{"id":5925,"date":"2021-01-17T00:17:41","date_gmt":"2021-01-17T00:17:41","guid":{"rendered":"https:\/\/www.studygate.com\/blog-cn\/?p=5925"},"modified":"2022-03-19T00:20:53","modified_gmt":"2022-03-19T00:20:53","slug":"statistics","status":"publish","type":"post","link":"https:\/\/www.studygate.com\/blog-cn\/statistics\/","title":{"rendered":"Statistics \u7edf\u8ba1\u5b66\u4e2d\u5e38\u7528\u7684\u6570\u636e\u5206\u6790\u65b9\u6cd5\u5927\u603b\u7ed3\uff0c\u8d85\u5f3a\u5e72\u8d27\uff01"},"content":{"rendered":"

\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u901a\u8fc7\u6570\u636e\u5206\u6790\uff0c\u5e76\u4e14\u63d0\u53d6\u5230\u6709\u7528\u7684\u4fe1\u606f\u662f\u6700\u91cd\u8981\u7684\u6280\u80fd\u4e4b\u4e00\u3002\u90a3\u4e48\u5728\u6570\u636e\u5982\u6b64\u4e4b\u591a\u3001\u65f6\u95f4\u5982\u6b64\u4e4b\u77ed\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u4f55\u7406\u89e3\u5e76\u5206\u6790\u6240\u83b7\u53d6\u7684\u6570\u636e\uff1f\u6709\u54ea\u4e9b\u5e38\u89c1\u7684\u7edf\u8ba1\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1f\u60f3\u4e86\u89e3\u6700\u5168\u9762\u7684\u7edf\u8ba1\u5b66\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1f\u8d70\u8fc7\u8def\u8fc7\uff0c\u8d85\u5f3a\u5e72\u8d27\u603b\u7ed3\u5e16\u4e0d\u8981\u9519\u8fc7\uff01<\/strong><\/h3>\n

<\/p>\n

\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u63cf\u8ff0\u5206\u6790<\/strong><\/h3>\n

\u63cf\u8ff0\u7edf\u8ba1\u662f\u901a\u8fc7\u56fe\u8868\u6216\u6570\u5b66\u65b9\u6cd5\uff0c\u5bf9\u6570\u636e\u8d44\u6599\u8fdb\u884c\u6574\u7406\u3001\u5206\u6790\uff0c\u5e76\u5bf9\u6570\u636e\u7684\u5206\u5e03\u72b6\u6001\u3001\u6570\u5b57\u7279\u5f81\u548c\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u8fdb\u884c\u4f30\u8ba1\u548c\u63cf\u8ff0\u7684\u65b9\u6cd5\u3002\u63cf\u8ff0\u7edf\u8ba1\u5206\u4e3a\u96c6\u4e2d\u8d8b\u52bf\u5206\u6790\u3001\u79bb\u4e2d\u8d8b\u52bf\u5206\u6790\u548c\u76f8\u5173\u5206\u6790\u4e09\u5927\u90e8\u5206\u3002<\/p>\n

1. \u96c6\u4e2d\u8d8b\u52bf\u5206\u6790<\/p>\n

\u96c6\u4e2d\u8d8b\u52bf\u53c8\u79f0\u201c\u6570\u636e\u7684\u4e2d\u5fc3\u4f4d\u7f6e\u201d\u3001\u201c\u96c6\u4e2d\u91cf\u6570\u201d\u7b49\u3002\u5b83\u662f\u4e00\u7ec4\u6570\u636e\u7684\u4ee3\u8868\u503c\u3002\u96c6\u4e2d\u8d8b\u52bf\u7684\u6982\u5ff5\u5c31\u662f\u5e73\u5747\u6570\u7684\u6982\u5ff5\uff0c\u5b83\u80fd\u591f\u5bf9\u603b\u4f53\u7684\u67d0\u4e00\u7279\u5f81\u5177\u6709\u4ee3\u8868\u6027\uff0c\u8868\u660e\u6240\u7814\u7a76\u7684\u8206\u8bba\u73b0\u8c61\u5728\u4e00\u5b9a\u65f6\u95f4\u3001\u7a7a\u95f4\u6761\u4ef6\u4e0b\u7684\u5171\u540c\u6027\u8d28\u548c\u4e00\u822c\u6c34\u5e73\u3002\u5c31\u53d8\u91cf\u6570\u5217\u800c\u8a00\uff0c\u7531\u4e8e\u6574\u4e2a\u53d8\u91cf\u6570\u5217\u662f\u4ee5\u5e73\u5747\u6570\u4e3a\u4e2d\u5fc3\u800c\u4e0a\u4e0b\u6ce2\u52a8\u7684\uff0c\u6240\u4ee5\u5e73\u5747\u6570\u53cd\u6620\u4e86\u603b\u4f53\u5206\u5e03\u7684\u96c6\u4e2d\u8d8b\u52bf\uff0c\u5b83\u662f\u8868\u660e\u603b\u4f53\u5206\u5e03\u7684\u4e00\u4e2a\u91cd\u8981\u7279\u5f81\u503c\u3002\u6839\u636e\u53d8\u91cf\u6570\u5217\u7684\u5e73\u5747\u6570\uff0c\u5c31\u53ef\u4ee5\u4e86\u89e3\u6240\u7814\u7a76\u603b\u4f53\u7684\u96c6\u4e2d\u8d8b\u52bf\u548c\u4e00\u822c\u7279\u5f81\u3002\u96c6\u4e2d\u8d8b\u52bf\u662f\u7528\u6765\u63cf\u8ff0\u8206\u8bba\u73b0\u8c61\u7684\u91cd\u8981\u7edf\u8ba1\u5206\u6790\u6307\u6807\uff0c\u5e38\u7528\u7684\u6709\u5e73\u5747\u6570\u3001\u4e2d\u4f4d\u6570\u548c\u4f17\u6570\u7b49\uff0c\u5b83\u4eec\u5728\u4e0d\u540c\u7c7b\u578b\u7684\u5206\u5e03\u6570\u5217\u4e2d\u6709\u4e0d\u540c\u7684\u6d4b\u5b9a\u65b9\u6cd5\u3002<\/p>\n

\u53d6\u5f97\u96c6\u4e2d\u8d8b\u52bf\u4ee3\u8868\u503c\u7684\u65b9\u6cd5\u6709\u4e24\u79cd\uff1a\u6570\u503c\u5e73\u5747\u6570\u548c\u4f4d\u7f6e\u5e73\u5747\u6570\u3002<\/p>\n

\u6570\u503c\u5e73\u5747\u6570\uff1a\u4ece\u603b\u4f53\u5404\u5355\u4f4d\u53d8\u91cf\u503c\u4e2d\u62bd\u8c61\u51fa\u5177\u6709\u4e00\u822c\u6c34\u5e73\u7684\u91cf\uff0c\u8fd9\u4e2a\u91cf\u4e0d\u662f\u5404\u4e2a\u5355\u4f4d\u7684\u5177\u4f53\u53d8\u91cf\u503c\uff0c\u4f46\u53c8\u8981\u53cd\u6620\u603b\u4f53\u5404\u5355\u4f4d\u7684\u4e00\u822c\u6c34\u5e73\uff0c\u8fd9\u79cd\u5e73\u5747\u6570\u79f0\u4e3a\u6570\u503c\u5e73\u5747\u6570\u3002\u6570\u503c\u5e73\u5747\u6570\u6709\u7b97\u672f\u5e73\u5747\u6570\u3001\u8c03\u548c\u5e73\u5747\u6570\u3001\u51e0\u4f55\u5e73\u5747\u6570\u7b49\u5f62\u5f0f\u3002<\/p>\n

\u4f4d\u7f6e\u5e73\u5747\u6570\uff1a\u4f4d\u7f6e\u5e73\u5747\u6570\u5c31\u662f\u6839\u636e\u603b\u4f53\u4e2d\u5904\u4e8e\u7279\u6b8a\u4f4d\u7f6e\u4e0a\u7684\u4e2a\u522b\u5355\u4f4d\u6216\u90e8\u5206\u5355\u4f4d\u7684\u6807\u5fd7\u503c\u6765\u786e\u5b9a\u7684\u4ee3\u8868\u503c\uff0c\u5b83\u5bf9\u4e8e\u6574\u4e2a\u603b\u4f53\u6765\u8bf4\uff0c\u5177\u6709\u975e\u5e38\u76f4\u89c2\u7684\u4ee3\u8868\u6027\uff0c\u56e0\u6b64\uff0c\u5e38\u7528\u6765\u53cd\u6620\u5206\u5e03\u7684\u96c6\u4e2d\u8d8b\u52bf\u3002<\/p>\n

2. \u79bb\u4e2d\u8d8b\u52bf\u5206\u6790<\/p>\n

\"\u6570\u636e\u5206\u6790\u65b9\u6cd5<\/p>\n

\u901a\u8fc7\u6570\u5b66\u6a21\u578b\u6a21\u62df\u5730\u7406\u7279\u5f81\u7684\u7a7a\u95f4\u5206\u5e03\u4e0e\u65f6\u95f4\u8fc7\u7a0b,\u628a\u5730\u7406\u8981\u7d20\u65f6\u7a7a\u5206\u5e03\u7684\u5b9e\u6d4b\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u4e0d\u8db3\u90e8\u5206\u5185\u63d2\u6216\u8005\u9884\u6d4b\u51fa\u6765\u3002<\/p>\n

\u79bb\u4e2d\u8d8b\u52bf\u5206\u6790\u4e3b\u8981\u9760\u5168\u8ddd\u3001\u56db\u5206\u5dee\u3001\u5e73\u5747\u5dee\u3001\u65b9\u5dee\uff08\u534f\u65b9\u5dee\uff1a\u7528\u6765\u5ea6\u91cf\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u5173\u7cfb\u7684\u7edf\u8ba1\u91cf\uff09\u3001\u6807\u51c6\u5dee\u7b49\u7edf\u8ba1\u6307\u6807\u6765\u7814\u7a76\u6570\u636e\u7684\u79bb\u4e2d\u8d8b\u52bf\u3002<\/p>\n

3. \u76f8\u5173\u5206\u6790<\/p>\n

\u76f8\u5173\u5206\u6790\u662f\u7814\u7a76\u4e24\u4e2a\u6216\u4e24\u4e2a\u4ee5\u4e0a\u5904\u4e8e\u540c\u7b49\u5730\u4f4d\u7684\u968f\u673a\u53d8\u91cf\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u7684\u7edf\u8ba1\u5206\u6790\u65b9\u6cd5\u3002\u4f8b\u5982\uff0c\u4eba\u7684\u8eab\u9ad8\u548c\u4f53\u91cd\u4e4b\u95f4\uff1b\u7a7a\u6c14\u4e2d\u7684\u76f8\u5bf9\u6e7f\u5ea6\u4e0e\u964d\u96e8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u90fd\u662f\u76f8\u5173\u5206\u6790\u7814\u7a76\u7684\u95ee\u9898\u3002\u76f8\u5173\u5206\u6790\u4e0e\u56de\u5f52\u5206\u6790\u4e4b\u95f4\u7684\u533a\u522b\uff1a\u56de\u5f52\u5206\u6790\u4fa7\u91cd\u4e8e\u7814\u7a76\u968f\u673a\u53d8\u91cf\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\uff0c\u4ee5\u4fbf\u7528\u4e00\u4e2a\u53d8\u91cf\u53bb\u9884\u6d4b\u53e6\u4e00\u4e2a\u53d8\u91cf;\u76f8\u5173\u5206\u6790\u4fa7\u91cd\u4e8e\u53d1\u73b0\u968f\u673a\u53d8\u91cf\u95f4\u7684\u79cd\u79cd\u76f8\u5173\u7279\u6027\u3002\u76f8\u5173\u5206\u6790\u5728\u5de5\u519c\u4e1a\u3001\u6c34\u6587\u3001\u6c14\u8c61\u3001\u793e\u4f1a\u7ecf\u6d4e\u548c\u751f\u7269\u5b66\u7b49\u65b9\u9762\u90fd\u6709\u5e94\u7528\u3002<\/p>\n

