{"id":75136,"date":"2026-02-11T15:33:26","date_gmt":"2026-02-11T07:33:26","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75136.html"},"modified":"2026-02-11T15:33:26","modified_gmt":"2026-02-11T07:33:26","slug":"python-%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90%e8%bf%9b%e9%98%b6%ef%bc%9a%e7%bb%9f%e8%ae%a1%e5%88%86%e6%9e%90%e4%b8%8e%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75136.html","title":{"rendered":"Python \u6570\u636e\u5206\u6790\u8fdb\u9636\uff1a\u7edf\u8ba1\u5206\u6790\u4e0e\u5047\u8bbe\u68c0\u9a8c"},"content":{"rendered":"

\u5f15\u8a00<\/span><\/span><\/h2>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5728\u6570\u636e\u5206\u6790\u9879\u76ee\u91cc,\u6211\u4eec\u7ecf\u5e38\u9700\u8981\u57fa\u4e8e\u6837\u672c\u6570\u636e\u505a\u51fa\u63a8\u65ad\u548c\u51b3\u7b56\u3002\u7edf\u8ba1\u5206\u6790\u4e0e\u5047\u8bbe\u68c0\u9a8c\u662f\u652f\u6491"\u4ece\u6570\u636e\u5230\u7ed3\u8bba"\u7684\u5173\u952e\u65b9\u6cd5\u3002\u638c\u63e1\u5b83\u4eec,\u53ef\u4ee5\u8ba9\u4f60\u66f4\u4e25\u8c28\u5730\u56de\u7b54"\u6548\u679c\u662f\u5426\u663e\u8457""\u5dee\u5f02\u662f\u5426\u771f\u5b9e"\u7b49\u95ee\u9898,\u907f\u514d\u88ab\u5076\u7136\u73b0\u8c61\u8bef\u5bfc\u3002<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u672c\u6587\u5c06\u7cfb\u7edf\u8bb2\u89e3:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u63cf\u8ff0\u7edf\u8ba1\u4e0e\u6982\u7387\u5206\u5e03\u7684\u57fa\u7840\u6982\u5ff5<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u5047\u8bbe\u68c0\u9a8c\u7684\u5b8c\u6574\u6d41\u7a0b\u4e0e\u5e38\u7528\u65b9\u6cd5<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u4f7f\u7528Python\u5b9e\u73b0\u5b8c\u6574\u5206\u6790,\u5305\u542b\u6570\u636e\u5904\u7406\u3001\u7edf\u8ba1\u68c0\u9a8c\u4e0e\u53ef\u89c6\u5316<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u7ed3\u5408\u771f\u5b9e\u6848\u4f8b,\u4ece\u6570\u636e\u52a0\u8f7d\u5230\u7ed3\u8bba\u89e3\u8bfb<\/span><\/span><\/p>\n

\u6838\u5fc3\u77e5\u8bc6\u70b9<\/span><\/span><\/h3>\n

1. \u63cf\u8ff0\u7edf\u8ba1<\/span><\/span><\/h4>\n

\u63cf\u8ff0\u7edf\u8ba1<\/span>\u00a0\u662f\u7528\u6570\u5b66\u65b9\u6cd5\u5bf9\u6570\u636e\u8fdb\u884c\u6982\u62ec\u548c\u63cf\u8ff0\u7684\u5206\u6790\u65b9\u6cd5\u3002<\/span><\/span><\/p>\n

\u96c6\u4e2d\u8d8b\u52bf\u6307\u6807<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5747\u503c(mean)<\/span>: \u6240\u6709\u6570\u503c\u7684\u603b\u548c\u9664\u4ee5\u6570\u91cf,\u53d7\u6781\u7aef\u503c\u5f71\u54cd\u5927<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u4e2d\u4f4d\u6570(median)<\/span>: \u6392\u5e8f\u540e\u4f4d\u4e8e\u4e2d\u95f4\u7684\u503c,\u4e0d\u53d7\u6781\u7aef\u503c\u5f71\u54cd<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u4f17\u6570(mode)<\/span>: \u51fa\u73b0\u9891\u7387\u6700\u9ad8\u7684\u6570\u503c<\/span><\/span><\/p>\n

\u79bb\u6563\u7a0b\u5ea6\u6307\u6807<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u65b9\u5dee(variance)<\/span>: \u5404\u6570\u636e\u70b9\u4e0e\u5747\u503c\u504f\u5dee\u7684\u5e73\u65b9\u548c\u7684\u5e73\u5747\u503c<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u6807\u51c6\u5dee(standard deviation)<\/span>: \u65b9\u5dee\u7684\u5e73\u65b9\u6839,\u8861\u91cf\u6570\u636e\u5206\u6563\u7a0b\u5ea6<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u6781\u5dee(range)<\/span>: \u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5dee<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u56db\u5206\u4f4d\u8ddd(IQR)<\/span>: \u4e0a\u56db\u5206\u4f4d\u6570\u4e0e\u4e0b\u56db\u5206\u4f4d\u6570\u7684\u5dee<\/span><\/span><\/p>\n

\u5206\u5e03\u5f62\u6001<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u504f\u5ea6(skewness)<\/span>: \u8861\u91cf\u5206\u5e03\u7684\u4e0d\u5bf9\u79f0\u6027<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u25e6 \u6b63\u504f(\u53f3\u504f): \u957f\u5c3e\u5728\u53f3\u4fa7<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u25e6 \u8d1f\u504f(\u5de6\u504f): \u957f\u5c3e\u5728\u5de6\u4fa7<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5cf0\u5ea6(kurtosis)<\/span>: \u8861\u91cf\u5206\u5e03\u7684\u5c16\u9510\u7a0b\u5ea6<\/span><\/span><\/p>\n

2. \u6982\u7387\u5206\u5e03<\/span><\/span><\/h4>\n
\u6b63\u6001\u5206\u5e03<\/span><\/span><\/h5>\n

\u6700\u91cd\u8981\u7684\u8fde\u7eed\u6982\u7387\u5206\u5e03,\u53c8\u79f0\u9ad8\u65af\u5206\u5e03,\u5176\u7279\u70b9:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u949f\u5f62\u66f2\u7ebf,\u5173\u4e8e\u5747\u503c\u5bf9\u79f0<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u7ea668%\u7684\u6570\u636e\u5728\u00b11\u4e2a\u6807\u51c6\u5dee\u5185,95%\u5728\u00b12\u4e2a\u6807\u51c6\u5dee\u5185<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u8bb8\u591a\u81ea\u7136\u73b0\u8c61\u90fd\u8fd1\u4f3c\u670d\u4ece\u6b63\u6001\u5206\u5e03<\/span><\/span><\/p>\n

t\u5206\u5e03<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u9002\u7528\u4e8e\u5c0f\u6837\u672c(n<30)\u4e14\u603b\u4f53\u6807\u51c6\u5dee\u672a\u77e5\u7684\u60c5\u51b5,\u7c7b\u4f3c\u4e8e\u6b63\u6001\u5206\u5e03\u4f46\u5c3e\u90e8\u66f4\u539a\u3002<\/span><\/span><\/p>\n

\u5361\u65b9\u5206\u5e03<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e3b\u8981\u7528\u4e8e:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u68c0\u9a8c\u5206\u7c7b\u53d8\u91cf\u7684\u72ec\u7acb\u6027<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u68c0\u9a8c\u65b9\u5dee\u662f\u5426\u7b49\u4e8e\u67d0\u4e2a\u503c<\/span><\/span><\/p>\n

F\u5206\u5e03<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e3b\u8981\u7528\u4e8e:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u65b9\u5dee\u5206\u6790(ANOVA)<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u6bd4\u8f83\u4e24\u4e2a\u65b9\u5dee<\/span><\/span><\/p>\n

3. \u5047\u8bbe\u68c0\u9a8c\u7684\u5b8c\u6574\u6d41\u7a0b<\/span><\/span><\/h4>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5047\u8bbe\u68c0\u9a8c\u662f\u7edf\u8ba1\u63a8\u65ad\u7684\u6838\u5fc3\u65b9\u6cd5,\u7528\u4e8e\u6839\u636e\u6837\u672c\u6570\u636e\u5224\u65ad\u5173\u4e8e\u603b\u4f53\u53c2\u6570\u7684\u5047\u8bbe\u662f\u5426\u6210\u7acb\u3002<\/span><\/span><\/p>\n

