{"id":3705,"date":"2013-08-08T23:08:29","date_gmt":"2013-08-08T15:08:29","guid":{"rendered":"http:\/\/lttt.blog.ustc.edu.cn\/?p=3705"},"modified":"2013-08-08T23:08:29","modified_gmt":"2013-08-08T15:08:29","slug":"%e5%ae%9e%e9%aa%8c%e6%95%b0%e6%8d%ae%e7%9a%84%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c%e5%b0%8f%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=3705","title":{"rendered":"\u5b9e\u9a8c\u6570\u636e\u7684\u5047\u8bbe\u68c0\u9a8c\u5c0f\u8bb0"},"content":{"rendered":"

\u5047\u8bbe\u68c0\u9a8c\u7684\u57fa\u672c\u77e5\u8bc6<\/h4>\n

\u5f80\u5f80\uff0c \u6211\u4eec\u6839\u636e\u5047\u8bbe\uff0c \u63d0\u51fa\u539f\u7406\u3002 \u800c\u8981\u9a8c\u8bc1\u8fd9\u4e00\u5047\u8bbe\u662f\u5426\u6210\u7acb\uff0c \u5c31\u9700\u8981\u505a\u5b9e\u9a8c\u3002 \u7136\u540e\u8fd0\u7528\u7edf\u8ba1\u5b66\u7684\u65b9\u6cd5\u6765\u8bf4\u660e\u5047\u8bbe\u6210\u7acb\u4e0e\u5426\u3002<\/p>\n

\u8fd9\u79cd\u5229\u7528\u7edf\u8ba1\u5b66\u539f\u7406\u6765\u9a8c\u8bc1\u5047\u8bbe\u7684\u65b9\u6cd5<\/em>\u5c31\u79f0\u4e3a\u5047\u8bbe\u68c0\u9a8c<\/strong>\u3002<\/p>\n

\u4e00\u822c\u800c\u8a00\uff0c \u5047\u8bbe\u68c0\u9a8c\u5206\u4e3a\u53c2\u6570\u68c0\u9a8c<\/strong>\u4e0e \u975e\u53c2\u6570\u68c0\u9a8c<\/strong>\uff0c \u5f53\u603b\u4f53\u7684\u5206\u5e03\u7c7b\u578b\u5df2\u77e5\u65f6\uff0c \u6211\u4eec\u53ea\u9700\u786e\u5b9a\u76f8\u5e94\u7684\u53c2\u6570\u3002 \u4e3e\u4e2a\u4f8b\u5b50\uff1a\u67d0\u7cd6\u5382\u7528\u81ea\u52a8\u5305\u88c5\u673a\u88c5\u7cd6\uff0c \u6bcf\u888b\u7cd6\u7684\u6807\u51c6<\/strong>\u91cd\u91cf\u4e3a1\u65a4\uff0c \u800c\u6839\u636e\u957f\u671f\u7ecf\u9a8c\u77e5\u9053\uff0c \u6bcf\u888b\u7684\u91cd\u91cf\u670d\u4ece\u6b63\u6001\u5206\u5e03($N(\\mu,0.015)$), \u73b0\u5728\u6211\u4eec\u60f3\u77e5\u9053\u67d0\u53f0\u673a\u5668\u662f\u5426\u5de5\u4f5c\u6b63\u5e38\uff0c \u90a3\u4e48\u5c31\u53ef\u4ee5\u968f\u673a\u62bd\u53d650\u888b\u8be5\u673a\u5668\u751f\u4ea7\u7684\u7cd6\uff0c\u6d4b\u91cf\u4ed6\u4eec\u7684\u91cd\u91cf\uff0c \u901a\u8fc7\u7edf\u8ba1\u5b66\u7684\u63a8\u5bfc\u5f97\u51fa\u7ed3\u8bba\u3002\u8fd9\u91cc\u7684\u5047\u8bbe\u5c31\u662f:<\/p>\n

<\/p>\n

H0:$\\mu=1$\u65a4<\/p>\n

\u4ece\u800c\u8981\u68c0\u9a8c\u7684\u5c31\u662f\u8fd9\u4e2a\u53c2\u6570$\\mu$\u3002<\/p>\n