\u4e3a\u4e86\u786e\u5b9a\u76f8\u5173\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u9996\u5148\u5e94\u8be5\u6536\u96c6\u4e00\u4e9b\u6570\u636e\uff0c\u8fd9\u4e9b\u6570\u636e\u5e94\u8be5\u662f\u6210\u5bf9\u7684\u3002\u4f8b\u5982\uff0c\u6bcf\u4eba\u7684\u8eab\u9ad8\u548c\u4f53\u91cd\u3002\u7136\u540e\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u63cf\u8ff0\u8fd9\u4e9b\u70b9\uff0c\u8fd9\u4e00\u7ec4\u70b9\u96c6\u79f0\u4e3a\u201c\u6563\u70b9\u56fe\u201d\u3002\u6839\u636e\u6563\u70b9\u56fe\uff0c\u5f53\u81ea\u53d8\u91cf\u53d6\u67d0\u4e00\u503c\u65f6\uff0c\u56e0\u53d8\u91cf\u5bf9\u5e94\u4e3a\u4e00\u6982\u7387\u5206\u5e03\uff0c\u5982\u679c\u5bf9\u4e8e\u6240\u6709\u7684\u81ea\u53d8\u91cf\u53d6\u503c\u7684\u6982\u7387\u5206\u5e03\u90fd\u76f8\u540c\uff0c\u5219\u8bf4\u660e\u56e0\u53d8\u91cf\u548c\u81ea\u53d8\u91cf\u662f\u6ca1\u6709\u76f8\u5173\u5173\u7cfb\u7684\u3002\u53cd\u4e4b\uff0c\u5982\u679c\uff0c\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u4e0d\u540c\uff0c\u56e0\u53d8\u91cf\u7684\u5206\u5e03\u4e5f\u4e0d\u540c\uff0c\u5219\u8bf4\u660e\u4e24\u8005\u662f\u5b58\u5728\u76f8\u5173\u5173\u7cfb\u7684\u3002<\/p>\n

\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u7a0b\u5ea6\u901a\u8fc7\u76f8\u5173\u7cfb\u6570r\u6765\u8868\u793a\u3002\u76f8\u5173\u7cfb\u6570r\u7684\u503c\u5728-1\u548c1\u4e4b\u95f4\uff0c\u4f46\u53ef\u4ee5\u662f\u6b64\u8303\u56f4\u5185\u7684\u4efb\u4f55\u503c\u3002\u6b63\u76f8\u5173\u65f6\uff0cr\u503c\u57280\u548c1\u4e4b\u95f4\uff0c\u6563\u70b9\u56fe\u662f\u659c\u5411\u4e0a\u7684\uff0c\u8fd9\u65f6\u4e00\u4e2a\u53d8\u91cf\u589e\u52a0\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u4e5f\u589e\u52a0\uff1b\u8d1f\u76f8\u5173\u65f6\uff0cr\u503c\u5728-1\u548c0\u4e4b\u95f4\uff0c\u6563\u70b9\u56fe\u662f\u659c\u5411\u4e0b\u7684\uff0c\u6b64\u65f6\u4e00\u4e2a\u53d8\u91cf\u589e\u52a0\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u5c06\u51cf\u5c11\u3002r\u7684\u7edd\u5bf9\u503c\u8d8a\u63a5\u8fd11\uff0c\u4e24\u53d8\u91cf\u7684\u5173\u8054\u7a0b\u5ea6\u8d8a\u5f3a\uff0cr\u7684\u7edd\u5bf9\u503c\u8d8a\u63a5\u8fd10\uff0c\u4e24\u53d8\u91cf\u7684\u5173\u8054\u7a0b\u5ea6\u8d8a\u5f31\u3002<\/p>\n

4. \u63a8\u8bba\u7edf\u8ba1<\/p>\n

\u63a8\u8bba\u7edf\u8ba1(inferential statistics)\u662f\u501f\u52a9\u62bd\u6837\u8c03\u67e5\uff0c\u4ece\u5c40\u90e8\u63a8\u65ad\u603b\u4f53\uff0c\u4ee5\u5bf9\u4e0d\u80af\u5b9a\u7684\u4e8b\u7269\u505a\u51fa\u51b3\u7b56\u7684\u4e00\u79cd\u7edf\u8ba1\u3002\u6709\u603b\u4f53\u53c2\u6570\u4f30\u8ba1\u4e0e\u5047\u8bbe\u68c0\u9a8c\u4e24\u79cd\u3002\u524d\u8005\u4ee5\u4e00\u6b21\u6027\u62bd\u6837\u5b9e\u9a8c\u4e3a\u4f9d\u636e\uff0c\u5bf9\u6574\u4e2a\u603b\u4f53\u7684\u67d0\u4e2a\u6570\u5b57\u7279\u5f81\u505a\u51fa\u4f30\u8ba1\u3002\u540e\u8005\u5219\u662f\u5bf9\u67d0\u79cd\u5047\u8bbe\u8fdb\u884c\u68c0\u9a8c\uff0c\u6839\u636e\u8ba1\u7b97\u7ed3\u679c\u63a8\u65ad\u6240\u505a\u7684\u5047\u8bbe\u662f\u5426\u53ef\u4ee5\u63a5\u53d7\u3002\u5982\u5e73\u5747\u6570\u3001\u6807\u51c6\u5dee\u3001\u76f8\u5173\u7cfb\u6570\u3001\u56de\u5f52\u7cfb\u6570\u7b49\u7279\u5f81\u7684\u603b\u4f53\u4f30\u8ba1\u53ca\u5dee\u5f02\u663e\u8457\u6027\u68c0\u9a8c\u3002\u63a8\u65ad\u7edf\u8ba1\u7684\u7406\u8bba\u57fa\u7840\u662f\u6982\u7387\u8bba\uff0c\u5b83\u66f4\u591a\u5730\u9700\u8981\u501f\u52a9\u62bd\u6837\u7406\u8bba\u4e0e\u65b9\u6cd5\u3002<\/p>\n

\u53c2\u6570\u4f30\u8ba1\u5c31\u662f\u6839\u636e\u62bd\u6837\u7ed3\u679c\uff0c\u79d1\u5b66\u5730\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u503c\u7684\u5927\u5c0f\u548c\u8303\u56f4\u3002\u53c2\u6570\u4f30\u8ba1\u6709\u4e24\u79cd\u65b9\u6cd5\uff1a\u2460\u70b9\u4f30\u8ba1\u3002\u5229\u7528\u6837\u672c\u7edf\u8ba1\u5355\u503c\u76f4\u63a5\u4f30\u8ba1\u672a\u77e5\u603b\u4f53\u53c2\u6570\u7684\u65b9\u6cd5\u3002\u5982\u4ece\u67d0\u5e02\u62bd\u53d6100\u540d\u5c11\u5e74\u72af\u4eba\u4f5c\u4e3a\u6837\u672c\uff0c\u8ba1\u7b97\u51fa\u4ed6\u4eec\u7684\u5e74\u9f84\u5747\u503c\u4e3a16.5\u5c81\uff0c\u7136\u540e\u5c06\u8be5\u503c\u4f5c\u4e3a\u5168\u5e02\u5c11\u5e74\u72af\u4eba\u7684\u5e73\u5747\u5e74\u9f84\u3002\u8fd9\u79cd\u4ee5\u70b9\u4ee3\u9762\u7684\u4f30\u8ba1\u65b9\u6cd5\u5373\u4e3a\u70b9\u4f30\u8ba1\u6cd5\u3002\u70b9\u4f30\u8ba1\u6cd5\u4e00\u822c\u53ea\u7528\u6765\u5bf9\u603b\u4f53\u53c2\u6570\u8fdb\u884c\u7c97\u7565\u7684\u4f30\u7b97\uff0c\u7531\u4e8e\u5b83\u4e0d\u80fd\u8bf4\u660e\u4f30\u8ba1\u7684\u51c6\u786e\u7a0b\u5ea6\u548c\u53ef\u9760\u5ea6\uff0c\u56e0\u6b64\u5f88\u5c11\u4f7f\u7528\u3002\u2461\u533a\u95f4\u4f30\u8ba1\u3002\u5728\u4e00\u5b9a\u7684\u628a\u63e1\u7a0b\u5ea6\u4e0a\u5bf9\u603b\u4f53\u53c2\u6570\u53ef\u80fd\u843d\u5165\u7684\u4e00\u4e2a\u6570\u503c\u8303\u56f4\u505a\u51fa\u4f30\u8ba1\u7684\u65b9\u6cd5\u3002\u5982\u8ba1\u7b97\u51fa\u67d0\u5e02\u5c11\u5e74\u72af\u4eba\u7684\u5e73\u5747\u5e74\u9f84\u53ef\u80fd\u572816-17\u5c81\u4e4b\u95f4\u7684\u8303\u56f4\u5185\uff0c\u8fd9\u79cd\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u5728\u4e00\u5b9a\u533a\u95f4\u7684\u63a8\u65ad\u65b9\u6cd5\u5c31\u662f\u533a\u95f4\u4f30\u8ba1\u6cd5\u3002<\/p>\n

\u5047\u8bbe\u68c0\u9a8c\u662f\u6839\u636e\u62bd\u6837\u8c03\u67e5\u7edf\u8ba1\u7ed3\u679c\u5728\u4e00\u5b9a\u53ef\u9760\u6027\u57fa\u7840\u4e0a\u5bf9\u539f\u6765\u7684\u5047\u8bbe\u4f5c\u51fa\u63a5\u53d7\u6216\u62d2\u7edd\u7684\u5224\u65ad\u3002\u5982\u8ba4\u4e3a\u201c\u67d0\u5e02\u72af\u7f6a\u4eba\u5458\u7684\u5a5a\u59fb\u72b6\u51b5\u4ee5\u672a\u5a5a\u4e3a\u4e3b\u201d\u5c31\u662f\u4e00\u4e2a\u547d\u9898\uff0c\u8be5\u5047\u8bbe\u662f\u5426\u6b63\u786e\uff0c\u8981\u7528\u4ece\u603b\u4f53\u62bd\u51fa\u7684\u6837\u672c\u8fdb\u884c\u68c0\u9a8c\uff0c\u5f97\u51fa\u627f\u8ba4\u6216\u63a8\u7ffb\u5047\u8bbe\u7684\u7ed3\u8bba\u3002\u56e0\u6b64\uff0c\u5047\u8bbe\u68c0\u9a8c\u4e5f\u53ea\u901a\u8fc7\u7814\u7a76\u6837\u672c\u5bf9\u4e8b\u5148\u4f5c\u51fa\u7684\u6709\u5173\u603b\u4f53\u7279\u5f81\u7684\u5047\u8bbe\u8fdb\u884c\u68c0\u9a8c\u7684\u57fa\u672c\u8fc7\u7a0b\u3002<\/p>\n