Step 1: \u5efa\u7acb\u5047\u8bbe<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u96f6\u5047\u8bbe(H0)<\/span>: \u9ed8\u8ba4\u72b6\u6001,\u901a\u5e38\u8868\u793a"\u6ca1\u6709\u5dee\u5f02""\u6ca1\u6709\u6548\u679c"<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5907\u62e9\u5047\u8bbe(H1)<\/span>: \u6211\u4eec\u60f3\u8bc1\u660e\u7684\u5047\u8bbe,\u8868\u793a"\u6709\u5dee\u5f02""\u6709\u6548\u679c"<\/span><\/span><\/p>\n

Step 2: \u9009\u62e9\u663e\u8457\u6027\u6c34\u5e73\u03b1<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u5e38\u7528\u503c: 0.05 (5%) \u6216 0.01 (1%)<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u03b1\u662f\u62d2\u7eddH0\u65f6\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef(\u5f03\u771f)\u7684\u6982\u7387<\/span><\/span><\/p>\n

Step 3: \u9009\u62e9\u68c0\u9a8c\u65b9\u6cd5\u5e76\u8ba1\u7b97\u7edf\u8ba1\u91cf<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6839\u636e\u6570\u636e\u7c7b\u578b\u548c\u7814\u7a76\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u68c0\u9a8c\u65b9\u6cd5(\u89c1\u540e\u6587\u65b9\u6cd5\u5bf9\u6bd4)<\/span><\/span><\/p>\n

Step 4: \u505a\u51fa\u51b3\u7b56<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>p\u503c\u6cd5<\/span>: \u6bd4\u8f83p\u503c\u4e0e\u03b1<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u25e6 p < \u03b1: \u62d2\u7eddH0,\u7ed3\u679c\u5177\u6709\u7edf\u8ba1\u663e\u8457\u6027<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u25e6 p \u2265 \u03b1: \u4e0d\u62d2\u7eddH0<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u4e34\u754c\u503c\u6cd5<\/span>: \u6bd4\u8f83\u7edf\u8ba1\u91cf\u4e0e\u4e34\u754c\u503c<\/span><\/span><\/p>\n

Step 5: \u89e3\u91ca\u7ed3\u8bba<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u7edf\u8ba1\u610f\u4e49<\/span>: \u7ed3\u679c\u662f\u5426\u5177\u6709\u7edf\u8ba1\u5b66\u610f\u4e49<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5b9e\u9645\u610f\u4e49<\/span>: \u7ed3\u679c\u5728\u73b0\u5b9e\u5e94\u7528\u4e2d\u7684\u4ef7\u503c\u548c\u5f71\u54cd<\/span><\/span><\/p>\n

4. \u5e38\u7528\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u5bf9\u6bd4<\/span><\/span><\/h4>\n\n\n\n\n\n\n\n\n
\n

\u68c0\u9a8c\u65b9\u6cd5<\/span><\/span><\/p>\n<\/td>\n

\n

\u6570\u636e\u7c7b\u578b<\/span><\/span><\/p>\n<\/td>\n

\n

\u9002\u7528\u573a\u666f<\/span><\/span><\/p>\n<\/td>\n

\n

Python\u51fd\u6570<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u5355\u6837\u672ct\u68c0\u9a8c<\/span><\/span><\/p>\n<\/td>\n

\n

\u8fde\u7eed<\/span><\/span><\/p>\n<\/td>\n

\n

\u68c0\u9a8c\u6837\u672c\u5747\u503c\u4e0e\u5df2\u77e5\u5747\u503c\u5dee\u5f02<\/span><\/span><\/p>\n<\/td>\n

\n

scipy.stats.ttest_1samp()<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u53cc\u6837\u672c\u72ec\u7acbt\u68c0\u9a8c<\/span><\/span><\/p>\n<\/td>\n

\n

\u8fde\u7eed,\u4e24\u7ec4\u72ec\u7acb<\/span><\/span><\/p>\n<\/td>\n

\n

\u6bd4\u8f83\u4e24\u7ec4\u72ec\u7acb\u6837\u672c\u7684\u5747\u503c\u5dee\u5f02<\/span><\/span><\/p>\n<\/td>\n

\n

scipy.stats.ttest_ind()<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u914d\u5bf9t\u68c0\u9a8c<\/span><\/span><\/p>\n<\/td>\n

\n

\u8fde\u7eed,\u6210\u5bf9\u6570\u636e<\/span><\/span><\/p>\n<\/td>\n

\n

\u6bd4\u8f83\u540c\u4e00\u7ec4\u5bf9\u8c61\u7684\u4e24\u6b21\u6d4b\u91cf\u5dee\u5f02<\/span><\/span><\/p>\n<\/td>\n

\n

scipy.stats.ttest_rel()<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u5361\u65b9\u72ec\u7acb\u6027\u68c0\u9a8c<\/span><\/span><\/p>\n<\/td>\n

\n

\u5206\u7c7b<\/span><\/span><\/p>\n<\/td>\n

\n

\u68c0\u9a8c\u4e24\u4e2a\u5206\u7c7b\u53d8\u91cf\u662f\u5426\u72ec\u7acb<\/span><\/span><\/p>\n<\/td>\n

\n

scipy.stats.chi2_contingency()<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u5355\u56e0\u7d20ANOVA<\/span><\/span><\/p>\n<\/td>\n

\n

\u8fde\u7eed,\u591a\u7ec4<\/span><\/span><\/p>\n<\/td>\n

\n

\u6bd4\u8f83\u4e09\u7ec4\u53ca\u4ee5\u4e0a\u72ec\u7acb\u6837\u672c\u7684\u5747\u503c\u5dee\u5f02<\/span><\/span><\/p>\n<\/td>\n

\n

scipy.stats.f_oneway()<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u4ee3\u7801\u5b9e\u8df5<\/span><\/span><\/h3>\n

\u73af\u5883\u51c6\u5907<\/span><\/span><\/h4>\n

\u9996\u5148\u5bfc\u5165\u5fc5\u8981\u7684Python\u5e93:<\/span><\/span><\/p>\n

import numpy as np
\nimport pandas as pd
\nfrom scipy import stats
\nimport statsmodels.api as sm
\nfrom statsmodels.formula.api import ols
\nimport matplotlib.pyplot as plt
\nimport seaborn as sns
\n# \u8bbe\u7f6e\u7ed8\u56fe\u98ce\u683c
\nsns.set(style="whitegrid", font_scale=1.2)
\nplt.rcParams['font.sans-serif'] = ['SimHei'] \u00a0# \u7528\u6765\u6b63\u5e38\u663e\u793a\u4e2d\u6587\u6807\u7b7e
\nplt.rcParams['axes.unicode_minus'] = False \u00a0# \u7528\u6765\u6b63\u5e38\u663e\u793a\u8d1f\u53f7<\/p>\n

1. \u63cf\u8ff0\u7edf\u8ba1\u5b9e\u8df5<\/span><\/span><\/h4>\n

\u751f\u6210\u793a\u4f8b\u6570\u636e\u5e76\u8fdb\u884c\u63cf\u8ff0\u7edf\u8ba1\u5206\u6790:<\/span><\/span><\/p>\n