\u7406\u89e3\u4e86\u4e0a\u8ff0\u53c2\u6570\u5047\u8bbe\u7684\u80cc\u666f\uff0c \u90a3\u4e48\u975e\u53c2\u6570\u5047\u8bbe\u5c31\u4e0d\u96be\u7406\u89e3\u4e86\uff1a\u5373\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u603b\u4f53\u7684\u5206\u5e03\uff0c \u8fd9\u65f6\u9700\u8981\u6839\u636e\u5b9e\u9a8c\u6570\u636e\u63d0\u4f9b\u7684\u4fe1\u606f\u5bf9\u603b\u4f53\u5206\u5e03\u7684\u79cd\u79cd\u5047\u8bbe\u8fdb\u884c\u68c0\u9a8c\uff0c\u5373\u8981\u68c0\u9a8c\u603b\u4f53\u662f\u5426\u670d\u4ece\u67d0\u79cd\u5047\u8bbe\u7684\u5206\u5e03<\/strong>\u3002 \u7531\u4e8e\u4e00\u822c\u7684\u4e66\u4e0a\u53ea\u63a8\u5bfc\u4e86\u6b63\u6001\u5206\u5e03\u4e0b\u7684\u5404\u79cd\u53c2\u6570\u68c0\u9a8c\uff0c \u56e0\u6b64\u6211\u4eec\u5728\u8fdb\u884c$F$-\u68c0\u9a8c\uff0c$T$-\u68c0\u9a8c\u65f6\uff0c \u5343\u4e07\u522b\u5fd8\u4e86\u7b2c\u4e00\u4ef6\u4e8b\u5c31\u662f\u8981\u505a\u975e\u53c2\u6570\u68c0\u9a8c\u4ee5\u786e\u5b9a\u5b9e\u9a8c\u6570\u636e\u662f\u5426\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002<\/strong><\/p>\n

\u8fd9\u91cc\uff0c \u4e00\u4e2a\u81ea\u7136\u7684\u95ee\u9898\u662f\uff0c\u662f\u4e0d\u662f\u4efb\u4f55\u4e00\u4e2a\u5206\u5e03\u90fd\u53ef\u4ee5\u548c\u67d0\u4e2a\u6b63\u6001\u5206\u5e03\u7b49\u4ef7\uff0c \u5373\u6839\u636e\u5df2\u77e5\u7684\u968f\u673a\u53d8\u91cf\uff08\u4ed6\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c \u4f46\u5206\u5e03\u5df2\u77e5\uff09\uff0c \u6211\u4eec\u80fd\u5426\u7ecf\u8fc7\u67d0\u79cd\u4e00\u4e00\u53d8\u6362\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u968f\u673a\u53d8\u91cf\uff0c \u4f7f\u5f97\u5b83\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\uff1f \u5982\u679c\u662f\u8fd9\u6837\uff0c \u6211\u4eec\u81ea\u7136\u53ea\u9700\u8981\u505a\u6b63\u6001\u5206\u5e03\u7684\u5404\u79cd\u53c2\u6570\u68c0\u9a8c\u4e86\u3002<\/p>\n

\u4f46\u662f\uff0c \u95ee\u9898\u7684\u56de\u7b54\u4f3c\u4e4e\u6ca1\u8fd9\u4e48\u7b80\u5355\u3002 \u4e00\u822c\u800c\u8a00\uff0c\u6b63\u6001\u5206\u5e03\u662f\u8bb8\u591a\u7edf\u8ba1\u65b9\u6cd5\u7684\u7406\u8bba\u57fa\u7840\uff1a\u5982t\u5206\u5e03\u3001F\u5206\u5e03\u3001x2\u5206\u5e03\u90fd\u662f\u5728\u6b63\u6001\u5206\u5e03\u7684\u57fa\u7840\u4e0a\u63a8\u5bfc\u51fa\u6765\u7684\uff0cu\u68c0\u9a8c\u4e5f\u662f\u4ee5\u6b63\u6001\u5206\u5e03\u4e3a\u57fa\u7840\u7684\u3002\u6b64\u5916\uff0ct\u5206\u5e03\u3001\u4e8c\u9879\u5206\u5e03\u3001Poisson\u5206\u5e03\u7684\u6781\u9650\u4e3a\u6b63\u6001\u5206\u5e03\uff0c\u5728\u4e00\u5b9a\u6761\u4ef6\u4e0b\uff0c\u53ef\u4ee5\u6309\u6b63\u6001\u5206\u5e03\u539f\u7406\u6765\u5904\u7406<\/strong>\u3002<\/p>\n