\u5047\u8bbe\u68c0\u9a8c\u4e3b\u8981\u89e3\u51b3\u4e24\u7c7b\u95ee\u9898\uff1a\u2460\u5bf9\u603b\u4f53\u7684\u67d0\u4e9b\u7279\u5f81\u63d0\u51fa\u9002\u5f53\u7684\u5047\u8bbe\u540e\uff0c\u5229\u7528\u62bd\u6837\u65b9\u6cd5\u8fdb\u884c\u68c0\u9a8c\u3002\u68c0\u9a8c\u7ed3\u679c\u6709\u4e24\u79cd\u60c5\u51b5\uff1a\u4e00\u662f\u68c0\u9a8c\u7ed3\u679c\u4e0e\u5047\u8bbe\u4e4b\u95f4\u5b58\u5728\u4e00\u5b9a\u7684\u504f\u5dee\uff1b\u4e8c\u662f\u68c0\u9a8c\u7ed3\u679c\u4e0e\u5047\u8bbe\u5b8c\u5168\u76f8\u7b26\u3002\u82e5\u662f\u7b2c\u4e00\u79cd\u60c5\u51b5\uff0c\u4e00\u5b9a\u8981\u4e86\u89e3\u504f\u5dee\u662f\u771f\u7684\u8868\u660e\u5047\u8bbe\u9519\u8bef\uff0c\u8fd8\u662f\u7531\u4e8e\u62bd\u6837\u8bef\u5dee\u9020\u6210\u7684\uff1b\u82e5\u662f\u7b2c\u4e8c\u79cd\u60c5\u51b5\uff0c\u4e5f\u4e0d\u80fd\u8d38\u7136\u8bf4\u5047\u8bbe\u662f\u6b63\u786e\u7684\uff0c\u4e5f\u53ef\u80fd\u662f\u7531\u4e8e\u62bd\u6837\u8bef\u5dee\u9020\u6210\u7684\u3002\u2461\u5bf9\u4ece\u4e24\u7ec4\u6216\u4e24\u7ec4\u4ee5\u4e0a\u6837\u672c\u8ba1\u7b97\u51fa\u7684\u7edf\u8ba1\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u8fdb\u884c\u663e\u8457\u6027\u8003\u9a8c\u3002\u7edf\u8ba1\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u6709\u53ef\u80fd\u662f\u5b83\u4eec\u6240\u4ee3\u8868\u7684\u4e0d\u540c\u603b\u4f53\u7684\u603b\u4f53\u53c2\u6570\u7684\u5dee\u5f02\uff0c\u4e5f\u6709\u53ef\u80fd\u662f\u540c\u4e00\u603b\u4f53\u4f46\u7531\u4e8e\u62bd\u6837\u8bef\u5dee\u9020\u6210\u7684\uff0c\u56e0\u800c\u8981\u8fdb\u884c\u663e\u8457\u6027\u8003\u9a8c\u3002\u5728\u663e\u8457\u6027\u8003\u9a8c\u4e2d\uff0c\u5982\u679c\u68c0\u9a8c\u7ed3\u679c\u5dee\u5f02\u663e\u8457\uff0c\u5c31\u53ef\u63a8\u65ad\u8fd9\u79cd\u5dee\u5f02\u4ee3\u8868\u603b\u4f53\u53c2\u6570\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u5426\u5219\u6837\u54c1\u53ef\u80fd\u6765\u81ea\u540c\u4e00\u603b\u4f53\uff0c\u6216\u8005\u8ba4\u4e3a\u603b\u4f53\u53c2\u6570\u95f4\u65e0\u771f\u5b9e\u5dee\u5f02\uff0c\u6216\u8005\u4e5f\u53ef\u8ba4\u4e3a\u6837\u672c\u7edf\u8ba1\u503c\u7684\u5dee\u5f02\u53ea\u662f\u7531\u4e8e\u62bd\u6837\u8bef\u5dee\u9020\u6210\u7684\u3002\u5728\u6b64\u5e94\u5f53\u6ce8\u610f\u7684\u662f\uff0c\u4efb\u4f55\u65f6\u5019\u90fd\u4e0d\u80fd\u51ed\u6837\u672c\u7edf\u8ba1\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u8f7b\u7387\u5f97\u51fa\u5b83\u4eec\u4ee3\u8868\u7684\u603b\u4f53\u7684\u53c2\u6570\u95f4\u5b58\u5728\u5dee\u5f02\u7684\u7ed3\u8bba\u3002<\/p>\n

\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u4fe1\u670d\u5206\u6790<\/strong><\/h3>\n

\u4fe1\u5ea6\uff08Reliability\uff09\u5373\u53ef\u9760\u6027\uff0c\u5b83\u662f\u6307\u91c7\u7528\u540c\u6837\u7684\u65b9\u6cd5\u5bf9\u540c\u4e00\u5bf9\u8c61\u91cd\u590d\u6d4b\u91cf\u65f6\u6240\u5f97\u7ed3\u679c\u7684\u4e00\u81f4\u6027\u7a0b\u5ea6\u3002\u4fe1\u5ea6\u6307\u6807\u591a\u4ee5\u76f8\u5173\u7cfb\u6570\u8868\u793a\uff0c\u5927\u81f4\u53ef\u5206\u4e3a\u4e09\u7c7b\uff1a\u7a33\u5b9a\u7cfb\u6570\uff08\u8de8\u65f6\u95f4\u7684\u4e00\u81f4\u6027\uff09\uff0c\u7b49\u503c\u7cfb\u6570\uff08\u8de8\u5f62\u5f0f\u7684\u4e00\u81f4\u6027\uff09\u548c\u5185\u5728\u4e00\u81f4\u6027\u7cfb\u6570\uff08\u8de8\u9879\u76ee\u7684\u4e00\u81f4\u6027\uff09\u3002\u4fe1\u5ea6\u5206\u6790\u7684\u65b9\u6cd5\u4e3b\u8981\u6709\u4ee5\u4e0b\u56db\u79cd\uff1a\u91cd\u6d4b\u4fe1\u5ea6\u6cd5\u3001\u590d\u672c\u4fe1\u5ea6\u6cd5\u3001\u6298\u534a\u4fe1\u5ea6\u6cd5\u3001\u03b1\u4fe1\u5ea6\u7cfb\u6570\u6cd5\u3002<\/p>\n

1. \u91cd\u6d4b\u4fe1\u5ea6\u6cd5<\/p>\n

\u91cd\u6d4b\u4fe1\u5ea6\uff08test-retest reliability\uff09\uff0c\u53c8\u79f0\u518d\u6d4b\u4fe1\u5ea6\u3001\u7a33\u5b9a\u6027\u7cfb\u6570\uff08coefficient of stability\uff09\uff0c\u53cd\u6620\u6d4b\u9a8c\u8de8\u8d8a\u65f6\u95f4\u7684\u7a33\u5b9a\u6027\u548c\u4e00\u81f4\u6027\uff0c\u5373\u5e94\u7528\u540c\u4e00\u6d4b\u9a8c\u65b9\u6cd5\uff0c\u5bf9\u540c\u4e00\u7ec4\u88ab\u8bd5\u8005\u5148\u540e\u4e24\u6b21\u8fdb\u884c\u6d4b\u67e5\uff0c\u7136\u540e\u8ba1\u7b97\u4e24\u6b21\u6d4b\u67e5\u6240\u5f97\u5206\u6570\u7684\u5173\u7cfb\u7cfb\u6570\u3002\u8be5\u4fe1\u5ea6\u80fd\u8868\u793a\u4e24\u6b21\u6d4b\u8bd5\u7ed3\u679c\u6709\u65e0\u53d8\u52a8\uff0c\u53cd\u6620\u4e86\u6d4b\u9a8c\u5206\u6570\u7684\u7a33\u5b9a\u7a0b\u5ea6\u3002\u76f8\u5173\u7a0b\u5ea6\u9ad8\uff0c\u8868\u793a\u524d\u540e\u6d4b\u91cf\u4e00\u81f4\u6027\u9ad8\uff0c\u7a33\u5b9a\u6027\u597d\u3002<\/p>\n

\u91cd\u6d4b\u7684\u8fc7\u7a0b\u8003\u8651\u4e86\u4e0d\u540c\u7684\u6761\u4ef6\uff08\u73af\u5883\u7684\u3001\u4eba\u7684\uff09\u5e26\u6765\u7684\u6d4b\u91cf\u7ed3\u679c\u7684\u8bef\u5dee\uff0c\u8fd9\u79cd\u8bef\u5dee\u4e0e\u4e24\u6b21\u65bd\u6d4b\u7684\u60c5\u5883\u76f8\u5173\u8054\u3002 \u5176\u4f18\u52bf\u662f\u80fd\u63d0\u4f9b\u6709\u5173\u6d4b\u9a8c\u7ed3\u679c\u662f\u5426\u968f\u65f6\u95f4\u800c\u6539\u53d8\u7684\u8d44\u6599\uff0c\u53ef\u4f5c\u4e3a\u9884\u6d4b\u53d7\u6d4b\u8005\u5c06\u6765\u884c\u4e3a\u8868\u73b0\u7684\u4f9d\u636e\u3002 \u5176\u4e0d\u8db3\u5728\u4e8e\u6613\u53d7\u7ec3\u4e60\u548c\u8bb0\u5fc6\u7684\u5f71\u54cd\uff0c\u7b2c\u4e00\u6b21\u6d4b\u8bd5\u6240\u53d1\u73b0\u7684\u9519\u8bef\u4e5f\u53ef\u80fd\u5bfc\u81f4\u7b2c\u4e8c\u6b21\u53cd\u5e94\u7684\u53d8\u5316\u800c\u589e\u52a0\u8bef\u5dee\u53d8\u5f02\u3002\u518d\u6d4b\u4fe1\u5ea6\u53ea\u9002\u7528\u4e8e\u6d4b\u91cf\u90a3\u4e9b\u4e0d\u4f1a\u968f\u65f6\u95f4\u7684\u53d8\u5316\u800c\u6539\u53d8\u7684\u7279\u8d28\u3002<\/p>\n

2. \u590d\u672c\u4fe1\u5ea6\u6cd5<\/p>\n

\u590d\u672c\u6cd5\uff08alternate-form method\uff09\u662f\u4fe1\u5ea6\uff08reliability\uff09\u7684\u4e00\u79cd\u8ba1\u7b97\u65b9\u6cd5\u3002\u7528\u4e00\u4e2a\u4e0e\u4e3b\u672c\u76f8\u4f3c\u7684\u590d\u672c\u65bd\u6d4b\u540c\u4e00\u7ec4\u88ab\u8bd5\uff0c\u8ba1\u7b97\u53d7\u6d4b\u8005\u5728\u8fd9\u4e24\u4efd\u6d4b\u9a8c\u4e2d\u6240\u5f97\u5206\u6570\u4e4b\u95f4\u7684\u76f8\u5173\uff0c\u5373\u53ef\u786e\u5b9a\u6d4b\u9a8c\u7684\u590d\u672c\u4fe1\u5ea6\u3002\u5e38\u89c1\u7684\u590d\u672c\u6cd5\u7684\u4f8b\u5b50\u5c31\u662f\u8003\u8bd5\u7684A\u5377\u548cB\u5377\u3002<\/p>\n

\u590d\u672c\u6cd5\u7684\u4f18\u70b9\uff1a
\n\u4e00\u4e2a\u6d4b\u9a8c\u6709\u4e24\u4e2a\u6216\u51e0\u4e2a\u590d\u672c\uff0c\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u6d4b\u91cf\u540c\u4e00\u79cd\u5c5e\u6027\u5177\u6709\u4e24\u4e2a\u6216\u51e0\u4e2a\u884c\u4e3a\u6837\u672c\u3002\u7531\u4e8e\u6d4b\u9898\u6570\u76ee\u7684\u589e\u52a0\uff0c\u5bf9\u4e8e\u4e0e\u6240\u6b32\u6d4b\u91cf\u7684\u5c5e\u6027\u76f8\u8054\u7cfb\u7684\u884c\u4e3a\u603b\u4f53\u7684\u4ee3\u8868\u6027\u589e\u5f3a\u3002\u56e0\u6b64\uff0c\u4e00\u4e2a\u6d4b\u9a8c\u7684\u4e24\u4e2a\u590d\u672c\u5728\u4e24\u4e09\u5929\u81f3\u4e00\u5468\u5bf9\u540c\u4e00\u7ec4\u88ab\u8bd5\u65bd\u6d4b\u65f6\uff0c\u83b7\u5f97\u7684\u590d\u672c\u4fe1\u5ea6\u7cfb\u6570\u662f\u76f8\u5f53\u51c6\u786e\u7684\u3002<\/p>\n

\u6d4b\u9a8c\u7684\u4e24\u4e2a\u590d\u672c\uff0c\u5982\u679c\u5728\u4e0d\u540c\u7684\u65f6\u95f4\u4f7f\u7528\uff0c\u5176\u4fe1\u5ea6\u65e2\u53ef\u4ee5\u53cd\u6620\u5728\u4e0d\u540c\u65f6\u95f4\u7684\u7a33\u5b9a\u6027\uff0c\u53c8\u53ef\u4ee5\u53cd\u6620\u5bf9\u4e8e\u4e0d\u540c\u6d4b\u9898\u7684\u4e00\u81f4\u6027\u3002\u5b83\u53cd\u6620\u4e86\u4e24\u4e2a\u5c42\u9762\u7684\u4fe1\u5ea6\u3002<\/p>\n

\u4e24\u4e2a\u590d\u672c\u5728\u540c\u65f6\u8fde\u7eed\u4f7f\u7528\u65f6\uff0c\u53ef\u4ee5\u907f\u514d\u518d\u6d4b\u4fe1\u5ea6\u7684\u4e00\u4e9b\u7f3a\u70b9\uff0c\u5982\u9996\u6d4b\u5bf9\u518d\u6d4b\u5728\u8bb0\u5fc6\u3001\u7ec3\u4e60\u6548\u679c\u7684\u5f71\u54cd\uff0c\u95f4\u9694\u671f\u95f4\u83b7\u5f97\u65b0\u77e5\u8bc6\u7684\u5f71\u54cd\uff0c\u4e24\u6b21\u65bd\u6d4b\u7684\u73af\u5883\u4e0d\u540c\u548c\u88ab\u8bd5\u4e3b\u89c2\u72b6\u6001\u4e0d\u540c\u7684\u5f71\u54cd\uff0c\u4ee5\u53ca\u4e3a\u4e86\u5e94\u4ed8\u6d4b\u9a8c\u6240\u4f5c\u8bad\u7ec3\u7684\u5f71\u54cd\u7b49\u3002<\/p>\n