# \u8bbe\u7f6e\u968f\u673a\u79cd\u5b50\u4fdd\u8bc1\u7ed3\u679c\u53ef\u590d\u73b0
\nnp.random.seed(42)
\n# \u751f\u6210\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\u6570\u636e
\ndata = np.random.normal(loc=50, scale=10, size=200)
\n# \u8f6c\u6362\u4e3aSeries\u4fbf\u4e8e\u5206\u6790
\ndata_series = pd.Series(data, name='\u793a\u4f8b\u6570\u636e')
\n# \u8ba1\u7b97\u63cf\u8ff0\u7edf\u8ba1\u91cf
\nprint("=== \u63cf\u8ff0\u7edf\u8ba1\u7ed3\u679c ===")
\nprint(f"\u6837\u672c\u6570\u91cf: {len(data_series)}")
\nprint(f"\u5747\u503c: {data_series.mean():.2f}")
\nprint(f"\u4e2d\u4f4d\u6570: {data_series.median():.2f}")
\nprint(f"\u6807\u51c6\u5dee: {data_series.std():.2f}")
\nprint(f"\u6700\u5c0f\u503c: {data_series.min():.2f}")
\nprint(f"\u6700\u5927\u503c: {data_series.max():.2f}")
\nprint(f"25%\u5206\u4f4d\u6570: {data_series.quantile(0.25):.2f}")
\nprint(f"75%\u5206\u4f4d\u6570: {data_series.quantile(0.75):.2f}")
\nprint(f"\u504f\u5ea6: {data_series.skew():.2f}")
\nprint(f"\u5cf0\u5ea6: {data_series.kurt():.2f}")<\/p>\n

\u8f93\u51fa\u793a\u4f8b:<\/span><\/span><\/p>\n

=== \u63cf\u8ff0\u7edf\u8ba1\u7ed3\u679c ===
\n\u6837\u672c\u6570\u91cf: 200
\n\u5747\u503c: 50.03
\n\u4e2d\u4f4d\u6570: 50.14
\n\u6807\u51c6\u5dee: 9.71
\n\u6700\u5c0f\u503c: 20.53
\n\u6700\u5927\u503c: 76.98
\n25%\u5206\u4f4d\u6570: 43.20
\n75%\u5206\u4f4d\u6570: 56.78
\n\u504f\u5ea6: 0.05
\n\u5cf0\u5ea6: -0.34<\/p>\n

2. \u6570\u636e\u53ef\u89c6\u5316<\/span><\/span><\/h4>\n

\u53ef\u89c6\u5316\u662f\u7406\u89e3\u6570\u636e\u5206\u5e03\u7684\u91cd\u8981\u624b\u6bb5:<\/span><\/span><\/p>\n

# \u521b\u5efa\u753b\u5e03
\nfig, axes = plt.subplots(2, 2, figsize=(14, 10))
\n# \u76f4\u65b9\u56fe+\u6838\u5bc6\u5ea6\u4f30\u8ba1
\nsns.histplot(data_series, kde=True, ax=axes[0, 0], color='steelblue', bins=20)
\naxes[0, 0].set_title('\u6570\u636e\u5206\u5e03\u4e0e\u6838\u5bc6\u5ea6\u4f30\u8ba1', fontsize=14)
\naxes[0, 0].set_xlabel('\u503c')
\naxes[0, 0].set_ylabel('\u9891\u6570')
\n# \u7bb1\u7ebf\u56fe
\nsns.boxplot(y=data_series, ax=axes[0, 1], color='lightgreen')
\naxes[0, 1].set_title('\u7bb1\u7ebf\u56fe', fontsize=14)
\naxes[0, 1].set_ylabel('\u503c')
\n# Q-Q\u56fe(\u68c0\u9a8c\u6b63\u6001\u6027)
\nsm.qqplot(data_series, line='45', ax=axes[1, 0])
\naxes[1, 0].set_title('Q-Q\u56fe(\u6b63\u6001\u6027\u68c0\u9a8c)', fontsize=14)
\n# \u5c0f\u63d0\u7434\u56fe
\nsns.violinplot(y=data_series, ax=axes[1, 1], color='orange')
\naxes[1, 1].set_title('\u5c0f\u63d0\u7434\u56fe', fontsize=14)
\naxes[1, 1].set_ylabel('\u503c')
\nplt.tight_layout()
\nplt.show()<\/p>\n

# \u6b63\u6001\u6027\u68c0\u9a8c
\nstatistic, p_value = stats.shapiro(data_series)
\nprint(f"\\\\n=== Shapiro-Wilk\u6b63\u6001\u6027\u68c0\u9a8c ===")
\nprint(f"\u7edf\u8ba1\u91cf: {statistic:.4f}, p\u503c: {p_value:.4f}")
\nprint(f"\u7ed3\u8bba: {'\u4e0d\u62d2\u7edd\u6b63\u6001\u6027\u5047\u8bbe' if p_value > 0.05 else '\u62d2\u7edd\u6b63\u6001\u6027\u5047\u8bbe'}")<\/p>\n

3. \u5355\u6837\u672ct\u68c0\u9a8c<\/span><\/span><\/h4>\n

\u68c0\u9a8c\u6837\u672c\u5747\u503c\u662f\u5426\u663e\u8457\u4e0d\u540c\u4e8e\u67d0\u4e2a\u5df2\u77e5\u503c:<\/span><\/span><\/p>\n

# \u573a\u666f: \u68c0\u9a8c\u4ea7\u54c1\u5e73\u5747\u91cd\u91cf\u662f\u5426\u4e3a50g
\nnull_mean = 50 \u00a0# \u96f6\u5047\u8bbe: \u603b\u4f53\u5747\u503c = 50
\n# \u6267\u884c\u5355\u6837\u672ct\u68c0\u9a8c
\nt_stat, p_value = stats.ttest_1samp(data_series, null_mean)
\nprint("=== \u5355\u6837\u672ct\u68c0\u9a8c\u7ed3\u679c ===")
\nprint(f"\u96f6\u5047\u8bbe: \u603b\u4f53\u5747\u503c = {null_mean}")
\nprint(f"\u5907\u62e9\u5047\u8bbe: \u603b\u4f53\u5747\u503c \u2260 {null_mean}")
\nprint(f"\u68c0\u9a8c\u7edf\u8ba1\u91cf t = {t_stat:.4f}")
\nprint(f"p\u503c = {p_value:.4f}")
\nprint(f"\u663e\u8457\u6027\u6c34\u5e73 \u03b1 = 0.05")
\n# \u505a\u51fa\u51b3\u7b56
\nalpha = 0.05
\nif p_value < alpha:
\n\u00a0\u00a0\u00a0\u00a0print(f"\\\\n\u51b3\u7b56: \u62d2\u7edd\u96f6\u5047\u8bbe (p < {alpha})")
\n\u00a0\u00a0\u00a0\u00a0print("\u7ed3\u8bba: \u6837\u672c\u5747\u503c\u4e0e{null_mean}\u5b58\u5728\u663e\u8457\u5dee\u5f02")
\nelse:
\n\u00a0\u00a0\u00a0\u00a0print(f"\\\\n\u51b3\u7b56: \u4e0d\u62d2\u7edd\u96f6\u5047\u8bbe (p \u2265 {alpha})")
\n\u00a0\u00a0\u00a0\u00a0print(f"\u7ed3\u8bba: \u6ca1\u6709\u8bc1\u636e\u8868\u660e\u6837\u672c\u5747\u503c\u4e0e{null_mean}\u5b58\u5728\u5dee\u5f02")
\n# \u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4
\nn = len(data_series)
\nse = data_series.std() \/ np.sqrt(n)
\nci_lower = data_series.mean() – stats.t.ppf(1 – alpha\/2, n-1) * se
\nci_upper = data_series.mean() + stats.t.ppf(1 – alpha\/2, n-1) * se
\nprint(f"\\\\n95%\u7f6e\u4fe1\u533a\u95f4: [{ci_lower:.2f}, {ci_upper:.2f}]")<\/p>\n

4. \u53cc\u6837\u672c\u72ec\u7acbt\u68c0\u9a8c<\/span><\/span><\/h4>\n

\u6bd4\u8f83\u4e24\u7ec4\u72ec\u7acb\u6837\u672c\u7684\u5747\u503c\u5dee\u5f02:<\/span><\/span><\/p>\n