\u975e\u53c2\u6570\u5047\u8bbe\u68c0\u9a8c<\/h4>\n

\u4f5c\u4e3a\u4f8b\u5b50\uff0c \u6211\u4eec\u5c06\u4ee5\u6b63\u6001\u5206\u5e03<\/strong>\u4e3a\u4f8b\u3002<\/p>\n

Example . <\/strong>\u5047\u8bbe\u67d0\u6b21\u5b9e\u9a8c\u6d4b\u5f97A,B\u4e24\u7ec450\u4e2a\u6570\u636e\u5982\u4e0b, \u8bd5\u95ee\u4ed6\u4eec\u662f\u5426\u53ef\u4ee5\u8ba4\u4e3a\u4ed6\u4eec\u662f\u6ee1\u8db3\u6b63\u6001\u5206\u5e03\u7684?<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
A<\/th>\nB<\/th>\n<\/tr>\n<\/thead>\n
0.54<\/td>\n0.05<\/td>\n<\/tr>\n
2.20<\/td>\n0.13<\/td>\n<\/tr>\n
0.58<\/td>\n0.17<\/td>\n<\/tr>\n
0.55<\/td>\n0.20<\/td>\n<\/tr>\n
0.27<\/td>\n0.23<\/td>\n<\/tr>\n
0.37<\/td>\n0.28<\/td>\n<\/tr>\n
0.77<\/td>\n0.29<\/td>\n<\/tr>\n
0.24<\/td>\n0.29<\/td>\n<\/tr>\n
0.70<\/td>\n0.30<\/td>\n<\/tr>\n
0.92<\/td>\n0.30<\/td>\n<\/tr>\n
0.36<\/td>\n0.38<\/td>\n<\/tr>\n
1.10<\/td>\n0.40<\/td>\n<\/tr>\n
0.47<\/td>\n0.43<\/td>\n<\/tr>\n
0.54<\/td>\n0.43<\/td>\n<\/tr>\n
0.62<\/td>\n0.44<\/td>\n<\/tr>\n
0.56<\/td>\n0.45<\/td>\n<\/tr>\n
0.45<\/td>\n0.47<\/td>\n<\/tr>\n
0.60<\/td>\n0.50<\/td>\n<\/tr>\n
0.58<\/td>\n0.52<\/td>\n<\/tr>\n
0.51<\/td>\n0.53<\/td>\n<\/tr>\n
1.68<\/td>\n0.54<\/td>\n<\/tr>\n
0.79<\/td>\n0.54<\/td>\n<\/tr>\n
0.88<\/td>\n0.55<\/td>\n<\/tr>\n
0.67<\/td>\n0.55<\/td>\n<\/tr>\n
1.20<\/td>\n0.57<\/td>\n<\/tr>\n
0.70<\/td>\n0.67<\/td>\n<\/tr>\n
0.90<\/td>\n0.68<\/td>\n<\/tr>\n
0.66<\/td>\n0.73<\/td>\n<\/tr>\n
0.77<\/td>\n0.75<\/td>\n<\/tr>\n
1.03<\/td>\n0.75<\/td>\n<\/tr>\n
0.39<\/td>\n0.76<\/td>\n<\/tr>\n
0.64<\/td>\n0.87<\/td>\n<\/tr>\n
0.45<\/td>\n0.88<\/td>\n<\/tr>\n
0.51<\/td>\n0.90<\/td>\n<\/tr>\n
0.59<\/td>\n0.93<\/td>\n<\/tr>\n
0.42<\/td>\n0.98<\/td>\n<\/tr>\n
0.55<\/td>\n1.00<\/td>\n<\/tr>\n
0.52<\/td>\n1.07<\/td>\n<\/tr>\n
1.15<\/td>\n1.13<\/td>\n<\/tr>\n
1.28<\/td>\n1.16<\/td>\n<\/tr>\n
0.73<\/td>\n1.20<\/td>\n<\/tr>\n
1.05<\/td>\n1.20<\/td>\n<\/tr>\n
1.60<\/td>\n1.21<\/td>\n<\/tr>\n
0.48<\/td>\n1.28<\/td>\n<\/tr>\n
0.99<\/td>\n1.30<\/td>\n<\/tr>\n
0.87<\/td>\n1.31<\/td>\n<\/tr>\n
0.91<\/td>\n1.32<\/td>\n<\/tr>\n
3.10<\/td>\n1.32<\/td>\n<\/tr>\n
0.25<\/td>\n1.35<\/td>\n<\/tr>\n
0.96<\/td>\n1.36<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u9996\u5148\uff0c\u6211\u4eec\u53ef\u4ee5\u4f5c\u76f4\u65b9\u56fe\u89c2\u5bdf\u4e0b\u662f\u5426\u7b26\u5408\u6b63\u6001\u5206\u5e03\u7684\u56fe\u5f62\uff0c \u4e3b\u8981\u662f\u770b\u56fe\u5f62\u7684\u5bf9\u79f0\u6027\u4ee5\u53ca\u662f\u5426\u662f\u5355\u5cf0\u3002\u5982\u679c\u4e0d\u5bf9\u79f0, \u8bf4\u660e\u6709\u90e8\u5206\u6570\u636e\u53d7\u5230\u9650\u5236(\u4f8b\u5982\u6d4b\u91cf\u624b\u6bb5), \u4e0d\u80fd\u5f97\u5230. \u82e5\u975e\u5355\u5cf0, \u8bf4\u660e\u6709\u5176\u4ed6\u56e0\u7d20\u7684\u5f71\u54cd. \u800c\u4e14\u8fd9\u79cd\u5f71\u54cd\u662f\u4e0d\u53ef\u5ffd\u7565\u7684.<\/p>\n