\u590d\u672c\u6cd5\u7684\u7f3a\u70b9\uff1a
\n\u7f16\u5236\u4e24\u4e2a\u5b8c\u5168\u76f8\u7b49\u7684\u6d4b\u9a8c\u662f\u5f88\u56f0\u96be\u7684\u3002\u5982\u679c\u4e24\u4e2a\u590d\u672c\u8fc7\u5206\u76f8\u4f3c\uff0c\u5219\u53d8\u6210\u518d\u6d4b\u7684\u5f62\u5f0f\uff1b\u800c\u8fc7\u5206\u4e0d\u76f8\u4f3c\uff0c\u53c8\u4f7f\u7b49\u503c\u7684\u6761\u4ef6\u4e0d\u5b58\u5728\uff0c\u4e24\u4e2a\u590d\u672c\u6d4b\u9a8c\u6709\u53ef\u80fd\u5728\u67d0\u79cd\u7a0b\u5ea6\u535c\u6d4b\u91cf\u4e86\u4e0d\u540c\u7684\u6027\u8d28\uff0c\u8fd9\u5c31\u4f1a\u4f4e\u4f30\u6d4b\u9a8c\u7684\u4fe1\u5ea6\u3002<\/p>\n

\u88ab\u8bd5\u8fde\u7eed\u63a5\u53d7\u6027\u8d28\u76f8\u4f3c\u7684\u4e24\u4e2a\u6d4b\u9a8c\uff0c\u53ef\u80fd\u51cf\u5c11\u5b8c\u6210\u6d4b\u9a8c\u7684\u79ef\u6781\u6027\u3002<\/p>\n

\u867d\u7136\u4e24\u4e2a\u590d\u672c\u6d4b\u9a8c\u7684\u9898\u76ee\u6750\u6599\u4e0d\u540c\uff0c\u4f46\u88ab\u8bd5\u4e00\u65e6\u638c\u63e1\u4e86\u89e3\u9898\u7684\u67d0\u4e00\u6a21\u5f0f\uff0c\u5c31\u80fd\u89e6\u7c7b\u65c1\u901a\uff0c\u6709\u53ef\u80fd\u5931\u53bb\u590d\u672c\u7684\u610f\u4e49\u3002<\/p>\n

3. \u6298\u534a\u4fe1\u5ea6\u6cd5<\/p>\n

\u6298\u534a\u4fe1\u5ea6\u6cd5\u662f\u5c06\u8c03\u67e5\u9879\u76ee\u5206\u4e3a\u4e24\u534a\uff0c\u8ba1\u7b97\u4e24\u534a\u5f97\u5206\u7684\u76f8\u5173\u7cfb\u6570\uff0c\u8fdb\u800c\u4f30\u8ba1\u6574\u4e2a\u91cf\u8868\u7684\u4fe1\u5ea6\u3002\u6298\u534a\u4fe1\u5ea6\u5c5e\u4e8e\u5185\u5728\u4e00\u81f4\u6027\u7cfb\u6570\uff0c\u6d4b\u91cf\u7684\u662f\u4e24\u534a\u9898\u9879\u5f97\u5206\u95f4\u7684\u4e00\u81f4\u6027\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e00\u822c\u4e0d\u9002\u7528\u4e8e\u4e8b\u5b9e\u5f0f\u95ee\u5377\uff08\u5982\u5e74\u9f84\u4e0e\u6027\u522b\u65e0\u6cd5\u76f8\u6bd4\uff09\uff0c\u5e38\u7528\u4e8e\u6001\u5ea6\u3001\u610f\u89c1\u5f0f\u95ee\u5377\u7684\u4fe1\u5ea6\u5206\u6790\u3002\u5728\u95ee\u5377\u8c03\u67e5\u4e2d\uff0c\u6001\u5ea6\u6d4b\u91cf\u6700\u5e38\u89c1\u7684\u5f62\u5f0f\u662f5\u7ea7\u674e\u514b\u7279\uff08Likert\uff09\u91cf\u8868\u3002<\/p>\n

\u8fdb\u884c\u6298\u534a\u4fe1\u5ea6\u5206\u6790\u65f6\uff0c\u5982\u679c\u91cf\u8868\u4e2d\u542b\u6709\u53cd\u610f\u9898\u9879\uff0c\u5e94\u5148\u5c06\u53cd\u610f\u9898\u9879\u7684\u5f97\u5206\u4f5c\u9006\u5411\u5904\u7406\uff0c\u4ee5\u4fdd\u8bc1\u5404\u9898\u9879\u5f97\u5206\u65b9\u5411\u7684\u4e00\u81f4\u6027\uff0c\u7136\u540e\u5c06\u5168\u90e8\u9898\u9879\u6309\u5947\u5076\u6216\u524d\u540e\u5206\u4e3a\u5c3d\u53ef\u80fd\u76f8\u7b49\u7684\u4e24\u534a\uff0c\u8ba1\u7b97\u4e8c\u8005\u7684\u76f8\u5173\u7cfb\u6570\uff08rhh\uff0c\u5373\u534a\u4e2a\u91cf\u8868\u7684\u4fe1\u5ea6\u7cfb\u6570\uff09\uff0c\u6700\u540e\u7528\u65af\u76ae\u5c14\u66fc-\u5e03\u6717\uff08Spearman-Brown\uff09\u516c\u5f0f\u6c42\u51fa\u6574\u4e2a\u91cf\u8868\u7684\u4fe1\u5ea6\u7cfb\u6570\uff08ru\uff09\u3002<\/p>\n

4.\u03b1\u4fe1\u5ea6\u7cfb\u6570\u6cd5<\/p>\n

Cronbach \u03b1\u4fe1\u5ea6\u7cfb\u6570\u662f\u6700\u5e38\u7528\u7684\u4fe1\u5ea6\u7cfb\u6570\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a\u03b1=(k\/(k-1))*(1-(\u2211Si^2)\/ST^2)<\/p>\n

\u5176\u4e2d\uff0cK\u4e3a\u91cf\u8868\u4e2d\u9898\u9879\u7684\u603b\u6570\uff0c Si^2\u4e3a\u7b2ci\u9898\u5f97\u5206\u7684\u9898\u5185\u65b9\u5dee\uff0c ST^2\u4e3a\u5168\u90e8\u9898\u9879\u603b\u5f97\u5206\u7684\u65b9\u5dee\u3002<\/p>\n

\u4ece\u516c\u5f0f\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u03b1\u7cfb\u6570\u8bc4\u4ef7\u7684\u662f\u91cf\u8868\u4e2d\u5404\u9898\u9879\u5f97\u5206\u95f4\u7684\u4e00\u81f4\u6027\uff0c\u5c5e\u4e8e\u5185\u5728\u4e00\u81f4\u6027\u7cfb\u6570\u3002\u8fd9\u79cd\u65b9\u6cd5\u9002\u7528\u4e8e\u6001\u5ea6\u3001\u610f\u89c1\u5f0f\u95ee\u5377\uff08\u91cf\u8868\uff09\u7684\u4fe1\u5ea6\u5206\u6790\u3002 \u603b\u91cf\u8868\u7684\u4fe1\u5ea6\u7cfb\u6570\u6700\u597d\u57280.8\u4ee5\u4e0a\uff0c0.7-0.8\u4e4b\u95f4\u53ef\u4ee5\u63a5\u53d7\uff1b\u5206\u91cf\u8868\u7684\u4fe1\u5ea6\u7cfb\u6570\u6700\u597d\u57280.7\u4ee5\u4e0a\uff0c0.6-0.7\u8fd8\u53ef\u4ee5\u63a5\u53d7\u3002Cronbach ‘s alpha\u7cfb\u6570\u5982\u679c\u57280.6\u4ee5\u4e0b\u5c31\u8981\u8003\u8651\u91cd\u65b0\u7f16\u95ee\u5377\u3002<\/p>\n

\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u5217\u8054\u8868\u5206\u6790<\/strong><\/h3>\n

\u5217\u8054\u8868\uff08contingency table\uff09\u662f\u89c2\u6d4b\u6570\u636e\u6309\u4e24\u4e2a\u6216\u66f4\u591a\u5c5e\u6027\uff08\u5b9a\u6027\u53d8\u91cf\uff09\u5206\u7c7b\u65f6\u6240\u5217\u51fa\u7684\u9891\u6570\u8868\u3002\u5b83\u662f\u7531\u4e24\u4e2a\u4ee5\u4e0a\u7684\u53d8\u91cf\u8fdb\u884c\u4ea4\u53c9\u5206\u7c7b\u7684\u9891\u6570\u5206\u5e03\u8868\u3002<\/p>\n

\u4e00\u822c\uff0c\u82e5\u603b\u4f53\u4e2d\u7684\u4e2a\u4f53\u53ef\u6309\u4e24\u4e2a\u5c5e\u6027A\u4e0eB\u5206\u7c7b\uff0cA\u6709r\u4e2a\u7b49\u7ea7A1,A2,\u2026\uff0cAr\uff0cB\u6709c\u4e2a\u7b49\u7ea7B1,B2,\u2026\uff0cBc,\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6\u5927\u5c0f\u4e3an\u7684\u6837\u672c\uff0c\u8bbe\u5176\u4e2d\u6709nij\u4e2a\u4e2a\u4f53\u7684\u5c5e\u6027\u5c5e\u4e8e\u7b49\u7ea7Ai\u548cBj\uff0cnij\u79f0\u4e3a \u9891\u6570\uff0c\u5c06r\u00d7c\u4e2anij\u6392\u5217\u4e3a\u4e00\u4e2ar\u884cc\u5217\u7684\u4e8c\u7ef4\u5217\u8054\u8868\uff0c\u7b80\u79f0r\u00d7c\u8868\u3002\u82e5\u6240\u8003\u8651\u7684\u5c5e\u6027\u591a\u4e8e\u4e24\u4e2a\uff0c\u4e5f\u53ef\u6309\u7c7b\u4f3c\u7684\u65b9\u5f0f\u4f5c\u51fa\u5217\u8054\u8868\uff0c\u79f0\u4e3a\u591a\u7ef4\u5217\u8054\u8868\u3002<\/p>\n

\u5217\u8054\u8868\u53c8\u79f0\u4ea4\u4e92\u5206\u7c7b\u8868\uff0c\u6240\u8c13\u4ea4\u4e92\u5206\u7c7b\uff0c\u662f\u6307\u540c\u65f6\u4f9d\u636e\u4e24\u4e2a\u53d8\u91cf\u7684\u503c\uff0c\u5c06\u6240\u7814\u7a76\u7684\u4e2a\u6848\u5206\u7c7b\u3002\u4ea4\u4e92\u5206\u7c7b\u7684\u76ee\u7684\u662f\u5c06\u4e24\u53d8\u91cf\u5206\u7ec4\uff0c\u7136\u540e\u6bd4\u8f83\u5404\u7ec4\u7684\u5206\u5e03\u72b6\u51b5\uff0c\u4ee5\u5bfb\u627e\u53d8\u91cf\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n

