlation_income_amount = ct.pearson_correlation(purchase_incomes, purchase_amounts) print(f"\n3. 收入与购买金额相关性:") print(f" 相关系数: {correlation_income_amount.statistic:.4f}") print(f" p值: {correlation_income_amount.p_value:.4f}") print(f" 显著相关: {correlation_income_amount.reject_null}") # 4. 推荐算法效果比较 algo_a_rate = np.mean(algo_a_clicks) algo_b_rate = np.mean(algo_b_clicks) # 双比例检验 from scipy.stats import fisher_exact contingency = [[np.sum(algo_b_clicks), len(algo_b_clicks) - np.sum(algo_b_clicks)], [np.sum(algo_a_clicks), len(algo_a_clicks) - np.sum(algo_a_clicks)]] odds_ratio, p_value = fisher_exact(contingency) print(f"\n4. 推荐算法效果比较:") print(f" 算法A点击率: {algo_a_rate:.4f}") print(f" 算法B点击率: {algo_b_rate:.4f}") print(f" 提升: {(algo_b_rate - algo_a_rate)/algo_a_rate*100:.2f}%") print(f" Fisher精确检验 p值: {p_value:.4f}") print(f" 算法B显著更好: {p_value < 0.05}") # 5. 购买金额分布分析 normality_test = nt.shapiro_wilk(purchase_amounts[:50]) # 抽样检验 print(f"\n5. 购买金额分布:") print(f" 中位数: {np.median(purchase_amounts):.2f}元") print(f" 75%分位数: {np.percentile(purchase_amounts, 75):.2f}元") print(f" 正态性检验 p值: {normality_test.p_value:.4f}") print(f" 近似正态分布: {not normality_test.reject_null}") # 6. 业务建议 print(f"\n6. 分析结论与建议:") if age_purchase_test.reject_null: avg_purchase_age = np.mean(purchase_ages) if avg_purchase_age > np.mean(age): print(" - 年龄较大的用户更倾向于购买，建议针对成熟用户群体设计产品") else: print(" - 年轻用户更活跃，建议加强年轻用户的转化策略") if correlation_income_amount.reject_null: print(" - 收入与购买金额正相关，可考虑收入分层的定价策略") if p_value < 0.05: improvement = (algo_b_rate - algo_a_rate) / algo_a_rate * 100 print(f" - 新推荐算法效果显著提升{improvement:.1f}%，建议全面推广") return { 'user_profile': {'age': np.mean(age), 'income': np.mean(income)}, 'conversion_rate': np.mean(purchases), 'avg_purchase_amount': np.mean(purchase_amounts), 'algo_improvement': (algo_b_rate - algo_a_rate) / algo_a_rate * 100 } 运行所有示例 ------------ .. code-block:: python def run_all_examples(): """运行所有应用示例""" print("统计检验模块应用示例集合") print("=" * 60) try: print("\n" + "="*20 + " 机器学习模型比较 " + "="*20) model_comparison_analysis() except Exception as e: print(f"模型比较分析出错: {e}") try: print("\n" + "="*25 + " A/B测试分析 " + "="*25) ab_test_analysis() except Exception as e: print(f"A/B测试分析出错: {e}") try: print("\n" + "="*25 + " 销售数据分析 " + "="*25) sales_analysis() except Exception as e: print(f"销售数据分析出错: {e}") try: print("\n" + "="*25 + " 质量控制分析 " + "="*25) quality_control_analysis() except Exception as e: print(f"质量控制分析出错: {e}") try: print("\n" + "="*25 + " 临床试验分析 " + "="*25) clinical_trial_analysis() except Exception as e: print(f"临床试验分析出错: {e}") try: print("\n" + "="*25 + " 教育研究分析 " + "="*25) education_research_analysis() except Exception as e: print(f"教育研究分析出错: {e}") try: print("\n" + "="*25 + " 金融数据分析 " + "="*25) financial_analysis() except Exception as e: print(f"金融数据分析出错: {e}") try: print("\n" + "="*20 + " 电商平台综合分析 " + "="*20) ecommerce_comprehensive_analysis() except Exception as e: print(f"电商综合分析出错: {e}") print("\n" + "="*60) print("所有示例运行完成！") if __name__ == "__main__": run_all_examples() 这些示例展示了统计检验模块在实际业务场景中的应用，涵盖了从数据科学到商业分析的各个领域。每个示例都提供了完整的分析流程，包括数据准备、假设检验、结果解释和业务建议。