\u76f4\u65b9\u56fe<\/h5>\n

\u4f5c\u76f4\u65b9\u56fe\u4e4b\u524d\uff0c \u6211\u4eec\u9700\u8981\u4e00\u4e9b\u7edf\u8ba1\u63cf\u8ff0\u91cf\uff1a\u6700\u5927\u503c<\/strong>\uff0c \u6700\u5c0f\u503c<\/strong>\uff0c \u6837\u672c\u5bb9\u91cf<\/strong>\u3002\u4e3a\u4e86\u548c\u6807\u51c6\u7684\u6b63\u6001\u5206\u5e03\u5bf9\u6bd4\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u5747\u503c<\/strong> \u548c \u65b9\u5dee<\/strong>\u3002 \u83b7\u53d6\u8fd9\u4e9b\u91cf\u7684\u5feb\u6377\u65b9\u6cd5\u5c31\u662f\u4f7f\u7528Excel\u7684\u5206\u6790\u7edf\u8ba1\u5de5\u5177:\u63cf\u8ff0\u7edf\u8ba1<\/strong>\u3002<\/p>\n

\u7531\u4e8eExcel\u9ed8\u8ba4\u6ca1\u6709\u6253\u5f00\u5206\u6790\u7edf\u8ba1\u5de5\u5177\uff0c \u6211\u4eec\u9700\u8981\u4f5c\u5982\u4e0b\u8bbe\u7f6e(\u4ee5Office 2013\u4e3a\u4f8b)\uff1a<\/p>\n

\u5355\u51fb\u6587\u4ef6<\/strong>\u2014>\u9009\u9879<\/strong>\u2014>\u6765\u5230Excel\u7684\u9009\u9879\uff0c \u5355\u51fb\u5de6\u8fb9\u7684\u52a0\u8f7d\u9879<\/strong>\uff0c \u8fd9\u65f6\u5728\u53f3\u8fb9\u7b2c\u4e00\u884c\u4f1a\u6709\u5206\u6790\u5de5\u5177\u5e93<\/strong>\uff0c \u5355\u51fb\u4ee5\u9009\u4e2d\u5b83\u2014>\u70b9\u51fb\u4e0b\u9762\u7684\u8f6c\u5230<\/strong>\u2014>\u6765\u5230\u52a0\u8f7d\u5b8f\u9762\u677f\uff0c \u5355\u51fb\u4ee5\u9009\u4e2d\u5206\u6790\u5de5\u5177\u5e93<\/strong> \u5e76 \u786e\u5b9a<\/strong>\u3002\u8fd9\u65f6\u4f60\u53ef\u770b\u5230Excel\u6570\u636e\u5b50\u9762\u677f\u7684\u6700\u540e\u591a\u4e86\u4e00\u9879\u6570\u636e\u5206\u6790<\/strong>\u3002<\/p><\/blockquote>\n