\u5217\u8054\u8868\u5206\u6790\u7684\u57fa\u672c\u95ee\u9898\u662f\uff0c\u5224\u660e\u6240\u8003\u5bdf\u7684\u5404\u5c5e\u6027\u4e4b\u95f4\u6709\u65e0\u5173\u8054\uff0c\u5373\u662f\u5426\u72ec\u7acb\u3002\u5982\u5728\u524d\u4f8b\u4e2d\uff0c\u95ee\u9898\u662f\uff1a\u4e00\u4e2a\u4eba\u662f\u5426\u8272\u76f2\u4e0e\u5176\u6027\u522b\u662f\u5426\u6709\u5173\uff1f\u5728r\u00d7\u0441\u8868\u4e2d\uff0c\u82e5\u4ee5pi\u3001pj\u548cpij\u5206\u522b\u8868\u793a\u603b\u4f53\u4e2d\u7684\u4e2a\u4f53\u5c5e\u4e8e\u7b49\u7ea7Ai\uff0c\u5c5e\u4e8e\u7b49\u7ea7Bj\u548c\u540c\u65f6\u5c5e\u4e8eAi\u3001Bj\u7684\u6982\u7387\uff08pi\uff0cpj\u79f0\u8fb9\u7f18\u6982\u7387\uff0cpij\u79f0\u683c\u6982\u7387\uff09,\u201cA\u3001B\u4e24\u5c5e\u6027\u65e0\u5173\u8054\u201d\u7684\u5047\u8bbe\u53ef\u4ee5\u8868\u8ff0\u4e3aH0\uff1apij=pi\u2022pj\uff0c(i=1\uff0c2\uff0c\u2026\uff0cr\uff1bj=1,2,\u2026\uff0c\u0441)\uff0c\u672a\u77e5\u53c2\u6570pij\u3001pi\u3001pj\u7684\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\uff08\u89c1\u70b9\u4f30\u8ba1\uff09\u5206\u522b\u4e3a\u884c\u548c\u53ca\u5217\u548c\uff08\u7edf\u79f0\u8fb9\u7f18\u548c\uff09 \u4e3a\u6837\u672c\u5927\u5c0f\u3002<\/p>\n

\u6839\u636eK.\u76ae\u5c14\u68ee(1904)\u7684\u62df\u5408\u4f18\u5ea6\u68c0\u9a8c\u6216\u4f3c\u7136\u6bd4\u68c0\u9a8c\uff08\u89c1\u5047\u8bbe\u68c0\u9a8c\uff09,\u5f53h0\u6210\u7acb\uff0c\u4e14\u4e00\u5207pi>0\u548cpj>0\u65f6\uff0c\u7edf\u8ba1\u91cf\u7684\u6e10\u8fd1\u5206\u5e03\u662f\u81ea\u7531\u5ea6\u4e3a(r\uff0d1)(\u0441\uff0d1) \u7684\u2169\u5206\u5e03\uff0c\u5f0f\u4e2dEij=(ni\u2022nj)\/n\u79f0\u4e3a\u671f\u671b\u9891\u6570\u3002\u5f53n\u8db3\u591f\u5927\uff0c\u4e14\u8868\u4e2d\u5404\u683c\u7684Eij\u90fd\u4e0d\u592a\u5c0f\u65f6\uff0c\u53ef\u4ee5\u636e\u6b64\u5bf9h0\u4f5c\u68c0\u9a8c\uff1a\u82e5\u2169\u503c\u8db3\u591f\u5927\uff0c\u5c31\u62d2\u7edd\u5047\u8bbeh0\uff0c\u5373\u8ba4\u4e3aA\u4e0eB\u6709\u5173\u8054\u3002\u5728\u524d\u9762\u7684\u8272\u89c9\u95ee\u9898\u4e2d\uff0c\u66fe\u6309\u6b64\u68c0\u9a8c\uff0c\u5224\u5b9a\u51fa\u6027\u522b\u4e0e\u8272\u89c9\u4e4b\u95f4\u5b58\u5728\u67d0\u79cd\u5173\u8054\u3002<\/p>\n

\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u82e5\u6837\u672c\u5927\u5c0fn\u4e0d\u5f88\u5927,\u5219\u4e0a\u8ff0\u57fa\u4e8e\u6e10\u8fd1\u5206\u5e03\u7684\u65b9\u6cd5\u5c31\u4e0d\u9002\u7528\u3002\u5bf9\u6b64\uff0c\u5728\u56db\u683c\u8868\u60c5\u5f62\uff0cR.A.\u8d39\u5e0c\u5c14(1935)\u63d0\u51fa\u4e86\u4e00\u79cd\u9002\u7528\u4e8e\u6240\u6709n\u7684\u7cbe\u786e\u68c0\u9a8c\u6cd5\u3002\u5176\u601d\u60f3\u662f\u5728\u56fa\u5b9a\u5404\u8fb9\u7f18\u548c\u7684\u6761\u4ef6\u4e0b\uff0c\u6839\u636e\u8d85\u51e0\u4f55\u5206\u5e03\uff08\u89c1\u6982\u7387\u5206\u5e03\uff09\uff0c\u53ef\u4ee5\u8ba1\u7b97\u89c2\u6d4b\u9891\u6570\u51fa\u73b0\u4efb\u610f\u4e00\u79cd\u7279\u5b9a\u6392\u5217\u7684\u6761\u4ef6\u6982\u7387\u3002\u628a\u5b9e\u9645\u51fa\u73b0\u7684\u89c2\u6d4b\u9891\u6570\u6392\u5217\uff0c\u4ee5\u53ca\u6bd4\u5b83\u5448\u73b0\u66f4\u591a\u5173\u8054\u8ff9\u8c61\u7684\u6240\u6709\u53ef\u80fd\u6392\u5217\u7684\u6761\u4ef6\u6982\u7387\u90fd\u7b97\u51fa\u6765\u5e76\u76f8\u52a0\uff0c\u82e5\u6240\u5f97\u7ed3\u679c\u5c0f\u4e8e\u7ed9\u5b9a\u7684\u663e\u8457\u6027\u6c34\u5e73\uff0c\u5219\u5224\u5b9a\u6240\u8003\u8651\u7684\u4e24\u4e2a\u5c5e\u6027\u5b58\u5728\u5173\u8054\uff0c\u4ece\u800c\u62d2\u7eddh0\u3002<\/p>\n

\u5728\u5224\u5b9a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u5173\u8054\u6027\u540e\uff0c\u53ef\u7528\u591a\u79cd\u5b9a\u91cf\u6307\u6807\u6765\u523b\u753b\u5176\u5173\u8054\u7a0b\u5ea6\u3002\u4f8b\u5982\uff0c\u5bf9\u4e00\u822c\u7684r\u00d7\u0441\u8868\uff0c\u53ef\u7528\u5217\u8054\u7cfb\u6570\u8868\u793a\u4e4b\u3002<\/p>\n

\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u76f8\u5173\u5206\u6790<\/strong><\/h3>\n

\u76f8\u5173\u5206\u6790\u662f\u7814\u7a76\u4e24\u4e2a\u6216\u4e24\u4e2a\u4ee5\u4e0a\u5904\u4e8e\u540c\u7b49\u5730\u4f4d\u7684\u968f\u673a\u53d8\u91cf\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u7684\u7edf\u8ba1\u5206\u6790\u65b9\u6cd5\u3002\u4f8b\u5982\uff0c\u4eba\u7684\u8eab\u9ad8\u548c\u4f53\u91cd\u4e4b\u95f4\uff1b\u7a7a\u6c14\u4e2d\u7684\u76f8\u5bf9\u6e7f\u5ea6\u4e0e\u964d\u96e8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u90fd\u662f\u76f8\u5173\u5206\u6790\u7814\u7a76\u7684\u95ee\u9898\u3002\u76f8\u5173\u5206\u6790\u4e0e\u56de\u5f52\u5206\u6790\u4e4b\u95f4\u7684\u533a\u522b\uff1a\u56de\u5f52\u5206\u6790\u4fa7\u91cd\u4e8e\u7814\u7a76\u968f\u673a\u53d8\u91cf\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\uff0c\u4ee5\u4fbf\u7528\u4e00\u4e2a\u53d8\u91cf\u53bb\u9884\u6d4b\u53e6\u4e00\u4e2a\u53d8\u91cf;\u76f8\u5173\u5206\u6790\u4fa7\u91cd\u4e8e\u53d1\u73b0\u968f\u673a\u53d8\u91cf\u95f4\u7684\u79cd\u79cd\u76f8\u5173\u7279\u6027\u3002\u76f8\u5173\u5206\u6790\u5728\u5de5\u519c\u4e1a\u3001\u6c34\u6587\u3001\u6c14\u8c61\u3001\u793e\u4f1a\u7ecf\u6d4e\u548c\u751f\u7269\u5b66\u7b49\u65b9\u9762\u90fd\u6709\u5e94\u7528\u3002<\/p>\n

\u76f8\u5173\u5206\u6790\u4e0e\u56de\u5f52\u5206\u6790\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u6709\u5bc6\u5207\u5173\u7cfb\u3002\u7136\u800c\u5728\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u6240\u5173\u5fc3\u7684\u662f\u4e00\u4e2a\u968f\u673a\u53d8\u91cfY\u5bf9\u53e6\u4e00\u4e2a\uff08\u6216\u4e00\u7ec4\uff09\u968f\u673a\u53d8\u91cfX\u7684\u4f9d\u8d56\u5173\u7cfb\u7684\u51fd\u6570\u5f62\u5f0f\u3002\u800c\u5728\u76f8\u5173\u5206\u6790\u4e2d \uff0c\u6240\u8ba8\u8bba\u7684\u53d8\u91cf\u7684\u5730\u4f4d\u4e00\u6837\uff0c\u5206\u6790\u4fa7\u91cd\u4e8e\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u79cd\u79cd\u76f8\u5173\u7279\u5f81\u3002\u4f8b\u5982\uff0c\u4ee5X\u3001Y\u5206\u522b\u8bb0\u5c0f\u5b66\u751f\u7684\u6570\u5b66\u4e0e\u8bed\u6587\u6210\u7ee9\uff0c\u611f\u5174\u8da3\u7684\u662f\u4e8c\u8005\u7684\u5173\u7cfb\u5982\u4f55\uff0c\u800c\u4e0d\u5728\u4e8e\u7531X\u53bb\u9884\u6d4bY\u3002 \u786e\u5b9a\u76f8\u5173\u5173\u7cfb\u7684\u5b58\u5728\uff0c\u76f8\u5173\u5173\u7cfb\u5448\u73b0\u7684\u5f62\u6001\u548c\u65b9\u5411\uff0c\u76f8\u5173\u5173\u7cfb\u7684\u5bc6\u5207\u7a0b\u5ea6\u3002\u5176\u4e3b\u8981\u65b9\u6cd5\u662f\u7ed8\u5236\u76f8\u5173\u56fe\u8868\u548c\u8ba1\u7b97\u76f8\u5173\u7cfb\u6570\u3002<\/p>\n

1\uff09\u76f8\u5173\u8868 \u7f16\u5236\u76f8\u5173\u8868\u524d\u9996\u5148\u8981\u901a\u8fc7\u5b9e\u9645\u8c03\u67e5\u53d6\u5f97\u4e00\u7cfb\u5217\u6210\u5bf9\u7684\u6807\u5fd7\u503c\u8d44\u6599\u4f5c\u4e3a\u76f8\u5173\u5206\u6790\u7684\u539f\u59cb\u6570\u636e\u3002 \u76f8\u5173\u8868\u7684\u5206\u7c7b\uff1a\u7b80\u5355\u76f8\u5173\u8868\u548c\u5206\u7ec4\u76f8\u5173\u8868\u3002\u5355\u53d8\u91cf\u5206\u7ec4\u76f8\u5173\u8868\uff1a\u81ea\u53d8\u91cf\u5206\u7ec4\u5e76\u8ba1\u7b97\u6b21\u6570\uff0c\u800c\u5bf9\u5e94\u7684\u56e0\u53d8\u91cf\u4e0d\u5206\u7ec4\uff0c\u53ea\u8ba1\u7b97\u5176\u5e73\u5747\u503c\uff1b\u8be5\u8868\u7279\u70b9\uff1a\u4f7f\u5197\u957f\u7684\u8d44\u6599\u7b80\u5316\uff0c\u80fd\u591f\u66f4\u6e05\u6670\u5730\u53cd\u6620\u51fa\u4e24\u53d8\u91cf\u4e4b\u95f4\u76f8\u5173\u5173\u7cfb\u3002\u53cc\u53d8\u91cf\u5206\u7ec4\u76f8\u5173\u8868\uff1a\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u90fd\u8fdb\u884c\u5206\u7ec4\u800c\u5236\u6210\u7684\u76f8\u5173\u8868\uff0c\u8fd9\u79cd\u8868\u5f62\u4f3c\u68cb\u76d8\uff0c\u6545\u53c8\u79f0\u68cb\u76d8\u5f0f\u76f8\u5173\u8868\u3002<\/p>\n