# \u573a\u666f: \u6bd4\u8f83\u4e24\u4e2a\u73ed\u7ea7\u5b66\u751f\u7684\u8003\u8bd5\u6210\u7ee9\u5dee\u5f02
\nnp.random.seed(123)
\nclass_A = np.random.normal(loc=75, scale=10, size=30)
\nclass_B = np.random.normal(loc=80, scale=12, size=30)
\n# \u63cf\u8ff0\u7edf\u8ba1\u5bf9\u6bd4
\nprint("=== \u73ed\u7ea7A\u6210\u7ee9\u63cf\u8ff0\u7edf\u8ba1 ===")
\nprint(f"\u5747\u503c: {class_A.mean():.2f}, \u6807\u51c6\u5dee: {class_A.std():.2f}")
\nprint("\\\\n=== \u73ed\u7ea7B\u6210\u7ee9\u63cf\u8ff0\u7edf\u8ba1 ===")
\nprint(f"\u5747\u503c: {class_B.mean():.2f}, \u6807\u51c6\u5dee: {class_B.std():.2f}")
\n# \u65b9\u5dee\u9f50\u6027\u68c0\u9a8c(Levene\u68c0\u9a8c)
\nlevene_stat, levene_p = stats.levene(class_A, class_B)
\nprint(f"\\\\n=== Levene\u65b9\u5dee\u9f50\u6027\u68c0\u9a8c ===")
\nprint(f"\u7edf\u8ba1\u91cf: {levene_stat:.4f}, p\u503c: {levene_p:.4f}")
\n# \u6839\u636e\u65b9\u5dee\u9f50\u6027\u7ed3\u679c\u9009\u62e9t\u68c0\u9a8c\u65b9\u6cd5
\nif levene_p > 0.05:
\n\u00a0\u00a0\u00a0\u00a0# \u65b9\u5dee\u9f50\u6027: \u4f7f\u7528equal_var=True
\n\u00a0\u00a0\u00a0\u00a0t_stat, p_value = stats.ttest_ind(class_A, class_B, equal_var=True)
\n\u00a0\u00a0\u00a0\u00a0test_type = "\u65b9\u5dee\u9f50\u6027t\u68c0\u9a8c"
\nelse:
\n\u00a0\u00a0\u00a0\u00a0# \u65b9\u5dee\u4e0d\u9f50: \u4f7f\u7528Welch's t\u68c0\u9a8c
\n\u00a0\u00a0\u00a0\u00a0t_stat, p_value = stats.ttest_ind(class_A, class_B, equal_var=False)
\n\u00a0\u00a0\u00a0\u00a0test_type = "Welch's t\u68c0\u9a8c(\u65b9\u5dee\u4e0d\u9f50)"
\nprint(f"\\\\n=== {test_type}\u7ed3\u679c ===")
\nprint(f"\u68c0\u9a8c\u7edf\u8ba1\u91cf t = {t_stat:.4f}")
\nprint(f"p\u503c = {p_value:.4f}")
\n# \u53ef\u89c6\u5316\u5bf9\u6bd4
\nplt.figure(figsize=(10, 6))
\nsns.boxplot(data=[class_A, class_B], palette=['lightblue', 'lightcoral'])
\nplt.xticks([0, 1], ['\u73ed\u7ea7A', '\u73ed\u7ea7B'])
\nplt.title('\u4e24\u4e2a\u73ed\u7ea7\u6210\u7ee9\u5206\u5e03\u5bf9\u6bd4', fontsize=14)
\nplt.ylabel('\u6210\u7ee9')
\nplt.show()<\/p>\n

5. \u914d\u5bf9t\u68c0\u9a8c<\/span><\/span><\/h4>\n

\u6bd4\u8f83\u540c\u4e00\u7ec4\u5bf9\u8c61\u5728\u4e24\u4e2a\u65f6\u95f4\u70b9\u6216\u6761\u4ef6\u4e0b\u7684\u5dee\u5f02:<\/span><\/span><\/p>\n

# \u573a\u666f: \u67d0\u51cf\u80a5\u8ba1\u5212\u524d\u540e\u4f53\u91cd\u5bf9\u6bd4
\nnp.random.seed(456)
\nbefore = np.random.normal(loc=75, scale=8, size=20)
\nafter = before – np.random.normal(loc=3, scale=2, size=20) \u00a0# \u5e73\u5747\u51cf\u91cd3kg
\n# \u6267\u884c\u914d\u5bf9t\u68c0\u9a8c
\nt_stat, p_value = stats.ttest_rel(before, after)
\nprint("=== \u914d\u5bf9t\u68c0\u9a8c\u7ed3\u679c ===")
\nprint(f"\u5e72\u9884\u524d\u5e73\u5747\u4f53\u91cd: {before.mean():.2f} kg")
\nprint(f"\u5e72\u9884\u540e\u5e73\u5747\u4f53\u91cd: {after.mean():.2f} kg")
\nprint(f"\u5e73\u5747\u53d8\u5316: {after.mean() – before.mean():.2f} kg")
\nprint(f"\u68c0\u9a8c\u7edf\u8ba1\u91cf t = {t_stat:.4f}")
\nprint(f"p\u503c = {p_value:.4f}")
\n# \u53ef\u89c6\u5316\u914d\u5bf9\u5dee\u5f02
\nplt.figure(figsize=(12, 5))
\n# \u5de6\u56fe: \u914d\u5bf9\u6570\u636e\u8fde\u7ebf
\nplt.subplot(1, 2, 1)
\nfor i in range(len(before)):
\n\u00a0\u00a0\u00a0\u00a0plt.plot([1, 2], [before[i], after[i]], 'k-', alpha=0.3)
\nplt.scatter([1]*len(before), before, s=80, label='\u5e72\u9884\u524d', color='blue')
\nplt.scatter([2]*len(after), after, s=80, label='\u5e72\u9884\u540e', color='red')
\nplt.xticks([1, 2], ['\u5e72\u9884\u524d', '\u5e72\u9884\u540e'])
\nplt.ylabel('\u4f53\u91cd(kg)')
\nplt.title('\u914d\u5bf9\u6570\u636e\u53d8\u5316')
\nplt.legend()
\n# \u53f3\u56fe: \u5dee\u5f02\u5206\u5e03
\ndifferences = after – before
\nplt.subplot(1, 2, 2)
\nsns.histplot(differences, kde=True, color='purple', bins=10)
\nplt.axvline(x=0, color='red', linestyle='–', label='\u65e0\u5dee\u5f02\u7ebf')
\nplt.axvline(x=differences.mean(), color='green', linestyle='–',
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0label=f'\u5e73\u5747\u53d8\u5316: {differences.mean():.2f}')
\nplt.xlabel('\u4f53\u91cd\u53d8\u5316(kg)')
\nplt.title('\u5dee\u5f02\u5206\u5e03')
\nplt.legend()
\nplt.tight_layout()
\nplt.show()<\/p>\n

6. \u5361\u65b9\u72ec\u7acb\u6027\u68c0\u9a8c<\/span><\/span><\/h4>\n

\u68c0\u9a8c\u4e24\u4e2a\u5206\u7c7b\u53d8\u91cf\u4e4b\u95f4\u662f\u5426\u76f8\u5173:<\/span><\/span><\/p>\n

# \u573a\u666f: \u7814\u7a76\u6027\u522b\u4e0e\u8d2d\u4e70\u504f\u597d\u662f\u5426\u76f8\u5173
\n# \u521b\u5efa\u5217\u8054\u8868
\nobserved = pd.DataFrame({
\n\u00a0\u00a0\u00a0\u00a0'\u8d2d\u4e70': [30, 45],
\n\u00a0\u00a0\u00a0\u00a0'\u4e0d\u8d2d\u4e70': [20, 25]
\n}, index=['\u7537\u6027', '\u5973\u6027'])
\nprint("=== \u89c2\u6d4b\u9891\u6570\u5217\u8054\u8868 ===")
\nprint(observed)
\n# \u6267\u884c\u5361\u65b9\u72ec\u7acb\u6027\u68c0\u9a8c
\nchi2, p_value, dof, expected = stats.chi2_contingency(observed)
\nprint(f"\\\\n=== \u5361\u65b9\u72ec\u7acb\u6027\u68c0\u9a8c\u7ed3\u679c ===")
\nprint(f"\u5361\u65b9\u7edf\u8ba1\u91cf: {chi2:.4f}")
\nprint(f"\u81ea\u7531\u5ea6: {dof}")
\nprint(f"p\u503c: {p_value:.4f}")
\n# \u663e\u793a\u671f\u671b\u9891\u6570
\nprint("\\\\n=== \u671f\u671b\u9891\u6570\u8868 ===")
\nexpected_df = pd.DataFrame(expected,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0index=observed.index,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0columns=observed.columns)
\nprint(expected_df)
\n# \u53ef\u89c6\u5316\u5217\u8054\u8868
\nplt.figure(figsize=(10, 6))
\n# \u70ed\u529b\u56fe
\nplt.subplot(1, 2, 1)
\nsns.heatmap(observed, annot=True, fmt='d', cmap='Blues', cbar=False)
\nplt.title('\u89c2\u6d4b\u9891\u6570')
\nplt.subplot(1, 2, 2)
\nsns.heatmap(expected_df, annot=True, fmt='.1f', cmap='Greens', cbar=False)
\nplt.title('\u671f\u671b\u9891\u6570(\u5047\u8bbe\u72ec\u7acb)')
\nplt.tight_layout()
\nplt.show()<\/p>\n