2\uff09\u76f8\u5173\u56fe\u5229\u7528\u76f4\u89d2\u5750\u6807\u7cfb\u7b2c\u4e00\u8c61\u9650\uff0c\u628a\u81ea\u53d8\u91cf\u7f6e\u4e8e\u6a2a\u8f74\u4e0a\uff0c\u56e0\u53d8\u91cf\u7f6e\u4e8e\u7eb5\u8f74\u4e0a\uff0c\u800c\u5c06\u4e24\u53d8\u91cf\u76f8\u5bf9\u5e94\u7684\u53d8\u91cf\u503c\u7528\u5750\u6807\u70b9\u5f62\u5f0f\u63cf\u7ed8\u51fa\u6765\uff0c\u7528\u4ee5\u8868\u660e\u76f8\u5173\u70b9\u5206\u5e03\u72b6\u51b5\u7684\u56fe\u5f62\u3002\u76f8\u5173\u56fe\u88ab\u5f62\u8c61\u5730\u79f0\u4e3a\u76f8\u5173\u6563\u70b9\u56fe\u3002\u56e0\u7d20\u6807\u5fd7\u5206\u4e86\u7ec4\uff0c\u7ed3\u679c\u6807\u5fd7\u8868\u73b0\u4e3a\u7ec4\u5e73\u5747\u6570\uff0c\u6240\u7ed8\u5236\u7684\u76f8\u5173\u56fe\u5c31\u662f\u4e00\u6761\u6298\u7ebf\uff0c\u8fd9\u79cd\u6298\u7ebf\u53c8\u53eb\u76f8\u5173\u66f2\u7ebf\u3002<\/p>\n

3\uff09\u76f8\u5173\u7cfb\u6570\uff1a<\/p>\n

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\u786e\u5b9a\u76f8\u5173\u5173\u7cfb\u7684\u6570\u5b66\u8868\u8fbe\u5f0f\u3002<\/p>\n

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\u53e6\u5916\uff0c\u7814\u7a76\u73b0\u8c61\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u67d0\u79cd\u4f9d\u5b58\u5173\u7cfb\uff0c\u5bf9\u5177\u4f53\u6709\u4f9d\u5b58\u5173\u7cfb\u7684\u73b0\u8c61\u63a2\u8ba8\u76f8\u5173\u65b9\u5411\u53ca\u76f8\u5173\u7a0b\u5ea6\u3002<\/p>\n

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\u590d\u76f8\u5173 \uff1a\u4e09\u4e2a\u6216\u4e09\u4e2a\u4ee5\u4e0a\u56e0\u7d20\u7684\u76f8\u5173\u5173\u7cfb\u53eb\u590d\u76f8\u5173\uff0c\u5373\u7814\u7a76\u65f6\u6d89\u53ca\u4e24\u4e2a\u6216\u4e24\u4e2a\u4ee5\u4e0a\u7684\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u76f8\u5173\uff1b<\/p>\n

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\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u65b9\u5dee\u5206\u6790<\/strong><\/h3>\n

\"\u6570\u636e\u5206\u6790\u65b9\u6cd5<\/p>\n

\u65b9\u5dee\u5206\u6790(Analysis of Variance\uff0c\u7b80\u79f0ANOVA)\uff0c\u53c8\u79f0\u201c\u53d8\u5f02\u6570\u5206\u6790\u201d\uff0c\u662fR.A.Fisher\u53d1\u660e\u7684\uff0c\u7528\u4e8e\u4e24\u4e2a\u53ca\u4e24\u4e2a\u4ee5\u4e0a\u6837\u672c\u5747\u6570\u5dee\u522b\u7684\u663e\u8457\u6027\u68c0\u9a8c\u3002 \u7531\u4e8e\u5404\u79cd\u56e0\u7d20\u7684\u5f71\u54cd\uff0c\u7814\u7a76\u6240\u5f97\u7684\u6570\u636e\u5448\u73b0\u6ce2\u52a8\u72b6\u3002\u9020\u6210\u6ce2\u52a8\u7684\u539f\u56e0\u53ef\u5206\u6210\u4e24\u7c7b\uff0c\u4e00\u662f\u4e0d\u53ef\u63a7\u7684\u968f\u673a\u56e0\u7d20\uff0c\u53e6\u4e00\u662f\u7814\u7a76\u4e2d\u65bd\u52a0\u7684\u5bf9\u7ed3\u679c\u5f62\u6210\u5f71\u54cd\u7684\u53ef\u63a7\u56e0\u7d20\u3002<\/p>\n

\u65b9\u5dee\u5206\u6790\u7684\u57fa\u672c\u539f\u7406\u662f\u8ba4\u4e3a\u4e0d\u540c\u5904\u7406\u7ec4\u7684\u5747\u6570\u95f4\u7684\u5dee\u522b\u57fa\u672c\u6765\u6e90\u6709\u4e24\u4e2a\uff1a<\/p>\n

1\uff09\u5b9e\u9a8c\u6761\u4ef6\uff0c\u5373\u4e0d\u540c\u7684\u5904\u7406\u9020\u6210\u7684\u5dee\u5f02\uff0c\u79f0\u4e3a\u7ec4\u95f4\u5dee\u5f02\u3002\u7528\u53d8\u91cf\u5728\u5404\u7ec4\u7684\u5747\u503c\u4e0e\u603b\u5747\u503c\u4e4b\u504f\u5dee\u5e73\u65b9\u548c\u7684\u603b\u548c\u8868\u793a\uff0c\u8bb0\u4f5cSSb\uff0c\u7ec4\u95f4\u81ea\u7531\u5ea6dfb\u3002<\/p>\n

2\uff09 \u968f\u673a\u8bef\u5dee\uff0c\u5982\u6d4b\u91cf\u8bef\u5dee\u9020\u6210\u7684\u5dee\u5f02\u6216\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\uff0c\u79f0\u4e3a\u7ec4\u5185\u5dee\u5f02\uff0c\u7528\u53d8\u91cf\u5728\u5404\u7ec4\u7684\u5747\u503c\u4e0e\u8be5\u7ec4\u5185\u53d8\u91cf\u503c\u4e4b\u504f\u5dee\u5e73\u65b9\u548c\u7684\u603b\u548c\u8868\u793a\uff0c \u8bb0\u4f5cSSw\uff0c\u7ec4\u5185\u81ea\u7531\u5ea6dfw\u3002<\/p>\n

\u603b\u504f\u5dee\u5e73\u65b9\u548c SSt = SSb + SSw\u3002 \u7ec4\u5185SSw\u3001\u7ec4\u95f4SSb\u9664\u4ee5\u5404\u81ea\u7684\u81ea\u7531\u5ea6(\u7ec4\u5185dfw =n-m\uff0c\u7ec4\u95f4dfb=m-1\uff0c\u5176\u4e2dn\u4e3a\u6837\u672c\u603b\u6570\uff0cm\u4e3a\u7ec4\u6570)\uff0c\u5f97\u5230\u5176\u5747\u65b9MSw\u548cMSb\uff0c\u4e00\u79cd\u60c5\u51b5\u662f\u5904\u7406\u6ca1\u6709\u4f5c\u7528\uff0c\u5373\u5404\u7ec4\u6837\u672c\u5747\u6765\u81ea\u540c\u4e00\u603b\u4f53\uff0cMSb\/MSw\u22481\u3002<\/p>\n

\u53e6\u4e00\u79cd\u60c5\u51b5\u662f\u5904\u7406\u786e\u5b9e\u6709\u4f5c\u7528\uff0c\u7ec4\u95f4\u5747\u65b9\u662f\u7531\u4e8e\u8bef\u5dee\u4e0e\u4e0d\u540c\u5904\u7406\u5171\u540c\u5bfc\u81f4\u7684\u7ed3\u679c\uff0c\u5373\u5404\u6837\u672c\u6765\u81ea\u4e0d\u540c\u603b\u4f53\u3002\u90a3\u4e48\uff0cMSb>>MSw(\u8fdc\u8fdc\u5927\u4e8e)\u3002 MSb\/MSw\u6bd4\u503c\u6784\u6210F\u5206\u5e03\u3002\u7528F\u503c\u4e0e\u5176\u4e34\u754c\u503c\u6bd4\u8f83\uff0c\u63a8\u65ad\u5404\u6837\u672c\u662f\u5426\u6765\u81ea\u76f8\u540c\u7684\u603b\u4f53\u3002<\/p>\n

\u65b9\u5dee\u5206\u6790\u7684\u57fa\u672c\u601d\u60f3\u662f\uff1a\u901a\u8fc7\u5206\u6790\u7814\u7a76\u4e0d\u540c\u6765\u6e90\u7684\u53d8\u5f02\u5bf9\u603b\u53d8\u5f02\u7684\u8d21\u732e\u5927\u5c0f\uff0c\u4ece\u800c\u786e\u5b9a\u53ef\u63a7\u56e0\u7d20\u5bf9\u7814\u7a76\u7ed3\u679c\u5f71\u54cd\u529b\u7684\u5927\u5c0f\u3002<\/p>\n

\u6839\u636e\u8d44\u6599\u8bbe\u8ba1\u7c7b\u578b\u7684\u4e0d\u540c\uff0c\u6709\u4ee5\u4e0b\u4e24\u79cd\u65b9\u5dee\u5206\u6790\u7684\u65b9\u6cd5\uff1a<\/p>\n

\u5bf9\u6210\u7ec4\u8bbe\u8ba1\u7684\u591a\u4e2a\u6837\u672c\u5747\u503c\u6bd4\u8f83\uff0c\u5e94\u91c7\u7528\u5b8c\u5168\u968f\u673a\u8bbe\u8ba1\u7684\u65b9\u5dee\u5206\u6790\uff0c\u5373\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u3002<\/p>\n

\u5bf9\u968f\u673a\u533a\u7ec4\u8bbe\u8ba1\u7684\u591a\u4e2a\u6837\u672c\u5747\u503c\u6bd4\u8f83\uff0c\u5e94\u91c7\u7528\u914d\u4f0d\u7ec4\u8bbe\u8ba1\u7684\u65b9\u5dee\u5206\u6790\uff0c\u5373\u4e24\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u3002<\/p>\n

\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1a\u56de\u5f52\u5206\u6790<\/strong><\/h3>\n

\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u56de\u5f52\u5206\u6790\uff08regression analysis)\u6307\u7684\u662f\u786e\u5b9a\u4e24\u79cd\u6216\u4e24\u79cd\u4ee5\u4e0a\u53d8\u91cf\u95f4\u76f8\u4e92\u4f9d\u8d56\u7684\u5b9a\u91cf\u5173\u7cfb\u7684\u4e00\u79cd\u7edf\u8ba1\u5206\u6790\u65b9\u6cd5\u3002\u56de\u5f52\u5206\u6790\u6309\u7167\u6d89\u53ca\u7684\u53d8\u91cf\u7684\u591a\u5c11\uff0c\u5206\u4e3a\u4e00\u5143\u56de\u5f52\u548c\u591a\u5143\u56de\u5f52\u5206\u6790\uff1b\u6309\u7167\u56e0\u53d8\u91cf\u7684\u591a\u5c11\uff0c\u53ef\u5206\u4e3a\u7b80\u5355\u56de\u5f52\u5206\u6790\u548c\u591a\u91cd\u56de\u5f52\u5206\u6790\uff1b\u6309\u7167\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u7c7b\u578b\uff0c\u53ef\u5206\u4e3a\u7ebf\u6027\u56de\u5f52\u5206\u6790\u548c\u975e\u7ebf\u6027\u56de\u5f52\u5206\u6790\u3002<\/p>\n

\u6709\u5404\u79cd\u5404\u6837\u7684\u56de\u5f52\u6280\u672f\u7528\u4e8e\u9884\u6d4b\u3002\u8fd9\u4e9b\u6280\u672f\u4e3b\u8981\u6709\u4e09\u4e2a\u5ea6\u91cf\uff08\u81ea\u53d8\u91cf\u7684\u4e2a\u6570\uff0c\u56e0\u53d8\u91cf\u7684\u7c7b\u578b\u4ee5\u53ca\u56de\u5f52\u7ebf\u7684\u5f62\u72b6\uff09\uff1a<\/p>\n

1. Linear Regression\u7ebf\u6027\u56de\u5f52<\/p>\n

\u8fd9\u662f\u6700\u4e3a\u4eba\u719f\u77e5\u7684\u5efa\u6a21\u6280\u672f\u4e4b\u4e00\u3002\u7ebf\u6027\u56de\u5f52\u901a\u5e38\u662f\u4eba\u4eec\u5728\u5b66\u4e60\u9884\u6d4b\u6a21\u578b\u65f6\u9996\u9009\u7684\u6280\u672f\u4e4b\u4e00\u3002<\/p>\n

\u5728\u8fd9\u79cd\u6280\u672f\u4e2d\uff0c\u56e0\u53d8\u91cf\u662f\u8fde\u7eed\u7684\uff0c\u81ea\u53d8\u91cf\u53ef\u4ee5\u662f\u8fde\u7eed\u7684\u4e5f\u53ef\u4ee5\u662f\u79bb\u6563\u7684\uff0c\u56de\u5f52\u7ebf\u7684\u6027\u8d28\u662f\u7ebf\u6027\u7684\u3002<\/p>\n

\u7ebf\u6027\u56de\u5f52\u4f7f\u7528\u6700\u4f73\u7684\u62df\u5408\u76f4\u7ebf\uff08\u4e5f\u5c31\u662f\u56de\u5f52\u7ebf\uff09\u5728\u56e0\u53d8\u91cf\uff08Y\uff09\u548c\u4e00\u4e2a\u6216\u591a\u4e2a\u81ea\u53d8\u91cf\uff08X\uff09\u4e4b\u95f4\u5efa\u7acb\u4e00\u79cd\u5173\u7cfb\u3002 \u591a\u5143\u7ebf\u6027\u56de\u5f52\u53ef\u8868\u793a\u4e3aY=a+b1*X +b2*X2+ e\uff0c\u5176\u4e2da\u8868\u793a\u622a\u8ddd\uff0cb\u8868\u793a\u76f4\u7ebf\u7684\u659c\u7387\uff0ce\u662f\u8bef\u5dee\u9879\u3002\u591a\u5143\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u6839\u636e\u7ed9\u5b9a\u7684\u9884\u6d4b\u53d8\u91cf\uff08s\uff09\u6765\u9884\u6d4b\u76ee\u6807\u53d8\u91cf\u7684\u503c\u3002<\/p>\n

2.Logistic Regression\u903b\u8f91\u56de\u5f52<\/p>\n

\u903b\u8f91\u56de\u5f52\u662f\u7528\u6765\u8ba1\u7b97\u201c\u4e8b\u4ef6=Success\u201d\u548c\u201c\u4e8b\u4ef6=Failure\u201d\u7684\u6982\u7387\u3002\u5f53\u56e0\u53d8\u91cf\u7684\u7c7b\u578b\u5c5e\u4e8e\u4e8c\u5143\uff081 \/ 0\uff0c\u771f\/\u5047\uff0c\u662f\/\u5426\uff09\u53d8\u91cf\u65f6\uff0c\u5e94\u8be5\u4f7f\u7528\u903b\u8f91\u56de\u5f52\u3002<\/p>\n

\u8fd9\u91cc\uff0cY\u7684\u503c\u4e3a0\u62161\uff0c\u5b83\u53ef\u4ee5\u7528\u4e0b\u65b9\u7a0b\u8868\u793a\u3002<\/p>\n

odds= p\/ (1-p) = probability of event occurrence \/ probability of not event occurrence ln(odds) = ln(p\/(1-p)) logit(p) = ln(p\/(1-p)) =b0+b1X1+b2X2+b3X3….+bkXk<\/p>\n

\u4e0a\u8ff0\u5f0f\u5b50\u4e2d\uff0cp\u8868\u8ff0\u5177\u6709\u67d0\u4e2a\u7279\u5f81\u7684\u6982\u7387\u3002\u4f60\u5e94\u8be5\u4f1a\u95ee\u8fd9\u6837\u4e00\u4e2a\u95ee\u9898\uff1a\u201c\u4e3a\u4ec0\u4e48\u8981\u5728\u516c\u5f0f\u4e2d\u4f7f\u7528\u5bf9\u6570log\u5462\uff1f\u201d\u3002 \u56e0\u4e3a\u5728\u8fd9\u91cc\u4f7f\u7528\u7684\u662f\u7684\u4e8c\u9879\u5206\u5e03\uff08\u56e0\u53d8\u91cf\uff09\uff0c\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u5bf9\u4e8e\u8fd9\u4e2a\u5206\u5e03\u6700\u4f73\u7684\u8fde\u7ed3\u51fd\u6570\u3002\u5b83\u5c31\u662fLogit\u51fd\u6570\u3002<\/p>\n

\u5728\u4e0a\u8ff0\u65b9\u7a0b\u4e2d\uff0c\u901a\u8fc7\u89c2\u6d4b\u6837\u672c\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u503c\u6765\u9009\u62e9\u53c2\u6570\uff0c\u800c\u4e0d\u662f\u6700\u5c0f\u5316\u5e73\u65b9\u548c\u8bef\u5dee\uff08\u5982\u5728\u666e\u901a\u56de\u5f52\u4f7f\u7528\u7684\uff09\u3002<\/p>\n

\"\u6570\u636e\u5206\u6790\u65b9\u6cd5<\/p>\n

3. Polynomial Regression\u591a\u9879\u5f0f\u56de\u5f52<\/p>\n

\u5bf9\u4e8e\u4e00\u4e2a\u56de\u5f52\u65b9\u7a0b\uff0c\u5982\u679c\u81ea\u53d8\u91cf\u7684\u6307\u6570\u5927\u4e8e1\uff0c\u90a3\u4e48\u5b83\u5c31\u662f\u591a\u9879\u5f0f\u56de\u5f52\u65b9\u7a0b\u3002<\/p>\n

\u5982\u4e0b\u65b9\u7a0b\u6240\u793a\uff1a y=a+b*x^2<\/p>\n

\u5728\u8fd9\u79cd\u56de\u5f52\u6280\u672f\u4e2d\uff0c\u6700\u4f73\u62df\u5408\u7ebf\u4e0d\u662f\u76f4\u7ebf\u3002\u800c\u662f\u4e00\u4e2a\u7528\u4e8e\u62df\u5408\u6570\u636e\u70b9\u7684\u66f2\u7ebf\u3002<\/p>\n

4. Stepwise Regression\u9010\u6b65\u56de\u5f52<\/p>\n

\u5728\u5904\u7406\u591a\u4e2a\u81ea\u53d8\u91cf\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u8fd9\u79cd\u5f62\u5f0f\u7684\u56de\u5f52\u3002\u5728\u8fd9\u79cd\u6280\u672f\u4e2d\uff0c\u81ea\u53d8\u91cf\u7684\u9009\u62e9\u662f\u5728\u4e00\u4e2a\u81ea\u52a8\u7684\u8fc7\u7a0b\u4e2d\u5b8c\u6210\u7684\uff0c\u5176\u4e2d\u5305\u62ec\u975e\u4eba\u4e3a\u64cd\u4f5c\u3002<\/p>\n

\u8fd9\u4e00\u58ee\u4e3e\u662f\u901a\u8fc7\u89c2\u5bdf\u7edf\u8ba1\u7684\u503c\uff0c\u5982R-square\uff0ct-stats\u548cAIC\u6307\u6807\uff0c\u6765\u8bc6\u522b\u91cd\u8981\u7684\u53d8\u91cf\u3002\u9010\u6b65\u56de\u5f52\u901a\u8fc7\u540c\u65f6\u6dfb\u52a0\/\u5220\u9664\u57fa\u4e8e\u6307\u5b9a\u6807\u51c6\u7684\u534f\u53d8\u91cf\u6765\u62df\u5408\u6a21\u578b\u3002<\/p>\n

\u4e0b\u9762\u5217\u51fa\u4e86\u4e00\u4e9b\u6700\u5e38\u7528\u7684\u9010\u6b65\u56de\u5f52\u65b9\u6cd5\uff1a \u6807\u51c6\u9010\u6b65\u56de\u5f52\u6cd5\u505a\u4e24\u4ef6\u4e8b\u60c5\u3002\u5373\u589e\u52a0\u548c\u5220\u9664\u6bcf\u4e2a\u6b65\u9aa4\u6240\u9700\u7684\u9884\u6d4b\u3002 \u5411\u524d\u9009\u62e9\u6cd5\u4ece\u6a21\u578b\u4e2d\u6700\u663e\u8457\u7684\u9884\u6d4b\u5f00\u59cb\uff0c\u7136\u540e\u4e3a\u6bcf\u4e00\u6b65\u6dfb\u52a0\u53d8\u91cf\u3002<\/p>\n

\u5411\u540e\u5254\u9664\u6cd5\u4e0e\u6a21\u578b\u7684\u6240\u6709\u9884\u6d4b\u540c\u65f6\u5f00\u59cb\uff0c\u7136\u540e\u5728\u6bcf\u4e00\u6b65\u6d88\u9664\u6700\u5c0f\u663e\u8457\u6027\u7684\u53d8\u91cf\u3002 \u8fd9\u79cd\u5efa\u6a21\u6280\u672f\u7684\u76ee\u7684\u662f\u4f7f\u7528\u6700\u5c11\u7684\u9884\u6d4b\u53d8\u91cf\u6570\u6765\u6700\u5927\u5316\u9884\u6d4b\u80fd\u529b\u3002\u8fd9\u4e5f\u662f\u5904\u7406\u9ad8\u7ef4\u6570\u636e\u96c6\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002<\/p>\n

5. Ridge Regression\u5cad\u56de\u5f52<\/p>\n

\u5f53\u6570\u636e\u4e4b\u95f4\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027\uff08\u81ea\u53d8\u91cf\u9ad8\u5ea6\u76f8\u5173\uff09\u65f6\uff0c\u5c31\u9700\u8981\u4f7f\u7528\u5cad\u56de\u5f52\u5206\u6790\u3002\u5728\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027\u65f6\uff0c\u5c3d\u7ba1\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08OLS\uff09\u6d4b\u5f97\u7684\u4f30\u8ba1\u503c\u4e0d\u5b58\u5728\u504f\u5dee\uff0c\u5b83\u4eec\u7684\u65b9\u5dee\u4e5f\u4f1a\u5f88\u5927\uff0c\u4ece\u800c\u4f7f\u5f97\u89c2\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u76f8\u5dee\u751a\u8fdc\u3002<\/p>\n

\u5cad\u56de\u5f52\u901a\u8fc7\u7ed9\u56de\u5f52\u4f30\u8ba1\u503c\u6dfb\u52a0\u4e00\u4e2a\u504f\u5dee\u503c\uff0c\u6765\u964d\u4f4e\u6807\u51c6\u8bef\u5dee\u3002<\/p>\n

\u5728\u7ebf\u6027\u7b49\u5f0f\u4e2d\uff0c\u9884\u6d4b\u8bef\u5dee\u53ef\u4ee5\u5212\u5206\u4e3a 2 \u4e2a\u5206\u91cf\uff0c\u4e00\u4e2a\u662f\u504f\u5dee\u9020\u6210\u7684\uff0c\u4e00\u4e2a\u662f\u65b9\u5dee\u9020\u6210\u7684\u3002\u9884\u6d4b\u8bef\u5dee\u53ef\u80fd\u4f1a\u7531\u8fd9\u4e24\u8005\u6216\u4e24\u8005\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u9020\u6210\u3002\u5728\u8fd9\u91cc\uff0c\u5c06\u8ba8\u8bba\u7531\u65b9\u5dee\u6240\u9020\u6210\u7684\u8bef\u5dee\u3002<\/p>\n

6. Lasso Regression\u5957\u7d22\u56de\u5f52<\/p>\n

\u5b83\u7c7b\u4f3c\u4e8e\u5cad\u56de\u5f52\uff0cLasso \uff08Least Absolute Shrinkage and Selection Operator\uff09\u4e5f\u4f1a\u5c31\u56de\u5f52\u7cfb\u6570\u5411\u91cf\u7ed9\u51fa\u60e9\u7f5a\u503c\u9879\u3002\u6b64\u5916\uff0c\u5b83\u80fd\u591f\u51cf\u5c11\u53d8\u5316\u7a0b\u5ea6\u5e76\u63d0\u9ad8\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u7cbe\u5ea6\u3002<\/p>\n

\u770b\u770b\u4e0b\u9762\u7684\u516c\u5f0f\uff1a L1=agrmin||y-x\u03b2|| +\u03bb||\u03b2||<\/p>\n