7. \u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790(ANOVA)<\/span><\/span><\/h4>\n

\u6bd4\u8f83\u4e09\u4e2a\u6216\u4ee5\u4e0a\u72ec\u7acb\u7ec4\u7684\u5747\u503c\u5dee\u5f02:<\/span><\/span><\/p>\n

# \u573a\u666f: \u6bd4\u8f83\u4e09\u79cd\u4e0d\u540c\u6559\u5b66\u65b9\u6cd5\u7684\u5b66\u751f\u6210\u7ee9
\nnp.random.seed(789)
\nmethod_A = np.random.normal(loc=72, scale=8, size=25)
\nmethod_B = np.random.normal(loc=78, scale=9, size=25)
\nmethod_C = np.random.normal(loc=81, scale=7, size=25)
\n# \u6267\u884c\u5355\u56e0\u7d20ANOVA
\nf_stat, p_value = stats.f_oneway(method_A, method_B, method_C)
\nprint("=== \u5355\u56e0\u7d20ANOVA\u7ed3\u679c ===")
\nprint(f"\u65b9\u6cd5A\u5747\u503c: {method_A.mean():.2f}")
\nprint(f"\u65b9\u6cd5B\u5747\u503c: {method_B.mean():.2f}")
\nprint(f"\u65b9\u6cd5C\u5747\u503c: {method_C.mean():.2f}")
\nprint(f"F\u7edf\u8ba1\u91cf: {f_stat:.4f}")
\nprint(f"p\u503c: {p_value:.4f}")
\n# \u51c6\u5907\u6570\u636e\u7528\u4e8e\u8be6\u7ec6ANOVA\u5206\u6790
\ndata_anova = pd.DataFrame({
\n\u00a0\u00a0\u00a0\u00a0'score': np.concatenate([method_A, method_B, method_C]),
\n\u00a0\u00a0\u00a0\u00a0'method': ['A']*25 + ['B']*25 + ['C']*25
\n})
\n# \u4f7f\u7528statsmodels\u8fdb\u884c\u8be6\u7ec6ANOVA\u5206\u6790
\nmodel = ols('score ~ C(method)', data=data_anova).fit()
\nanova_table = sm.stats.anova_lm(model, typ=2)
\nprint("\\\\n=== ANOVA\u8be6\u7ec6\u8868 ===")
\nprint(anova_table)
\n# \u4e8b\u540e\u68c0\u9a8c(Tukey HSD)
\nfrom statsmodels.stats.multicomp import pairwise_tukeyhsd
\ntukey = pairwise_tukeyhsd(endog=data_anova['score'],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0groups=data_anova['method'],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0alpha=0.05)
\nprint("\\\\n=== Tukey HSD\u4e8b\u540e\u68c0\u9a8c\u7ed3\u679c ===")
\nprint(tukey)
\n# \u53ef\u89c6\u5316
\nplt.figure(figsize=(12, 5))
\n# \u7bb1\u7ebf\u56fe
\nplt.subplot(1, 2, 1)
\nsns.boxplot(x='method', y='score', data=data_anova,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0palette=['lightblue', 'lightgreen', 'lightcoral'])
\nplt.title('\u4e09\u79cd\u65b9\u6cd5\u6210\u7ee9\u5206\u5e03\u5bf9\u6bd4')
\nplt.xlabel('\u6559\u5b66\u65b9\u6cd5')
\nplt.ylabel('\u6210\u7ee9')
\n# \u5747\u503c\u6761\u5f62\u56fe+\u8bef\u5dee\u68d2
\nplt.subplot(1, 2, 2)
\nmeans = data_anova.groupby('method')['score'].mean()
\nstds = data_anova.groupby('method')['score'].std()
\nbars = plt.bar(means.index, means.values,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0yerr=stds.values,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0capsize=5,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0color=['lightblue', 'lightgreen', 'lightcoral'])
\nplt.title('\u5404\u65b9\u6cd5\u5747\u503c\u5bf9\u6bd4')
\nplt.xlabel('\u6559\u5b66\u65b9\u6cd5')
\nplt.ylabel('\u5e73\u5747\u6210\u7ee9')
\n# \u6dfb\u52a0\u6570\u503c\u6807\u7b7e
\nfor bar, mean in zip(bars, means.values):
\n\u00a0\u00a0\u00a0\u00a0plt.text(bar.get_x() + bar.get_width()\/2, bar.get_height() + 0.5,
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0f'{mean:.1f}', ha='center', va='bottom')<\/p>\n

plt.tight_layout()
\nplt.show()<\/p>\n

\u5b8c\u6574\u6848\u4f8b\u5206\u6790<\/span><\/span><\/h3>\n

\u6848\u4f8b: \u9e22\u5c3e\u82b1\u6570\u636e\u96c6\u5206\u6790<\/span><\/span><\/h4>\n
1. \u95ee\u9898\u5b9a\u4e49<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6211\u4eec\u60f3\u77e5\u9053: \u9e22\u5c3e\u82b1\u7684\u4e09\u4e2a\u7269\u79cd(setosa, versicolor, virginica)\u5728\u82b1\u843c\u957f\u5ea6(sepal_length)\u4e0a\u662f\u5426\u5b58\u5728\u663e\u8457\u5dee\u5f02?<\/span><\/span><\/p>\n

2. \u6570\u636e\u52a0\u8f7d\u4e0e\u63a2\u7d22<\/span><\/span><\/h5>\n

# \u52a0\u8f7d\u9e22\u5c3e\u82b1\u6570\u636e\u96c6
\niris = sns.load_dataset('iris')
\nprint("=== \u6570\u636e\u96c6\u57fa\u672c\u4fe1\u606f ===")
\nprint(f"\u6570\u636e\u5f62\u72b6: {iris.shape}")
\nprint(f"\\\\n\u524d5\u884c\u6570\u636e:")
\nprint(iris.head())
\nprint(f"\\\\n\u7269\u79cd\u5206\u5e03:")
\nprint(iris['species'].value_counts())
\nprint(f"\\\\n\u63cf\u8ff0\u7edf\u8ba1(\u6309\u7269\u79cd\u5206\u7ec4):")
\nprint(iris.groupby('species')['sepal_length'].describe())<\/p>\n