Lasso \u56de\u5f52\u4e0eRidge\u56de\u5f52\u6709\u4e00\u70b9\u4e0d\u540c\uff0c\u5b83\u4f7f\u7528\u7684\u60e9\u7f5a\u51fd\u6570\u662fL1\u8303\u6570\uff0c\u800c\u4e0d\u662fL2\u8303\u6570\u3002\u8fd9\u5bfc\u81f4\u60e9\u7f5a\uff08\u6216\u7b49\u4e8e\u7ea6\u675f\u4f30\u8ba1\u7684\u7edd\u5bf9\u503c\u4e4b\u548c\uff09\u503c\u4f7f\u4e00\u4e9b\u53c2\u6570\u4f30\u8ba1\u7ed3\u679c\u7b49\u4e8e\u96f6\u3002\u4f7f\u7528\u60e9\u7f5a\u503c\u8d8a\u5927\uff0c\u8fdb\u4e00\u6b65\u4f30\u8ba1\u4f1a\u4f7f\u5f97\u7f29\u5c0f\u503c\u8d8a\u8d8b\u8fd1\u4e8e\u96f6\u3002\u8fd9\u5c06\u5bfc\u81f4\u8981\u4ece\u7ed9\u5b9a\u7684n\u4e2a\u53d8\u91cf\u4e2d\u9009\u62e9\u53d8\u91cf\u3002<\/p>\n

\u5982\u679c\u9884\u6d4b\u7684\u4e00\u7ec4\u53d8\u91cf\u662f\u9ad8\u5ea6\u76f8\u5173\u7684\uff0cLasso \u4f1a\u9009\u51fa\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u5e76\u4e14\u5c06\u5176\u5b83\u7684\u6536\u7f29\u4e3a\u96f6\u3002<\/p>\n

7.ElasticNet\u56de\u5f52<\/p>\n

ElasticNet\u662fLasso\u548cRidge\u56de\u5f52\u6280\u672f\u7684\u6df7\u5408\u4f53\u3002\u5b83\u4f7f\u7528L1\u6765\u8bad\u7ec3\u5e76\u4e14L2\u4f18\u5148\u4f5c\u4e3a\u6b63\u5219\u5316\u77e9\u9635\u3002\u5f53\u6709\u591a\u4e2a\u76f8\u5173\u7684\u7279\u5f81\u65f6\uff0cElasticNet\u662f\u5f88\u6709\u7528\u7684\u3002Lasso \u4f1a\u968f\u673a\u6311\u9009\u4ed6\u4eec\u5176\u4e2d\u7684\u4e00\u4e2a\uff0c\u800cElasticNet\u5219\u4f1a\u9009\u62e9\u4e24\u4e2a\u3002<\/p>\n

Lasso\u548cRidge\u4e4b\u95f4\u7684\u5b9e\u9645\u7684\u4f18\u70b9\u662f\uff0c\u5b83\u5141\u8bb8ElasticNet\u7ee7\u627f\u5faa\u73af\u72b6\u6001\u4e0bRidge\u7684\u4e00\u4e9b\u7a33\u5b9a\u6027\u3002 \u6570\u636e\u63a2\u7d22\u662f\u6784\u5efa\u9884\u6d4b\u6a21\u578b\u7684\u5fc5\u7136\u7ec4\u6210\u90e8\u5206\u3002\u5728\u9009\u62e9\u5408\u9002\u7684\u6a21\u578b\u65f6\uff0c\u6bd4\u5982\u8bc6\u522b\u53d8\u91cf\u7684\u5173\u7cfb\u548c\u5f71\u54cd\u65f6\uff0c\u5b83\u5e94\u8be5\u662f\u9996\u9009\u7684\u4e00\u6b65\u3002\u6bd4\u8f83\u9002\u5408\u4e8e\u4e0d\u540c\u6a21\u578b\u7684\u4f18\u70b9\uff0c\u53ef\u4ee5\u5206\u6790\u4e0d\u540c\u7684\u6307\u6807\u53c2\u6570\uff0c\u5982\u7edf\u8ba1\u610f\u4e49\u7684\u53c2\u6570\uff0cR-square\uff0cAdjusted R-square\uff0cAIC\uff0cBIC\u4ee5\u53ca\u8bef\u5dee\u9879\uff0c\u53e6\u4e00\u4e2a\u662fMallows\u2019 Cp\u51c6\u5219\u3002<\/p>\n

\u8fd9\u4e2a\u4e3b\u8981\u662f\u901a\u8fc7\u5c06\u6a21\u578b\u4e0e\u6240\u6709\u53ef\u80fd\u7684\u5b50\u6a21\u578b\u8fdb\u884c\u5bf9\u6bd4\uff08\u6216\u8c28\u614e\u9009\u62e9\u4ed6\u4eec\uff09\uff0c\u68c0\u67e5\u5728\u4f60\u7684\u6a21\u578b\u4e2d\u53ef\u80fd\u51fa\u73b0\u7684\u504f\u5dee\u3002<\/p>\n

\u5bf9\u7edf\u8ba1Statistics\u8bfe\u7a0b\u6709\u7591\u95ee\uff0c\u60f3\u5bfb\u6c42\u8fdb\u4e00\u6b65\u5b66\u672f\u5e2e\u52a9\uff1f\u6b22\u8fce\u8054\u7cfbStudyGate\uff0c\u5404\u7c7b\u7406\u5de5\u5546\u79d1\u5199\u4f5c\u7b54\u7591\u89e3\u60d1\uff0c\u4e3a\u4f60\u7684\u7559\u5b66\u4e4b\u8def\u503e\u60c5\u52a9\u529b\uff01\u6211\u4eec\u7684\u670d\u52a1\u5305\u542b\u5fae\u79ef\u5206\u4f5c\u4e1a<\/a>\u3001\u6570\u5b66\u4f5c\u4e1a<\/a>\u3001\u6570\u5b66\u4f5c\u4e1a<\/a>\u3001\u7269\u7406\u4f5c\u4e1a<\/a>\u3001\u5316\u5b66\u4f5c\u4e1a<\/a>\u3001\u751f\u7269\u4f5c\u4e1a<\/a>\u3001Lab Report<\/a>\u3001Project\u4f5c\u4e1a\u8f85\u5bfc<\/a>\u3002<\/p>\n

\"studygate\u4f5c\u4e1a\u4ee3\u5199\"<\/p>\n

Step 1\uff1a\u63d0\u4ea4\u4f5c\u4e1a\u8981\u6c42<\/p>\n

\u4e09\u5206\u949f\u5373\u53ef\u5b8c\u6210\u4e0b\u5355\uff0c\u4e0b\u5355\u65f6\u53ef\u4ee5\u9009\u62e9\u4f5c\u4e1a\u9700\u8981\u7684\u65f6\u95f4\u548c\u5177\u4f53\u8981\u6c42\u3002<\/p>\n

Step 2\uff1a\u9009\u62e9\u4e13\u4e1a\u5bfc\u5e08<\/p>\n

\u4f5c\u4e1a\u63d0\u4ea4\u6210\u529f\u4e4b\u540e\uff0c\u5bfc\u5e08\u5ba1\u6838\u8981\u6c42\uff0c\u786e\u8ba4\u4e4b\u540e\u4f1a\u8054\u7cfb\u62a5\u4ef7\uff0c\u53ef\u81ea\u7531\u9009\u62e9\u4e13\u4e1a\u5b66\u79d1\u76f8\u5173\u5bfc\u5e08\uff0c\u5e76\u4e14\u786e\u8ba4\u4f5c\u4e1a\u6700\u7ec8\u4ef7\u683c\u3002<\/p>\n

Step 3\uff1a\u5b8c\u6210\u8ba2\u5355, \u51c6\u65f6\u4ea4\u4ed8<\/p>\n

\u5bfc\u5e08\u5f00\u59cb\u5904\u7406\u8ba2\u5355\u3002\u5728\u6b64\u671f\u95f4\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u90fd\u53ef\u4ee5\u767b\u5f55\u8d26\u53f7\u548c\u5bfc\u5e08\u968f\u65f6\u6c9f\u901a\u3002\u4f5c\u4e1a\u5b8c\u6210\u540e\uff0c\u7cfb\u7edf\u81ea\u52a8\u53d1\u9001\u81f3\u4f60\u7684\u90ae\u7bb1\uff0c\u6240\u6709\u4fe1\u606f\u5b89\u5168\u4fdd\u5bc6\u3002\u4f60\u4e5f\u53ef\u4ee5\u767b\u5f55\u8d26\u53f7\u76f4\u63a5\u4e0b\u8f7d\u3002<\/p>\n

Step 4\uff1a\u6536\u5230\u7b54\u684814\u5929\u4e4b\u5185\u786e\u8ba4\uff0c100%\u6ee1\u610f\u4fdd\u8bc1<\/p>\n

\u6536\u5230\u4f5c\u4e1a\u4e4b\u540e14\u5929\u4e4b\u5185\uff0c\u5982\u679c\u5bf9\u4f5c\u4e1a\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u90fd\u53ef\u4ee5\u8054\u7cfb\u5bfc\u5e08\u8fdb\u884c\u4fee\u6539\u3002100%\u6ee1\u610f\u4fdd\u8bc1\uff0c\u53ea\u6709\u4f60\u9009\u62e9\u6ee1\u610f\u7b54\u6848\u4e4b\u540e\uff0c\u6211\u4eec\u624d\u4f1a\u6263\u6b3e\uff0c\u5b89\u5168\u6709\u4fdd\u969c\u3002<\/p>\n

Step 5\uff1a\u5bf9\u5bfc\u5e08\u63d0\u51fa\u8bc4\u4ef7<\/p>\n

\u6211\u4eec\u62e5\u6709\u4e25\u683c\u7684\u5bfc\u5e08\u8003\u6838\u8bc4\u4ef7\u673a\u5236\uff0c\u670d\u52a1\u597d\u4e0d\u597d\uff0c\u5168\u7531\u4f60\u8bf4\u4e86\u7b97\uff01\u4f60\u7684\u8ba4\u540c\u662f\u6211\u4eec\u524d\u8fdb\u7684\u52a8\u529b\u3002<\/p>\n

StudyGate<\/strong>\u4e13\u4e1a\u7406\u5de5\u79d1\u4f5c\u4e1a\u8f85\u5bfc<\/a>\uff0c\u6700\u9760\u8c31\u7684\u7edf\u8ba1\u4f5c\u4e1a\u8f85\u5bfc<\/a>\uff01<\/strong><\/p>\n

\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u6b22\u8fce\u968f\u65f6\u54a8\u8be2\u7f51\u9875\u5ba2\u670d\uff01<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

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\/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Statistics \u7edf\u8ba1\u5b66\u4e2d\u5e38\u7528\u7684\u6570\u636e\u5206\u6790\u65b9\u6cd5\u5927\u603b\u7ed3\uff0c\u8d85\u5f3a\u5e72\u8d27\uff01\" \/>\n<meta property=\"og:description\" content=\"\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u901a\u8fc7\u6570\u636e\u5206\u6790\uff0c\u5e76\u4e14\u63d0\u53d6\u5230\u6709\u7528\u7684\u4fe1\u606f\u662f\u6700\u91cd\u8981\u7684\u6280\u80fd\u4e4b\u4e00\u3002\u90a3\u4e48\u6709\u54ea\u4e9b\u5e38\u89c1\u7684\u7edf\u8ba1\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1f\u60f3\u4e86\u89e3\u6700\u5168\u9762\u7684\u7edf\u8ba1\u5b66\u6570\u636e\u5206\u6790\u65b9\u6cd5\uff1f\u8d70\u8fc7\u8def\u8fc7\uff0c\u8d85\u5f3a\u5e72\u8d27\u603b\u7ed3\u5e16\u4e0d\u8981\u9519\u8fc7\uff01\u9700\u8981\u7edf\u8ba1\u5b66\u4e13\u4e1a\u5e2e\u52a9\uff1f \u8bf7\u968f\u65f6\u8054\u7cfbStudyGate\uff01\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.studygate.com\/blog-cn\/statistics\/\" \/>\n<meta property=\"og:site_name\" content=\"Studygate CN\" \/>\n<meta property=\"article:published_time\" content=\"2021-01-17T00:17:41+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-19T00:20:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.studygate.com\/blog-cn\/wp-content\/uploads\/sites\/2\/2021\/01\/-1-e1610839840617.png\" \/>\n\t<meta property=\"og:image:width\" content=\"413\" \/>\n\t<meta property=\"og:image:height\" content=\"200\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"StudyGate\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"StudyGate\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO 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