3. \u53ef\u89c6\u5316\u63a2\u7d22<\/span><\/span><\/h5>\n

# \u8bbe\u7f6e\u753b\u5e03
\nfig, axes = plt.subplots(2, 2, figsize=(14, 10))
\n# \u7bb1\u7ebf\u56fe
\nsns.boxplot(x='species', y='sepal_length', data=iris, ax=axes[0, 0],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0palette='Set2')
\naxes[0, 0].set_title('\u4e0d\u540c\u7269\u79cd\u82b1\u843c\u957f\u5ea6\u7bb1\u7ebf\u56fe', fontsize=14)
\naxes[0, 0].set_xlabel('\u7269\u79cd')
\naxes[0, 0].set_ylabel('\u82b1\u843c\u957f\u5ea6(cm)')
\n# \u5c0f\u63d0\u7434\u56fe
\nsns.violinplot(x='species', y='sepal_length', data=iris, ax=axes[0, 1],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0palette='Set2')
\naxes[0, 1].set_title('\u4e0d\u540c\u7269\u79cd\u82b1\u843c\u957f\u5ea6\u5c0f\u63d0\u7434\u56fe', fontsize=14)
\naxes[0, 1].set_xlabel('\u7269\u79cd')
\naxes[0, 1].set_ylabel('\u82b1\u843c\u957f\u5ea6(cm)')
\n# \u76f4\u65b9\u56fe
\nfor i, species in enumerate(['setosa', 'versicolor', 'virginica']):
\n\u00a0\u00a0\u00a0\u00a0axes[1, 0].hist(iris[iris['species']==species]['sepal_length'],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0alpha=0.7, label=species, bins=15)
\naxes[1, 0].set_title('\u82b1\u843c\u957f\u5ea6\u5206\u5e03\u76f4\u65b9\u56fe', fontsize=14)
\naxes[1, 0].set_xlabel('\u82b1\u843c\u957f\u5ea6(cm)')
\naxes[1, 0].set_ylabel('\u9891\u6570')
\naxes[1, 0].legend()
\n# Q-Q\u56fe(\u68c0\u9a8csetosa\u7684\u6b63\u6001\u6027)
\nsetosa_data = iris[iris['species']=='setosa']['sepal_length']
\nsm.qqplot(setosa_data, line='45', ax=axes[1, 1])
\naxes[1, 1].set_title('Setosa\u82b1\u843c\u957f\u5ea6Q-Q\u56fe', fontsize=14)
\nplt.tight_layout()
\nplt.show()<\/p>\n

4. \u6b63\u6001\u6027\u68c0\u9a8c<\/span><\/span><\/h5>\n

print("=== \u5404\u7269\u79cd\u82b1\u843c\u957f\u5ea6\u6b63\u6001\u6027\u68c0\u9a8c(Shapiro-Wilk) ===")
\nfor species in iris['species'].unique():
\n\u00a0\u00a0\u00a0\u00a0data = iris[iris['species']==species]['sepal_length']
\n\u00a0\u00a0\u00a0\u00a0stat, p = stats.shapiro(data)
\n\u00a0\u00a0\u00a0\u00a0print(f"{species}: \u7edf\u8ba1\u91cf={stat:.4f}, p\u503c={p:.4f}, "
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0f"{'\u6ee1\u8db3\u6b63\u6001\u6027' if p > 0.05 else '\u4e0d\u6ee1\u8db3\u6b63\u6001\u6027'}")<\/p>\n

5. \u65b9\u5dee\u9f50\u6027\u68c0\u9a8c<\/span><\/span><\/h5>\n

from scipy.stats import levene
\nsetosa = iris[iris['species']=='setosa']['sepal_length']
\nversicolor = iris[iris['species']=='versicolor']['sepal_length']
\nvirginica = iris[iris['species']=='virginica']['sepal_length']
\nstat, p = levene(setosa, versicolor, virginica)
\nprint(f"\\\\n=== Levene\u65b9\u5dee\u9f50\u6027\u68c0\u9a8c ===")
\nprint(f"\u7edf\u8ba1\u91cf: {stat:.4f}, p\u503c: {p:.4f}")
\nprint(f"\u7ed3\u8bba: {'\u6ee1\u8db3\u65b9\u5dee\u9f50\u6027' if p > 0.05 else '\u65b9\u5dee\u4e0d\u9f50'}")<\/p>\n

6. \u6267\u884c\u5355\u56e0\u7d20ANOVA<\/span><\/span><\/h5>\n

# \u65b9\u6cd51: \u4f7f\u7528scipy
\nf_stat, p_value = stats.f_oneway(setosa, versicolor, virginica)
\nprint("=== \u5355\u56e0\u7d20ANOVA\u7ed3\u679c(scipy) ===")
\nprint(f"F\u7edf\u8ba1\u91cf: {f_stat:.4f}")
\nprint(f"p\u503c: {p_value:.4f}")
\n# \u65b9\u6cd52: \u4f7f\u7528statsmodels(\u66f4\u8be6\u7ec6)
\nmodel = ols('sepal_length ~ C(species)', data=iris).fit()
\nanova_table = sm.stats.anova_lm(model, typ=2)
\nprint("\\\\n=== ANOVA\u8be6\u7ec6\u8868(statsmodels) ===")
\nprint(anova_table)
\n# \u8ba1\u7b97\u6548\u5e94\u91cf(eta\u5e73\u65b9)
\nss_total = anova_table['sum_sq'].sum()
\nss_between = anova_table.loc['C(species)', 'sum_sq']
\neta_squared = ss_between \/ ss_total
\nprint(f"\\\\n=== \u6548\u5e94\u91cf ===")
\nprint(f"eta\u5e73\u65b9 = {eta_squared:.4f}")
\nprint(f"\u89e3\u91ca: \u7269\u79cd\u53ef\u4ee5\u89e3\u91ca\u82b1\u843c\u957f\u5ea6\u53d8\u5f02\u7684{eta_squared*100:.2f}%")<\/p>\n

7. \u4e8b\u540e\u591a\u91cd\u6bd4\u8f83<\/span><\/span><\/h5>\n

# Tukey HSD\u4e8b\u540e\u68c0\u9a8c
\ntukey = pairwise_tukeyhsd(endog=iris['sepal_length'],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0groups=iris['species'],
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0alpha=0.05)
\nprint("=== Tukey HSD\u4e8b\u540e\u68c0\u9a8c\u7ed3\u679c ===")
\nprint(tukey)
\n# \u53ef\u89c6\u5316Tukey\u7ed3\u679c
\nfrom statsmodels.stats.multicomp import MultiComparison
\nmc = MultiComparison(iris['sepal_length'], iris['species'])
\nresult = mc.tukeyhsd()
\nresult.plot_simultaneous(comparison_name='setosa',
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0xlabel='\u82b1\u843c\u957f\u5ea6\u5747\u503c\u5dee\u5f02',
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0title='95%\u7f6e\u4fe1\u533a\u95f4\u5dee\u5f02\u56fe')
\nplt.show()<\/p>\n

8. \u7ed3\u8bba\u89e3\u8bfb<\/span><\/span><\/h5>\n

\u7edf\u8ba1\u610f\u4e49:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 ANOVA\u7684p\u503c < 0.001, \u8fdc\u5c0f\u4e8e\u663e\u8457\u6027\u6c34\u5e730.05<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u62d2\u7edd\u96f6\u5047\u8bbe,\u8bf4\u660e\u81f3\u5c11\u6709\u4e24\u4e2a\u7269\u79cd\u7684\u82b1\u843c\u957f\u5ea6\u5747\u503c\u5b58\u5728\u663e\u8457\u5dee\u5f02<\/span><\/span><\/p>\n

\u5b9e\u9645\u610f\u4e49:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 eta\u5e73\u65b9 = 0.618, \u7269\u79cd\u53ef\u4ee5\u89e3\u91ca\u82b1\u843c\u957f\u5ea661.8%\u7684\u53d8\u5f02<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6548\u5e94\u91cf,\u8bf4\u660e\u7269\u79cd\u662f\u5f71\u54cd\u82b1\u843c\u957f\u5ea6\u7684\u5173\u952e\u56e0\u7d20<\/span><\/span><\/p>\n

\u5177\u4f53\u5dee\u5f02:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 Tukey HSD\u68c0\u9a8c\u663e\u793a,\u4e09\u7ec4\u4e24\u4e24\u4e4b\u95f4\u7684\u5dee\u5f02\u90fd\u5177\u6709\u7edf\u8ba1\u663e\u8457\u6027<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 virginica\u7684\u82b1\u843c\u6700\u957f(\u5747\u503c\u7ea66.59cm), setosa\u6700\u77ed(\u5747\u503c\u7ea65.01cm)<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u8fd9\u4e0e\u751f\u7269\u5b66\u8ba4\u77e5\u4e00\u81f4,\u53ef\u4ee5\u7528\u4e8e\u7269\u79cd\u8bc6\u522b<\/span><\/span><\/p>\n

\u603b\u7ed3\u4e0e\u7ecf\u9a8c\u5206\u4eab<\/span><\/span><\/h3>\n

1. \u7edf\u8ba1\u5206\u6790\u5b8c\u6574\u6d41\u7a0b<\/span><\/span><\/h4>\n

\u6570\u636e\u6536\u96c6 \u2192 \u6570\u636e\u6e05\u6d17 \u2192 \u63a2\u7d22\u6027\u5206\u6790(\u53ef\u89c6\u5316+\u63cf\u8ff0\u7edf\u8ba1) \u2192
\n\u6b63\u6001\u6027\u68c0\u9a8c \u2192 \u65b9\u5dee\u9f50\u6027\u68c0\u9a8c \u2192 \u9009\u62e9\u5408\u9002\u68c0\u9a8c\u65b9\u6cd5 \u2192
\n\u6267\u884c\u68c0\u9a8c \u2192 \u7ed3\u679c\u89e3\u91ca \u2192 \u4e1a\u52a1\u51b3\u7b56<\/p>\n

2. \u5e38\u89c1\u8bef\u533a\u4e0e\u907f\u5751\u6307\u5357<\/span><\/span><\/h4>\n
\u8bef\u533a1: \u76f2\u76ee\u4f7f\u7528t\u68c0\u9a8c,\u4e0d\u68c0\u67e5\u524d\u63d0\u6761\u4ef6<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u95ee\u9898<\/span>: \u76f4\u63a5\u5bf9\u504f\u6001\u5206\u5e03\u6216\u5f02\u5e38\u503c\u591a\u7684\u6570\u636e\u505at\u68c0\u9a8c<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5efa\u8bae<\/span>: \u5148\u505a\u6b63\u6001\u6027\u68c0\u9a8c\u548c\u53ef\u89c6\u5316,\u4e0d\u6ee1\u8db3\u65f6\u8003\u8651\u975e\u53c2\u6570\u68c0\u9a8c(Mann-Whitney U<\/span> \u7b49)<\/span><\/span><\/p>\n

\u8bef\u533a2: \u6df7\u6dc6\u7edf\u8ba1\u663e\u8457\u6027\u548c\u5b9e\u9645\u610f\u4e49<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u95ee\u9898<\/span>: \u5927\u6837\u672c\u4e0b\u5fae\u5c0f\u7684\u5dee\u5f02\u4e5f\u4f1a\u7edf\u8ba1\u663e\u8457(p<0.05),\u4f46\u5b9e\u9645\u4ef7\u503c\u4e0d\u5927<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5efa\u8bae<\/span>: \u5173\u6ce8\u6548\u5e94\u91cf(\u5982Cohen's d, eta\u5e73\u65b9),\u4e0d\u53ea\u770bp\u503c<\/span><\/span><\/p>\n

\u8bef\u533a3: \u591a\u91cd\u6bd4\u8f83\u672a\u505a\u6821\u6b63<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u95ee\u9898<\/span>: \u540c\u65f6\u505a\u591a\u7ec4\u6bd4\u8f83\u4f1a\u589e\u52a0\u7b2c\u4e00\u7c7b\u9519\u8bef\u6982\u7387<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5efa\u8bae<\/span>: \u4f7f\u7528Bonferroni\u6821\u6b63\u6216Tukey HSD\u7b49\u65b9\u6cd5<\/span><\/span><\/p>\n

\u8bef\u533a4: p<0.05\u5c31\u662f"\u663e\u8457"\u5417?<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u95ee\u9898<\/span>: \u5c060.05\u4f5c\u4e3a\u7edd\u5bf9\u95e8\u69db,\u5ffd\u89c6p\u503c\u672c\u8eab\u7684\u5927\u5c0f<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5efa\u8bae<\/span>: \u62a5\u544a\u7cbe\u786e\u7684p\u503c,\u7ed3\u5408\u7814\u7a76\u80cc\u666f\u5224\u65ad<\/span><\/span><\/p>\n

\u8bef\u533a5: \u5ffd\u89c6\u7f6e\u4fe1\u533a\u95f4<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u95ee\u9898<\/span>: \u53ea\u5173\u6ce8\u70b9\u4f30\u8ba1(\u5982\u5747\u503c),\u5ffd\u89c6\u4f30\u8ba1\u7684\u4e0d\u786e\u5b9a\u6027<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 <\/span>\u5efa\u8bae<\/span>: \u62a5\u544a95%\u7f6e\u4fe1\u533a\u95f4,\u7ed9\u51fa\u66f4\u5168\u9762\u7684\u4fe1\u606f<\/span><\/span><\/p>\n

3. \u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u9009\u62e9\u51b3\u7b56\u6811<\/span><\/span><\/h4>\n

\u5f00\u59cb
\n\u2502
\n\u251c\u2500 \u6570\u636e\u7c7b\u578b?
\n\u2502 \u00a0\u00a0\u251c\u2500 \u5206\u7c7b\u53d8\u91cf \u2192 \u5361\u65b9\u72ec\u7acb\u6027\u68c0\u9a8c \/ Fisher\u7cbe\u786e\u68c0\u9a8c
\n\u2502 \u00a0\u00a0\u2514\u2500 \u8fde\u7eed\u53d8\u91cf \u2192 \u7ee7\u7eed\u4e0b\u4e00\u6b65
\n\u2502
\n\u251c\u2500 \u6bd4\u8f83\u51e0\u7ec4?
\n\u2502 \u00a0\u00a0\u251c\u2500 1\u7ec4 \u2192 \u5355\u6837\u672ct\u68c0\u9a8c \/ Wilcoxon\u7b26\u53f7\u79e9\u68c0\u9a8c
\n\u2502 \u00a0\u00a0\u251c\u2500 2\u7ec4 \u2192 \u7ee7\u7eed\u4e0b\u4e00\u6b65
\n\u2502 \u00a0\u00a0\u2514\u2500 \u22653\u7ec4 \u2192 ANOVA \/ Kruskal-Wallis\u68c0\u9a8c
\n\u2502
\n\u251c\u2500 \u4e24\u7ec4\u662f\u5426\u72ec\u7acb?
\n\u2502 \u00a0\u00a0\u251c\u2500 \u72ec\u7acb \u2192 \u72ec\u7acb\u53cc\u6837\u672ct\u68c0\u9a8c \/ Mann-Whitney U\u68c0\u9a8c
\n\u2502 \u00a0\u00a0\u2514\u2500 \u914d\u5bf9 \u2192 \u914d\u5bf9t\u68c0\u9a8c \/ Wilcoxon\u7b26\u53f7\u79e9\u68c0\u9a8c
\n\u2502
\n\u2514\u2500 \u6b63\u6001\u6027\u68c0\u9a8c
\n\u00a0\u00a0\u00a0\u00a0\u251c\u2500 \u6ee1\u8db3\u6b63\u6001\u6027 \u2192 \u53c2\u6570\u68c0\u9a8c(t\u68c0\u9a8c\/ANOVA)
\n\u00a0\u00a0\u00a0\u00a0\u2514\u2500 \u4e0d\u6ee1\u8db3\u6b63\u6001\u6027 \u2192 \u975e\u53c2\u6570\u68c0\u9a8c<\/p>\n

4. \u5b9e\u9645\u9879\u76ee\u7ecf\u9a8c\u6280\u5de7<\/span><\/span><\/h4>\n
\u6280\u5de71: \u59cb\u7ec8\u8bbe\u7f6e\u968f\u673a\u79cd\u5b50<\/span><\/span><\/h5>\n

np.random.seed(42) \u00a0# \u786e\u4fdd\u7ed3\u679c\u53ef\u590d\u73b0<\/p>\n

\u6280\u5de72: \u53ef\u89c6\u5316\u5148\u884c,\u540e\u505a\u68c0\u9a8c<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u5148\u7528\u7bb1\u7ebf\u56fe\u3001\u76f4\u65b9\u56fe\u3001Q-Q\u56fe\u7b49\u4e86\u89e3\u6570\u636e\u5206\u5e03<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u5f02\u5e38\u503c\u548c\u975e\u6b63\u6001\u5728\u53ef\u89c6\u5316\u4e2d\u4e00\u76ee\u4e86\u7136<\/span><\/span><\/p>\n

\u6280\u5de73: \u62a5\u544a\u5b8c\u6574\u7ed3\u679c<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e0d\u8981\u53ea\u8bf4"\u6709\u663e\u8457\u6027\u5dee\u5f02",\u5e94\u5305\u542b:<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u68c0\u9a8c\u65b9\u6cd5\u540d\u79f0<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u68c0\u9a8c\u7edf\u8ba1\u91cf\u503c<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u7cbe\u786e\u7684p\u503c<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u6548\u5e94\u91cf<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 95%\u7f6e\u4fe1\u533a\u95f4<\/span><\/span><\/p>\n

\u6280\u5de74: \u6ce8\u610f\u6837\u672c\u91cf<\/span><\/span><\/h5>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u6837\u672c\u91cf\u592a\u5c0f(n<30): \u614e\u7528\u53c2\u6570\u68c0\u9a8c,\u8003\u8651\u975e\u53c2\u6570\u68c0\u9a8c<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2022 \u6837\u672c\u91cf\u592a\u5927(n>1000): \u5173\u6ce8\u6548\u5e94\u91cf,\u4e0d\u8981\u88ab\u5fae\u5c0f\u5dee\u5f02\u8bef\u5bfc<\/span><\/span><\/p>\n

\u6280\u5de75: \u4ee3\u7801\u590d\u7528\u4e0e\u5c01\u88c5<\/span><\/span><\/h5>\n

\u5c06\u5e38\u7528\u68c0\u9a8c\u5c01\u88c5\u6210\u51fd\u6570:<\/span><\/span><\/p>\n

def compare_two_groups(data1, data2, group1_name, group2_name):
\n\u00a0\u00a0\u00a0\u00a0"""\u6bd4\u8f83\u4e24\u7ec4\u6570\u636e,\u8f93\u51fa\u5b8c\u6574\u5206\u6790\u62a5\u544a"""
\n\u00a0\u00a0\u00a0\u00a0# \u63cf\u8ff0\u7edf\u8ba1
\n\u00a0\u00a0\u00a0\u00a0print(f"=== {group1_name} vs {group2_name} ===")
\n\u00a0\u00a0\u00a0\u00a0print(f"{group1_name}: n={len(data1)}, \u5747\u503c={data1.mean():.2f}, \u6807\u51c6\u5dee={data1.std():.2f}")
\n\u00a0\u00a0\u00a0\u00a0print(f"{group2_name}: n={len(data2)}, \u5747\u503c={data2.mean():.2f}, \u6807\u51c6\u5dee={data2.std():.2f}")
\n\u00a0\u00a0\u00a0\u00a0# \u6b63\u6001\u6027\u68c0\u9a8c
\n\u00a0\u00a0\u00a0\u00a0_, p1 = stats.shapiro(data1)
\n\u00a0\u00a0\u00a0\u00a0_, p2 = stats.shapiro(data2)
\n\u00a0\u00a0\u00a0\u00a0normal = (p1 > 0.05) and (p2 > 0.05)
\n\u00a0\u00a0\u00a0\u00a0print(f"\u6b63\u6001\u6027: {group1_name}(p={p1:.3f}), {group2_name}(p={p2:.3f})")
\n\u00a0\u00a0\u00a0\u00a0# \u65b9\u5dee\u9f50\u6027\u68c0\u9a8c
\n\u00a0\u00a0\u00a0\u00a0_, levene_p = stats.levene(data1, data2)
\n\u00a0\u00a0\u00a0\u00a0equal_var = levene_p > 0.05
\n\u00a0\u00a0\u00a0\u00a0print(f"\u65b9\u5dee\u9f50\u6027: p={levene_p:.3f}")
\n\u00a0\u00a0\u00a0\u00a0# \u9009\u62e9\u68c0\u9a8c\u65b9\u6cd5
\n\u00a0\u00a0\u00a0\u00a0if normal:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if equal_var:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0t_stat, p_value = stats.ttest_ind(data1, data2, equal_var=True)
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0method = "\u72ec\u7acb\u53cc\u6837\u672ct\u68c0\u9a8c"
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0else:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0t_stat, p_value = stats.ttest_ind(data1, data2, equal_var=False)
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0method = "Welch's t\u68c0\u9a8c"
\n\u00a0\u00a0\u00a0\u00a0else:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0t_stat, p_value = stats.mannwhitneyu(data1, data2)
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0method = "Mann-Whitney U\u68c0\u9a8c"
\n\u00a0\u00a0\u00a0\u00a0print(f"\\\\n\u68c0\u9a8c\u65b9\u6cd5: {method}")
\n\u00a0\u00a0\u00a0\u00a0print(f"\u7edf\u8ba1\u91cf: {t_stat:.4f}")
\n\u00a0\u00a0\u00a0\u00a0print(f"p\u503c: {p_value:.4f}")
\n\u00a0\u00a0\u00a0\u00a0# \u6548\u5e94\u91cf
\n\u00a0\u00a0\u00a0\u00a0if normal:
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0pooled_std = np.sqrt(((len(data1)-1)*data1.std()**2 +
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(len(data2)-1)*data2.std()**2) \/
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(len(data1)+len(data2)-2))
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0cohens_d = (data1.mean() – data2.mean()) \/ pooled_std
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0print(f"Cohen's d: {cohens_d:.4f}")
\n\u00a0\u00a0\u00a0\u00a0return p_value
\n# \u4f7f\u7528\u793a\u4f8b
\ncompare_two_groups(method_A, method_B, "\u65b9\u6cd5A", "\u65b9\u6cd5B")<\/p>\n

\u7ed3\u8bed<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u7edf\u8ba1\u5206\u6790\u4e0e\u5047\u8bbe\u68c0\u9a8c\u662f\u6570\u636e\u79d1\u5b66\u5de5\u4f5c\u8005\u7684\u5fc5\u5907\u6280\u80fd\u3002\u5e0c\u671b\u901a\u8fc7\u672c\u6587\u7684\u5b66\u4e60,\u4f60\u4e0d\u4ec5\u638c\u63e1\u4e86\u5404\u79cd\u68c0\u9a8c\u65b9\u6cd5\u7684\u5b9e\u73b0\u4ee3\u7801,\u66f4\u91cd\u8981\u7684\u662f\u7406\u89e3\u4e86\u5b83\u4eec\u7684\u9002\u7528\u573a\u666f\u548c\u80cc\u540e\u7684\u7edf\u8ba1\u539f\u7406\u3002\u8bb0\u4f4f:\u5de5\u5177\u662f\u624b\u6bb5,\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u624d\u662f\u76ee\u7684\u3002\u5728\u771f\u5b9e\u9879\u76ee\u4e2d,\u59cb\u7ec8\u7ed3\u5408\u4e1a\u52a1\u80cc\u666f\u6765\u89e3\u91ca\u7edf\u8ba1\u7ed3\u679c,\u624d\u80fd\u8ba9\u6570\u636e\u5206\u6790\u771f\u6b63\u4ea7\u751f\u4ef7\u503c\u3002<\/span><\/span><\/p>\n

\u6b22\u8fce\u5728\u8bc4\u8bba\u533a\u4ea4\u6d41\u5b66\u4e60\u5fc3\u5f97,\u4e5f\u6b22\u8fce\u5206\u4eab\u4f60\u5728\u9879\u76ee\u4e2d\u9047\u5230\u7684\u7edf\u8ba1\u5206\u6790\u95ee\u9898!<\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u672c\u6587\u4ee3\u7801\u5728Python 3.8+\u73af\u5883\u4e0b\u6d4b\u8bd5\u901a\u8fc7,\u4e3b\u8981\u4f9d\u8d56\u5e93\u7248\u672c:<\/span><\/span><\/p>\n

NumPy 1.21+, Pandas 1.3+, SciPy 1.7+, Statsmodels 0.13+, Matplotlib 3.4+, Seaborn 0.11+<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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