\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u6253\u5f00\u4e86Excel\u7684\u6570\u636e\u5206\u6790\u5de5\u5177\u3002<\/p>\n

\u4e0b\u9762\u6211\u4eec\u6765\u719f\u6089\u4e0b\u8fd9\u4e2a\u5206\u6790\u5de5\u5177\u5e93\uff0c \u6784\u9020\u4f5c\u76f4\u65b9\u56fe\u7684\u7b2c\u4e00\u6b65\u6240\u9700\u8981\u7684\u57fa\u672c\u7edf\u8ba1\u4fe1\u606f\u3002<\/p>\n

\u7edf\u8ba1\u63cf\u8ff0<\/h6>\n
    \n
  1. \u5355\u51fb\u6570\u636e<\/strong>\u9762\u677f\u4e0b\u7684 \u6570\u636e\u5206\u6790<\/strong>\uff0c \u9009\u62e9\u63cf\u8ff0\u7edf\u8ba1<\/strong><\/li>\n
  2. \u5728\u8f93\u5165\u533a\u57df<\/strong>\u5185\uff1a\u9009\u5b9a\u5f85\u5206\u6790\u6570\u636e\u533a\u57df\uff0c \u53ef\u4ee5\u9009\u62e9\u591a\u884c\u6216\u8005\u591a\u5217<\/li>\n
  3. \u9009\u62e9\u4f60\u5c06\u8981\u5206\u6790\u7684\u6570\u636e\u662f\u4ee5\u5217<\/strong>\u8fd8\u662f\u4ee5\u884c<\/strong>\u7684\u65b9\u5f0f\u5448\u73b0\u7684<\/li>\n
  4. \u5982\u679c\u6240\u9009\u62e9\u7684\u533a\u57df\u6709\u6570\u636e\u6807\u8bc6<\/strong>\uff0c \u52fe\u9009\u6807\u8bc6<\/strong><\/li>\n
  5. \u5728\u8f93\u51fa\u533a\u57df\u9009\u62e9\u8f93\u51fa\u5230\u5f53\u524d\u5de5\u4f5c\u8868\u8fd8\u662f\u65b0\u7684\u5de5\u4f5c\u8868<\/li>\n
  6. \u52fe\u9009\u6c47\u603b\u7edf\u8ba1<\/strong>\uff08\u8f93\u51fa\u57fa\u672c\u7edf\u8ba1\u91cf\uff09<\/li>\n
  7. \u786e\u5b9a<\/strong>\u4fbf\u53ef\u751f\u6210\u7edf\u8ba1\u63cf\u8ff0<\/li>\n<\/ol>\n

    \u6548\u679c\u5982\u56fe\u6240\u793a(\u6211\u6bcf\u6b21\u90fd\u5c06\u6570\u636e\u683c\u5f0f\u8bbe\u7f6e\u4e3a\u4fdd\u7559\u4e24\u4f4d\u5c0f\u6570):
    \n\"\"
    \n\u8fd9\u91ccA,B\u4e24\u5217\u662f\u6570\u636e, \u6211\u6ca1\u6709\u5b8c\u5168\u622a\u56fe. D-G\u5217\u662f\u6c47\u603b\u7edf\u8ba1.<\/p>\n

    \u7ec4\u6570\u7684\u8ba1\u7b97<\/h6>\n

    \u6211\u4eec\u5df2\u5c06\u4f5c\u76f4\u65b9\u56fe\u7684\u7b2c\u4e00\u6b65\u505a\u597d\u4e86, \u5373\u6709\u4e86\u57fa\u672c\u7684\u7edf\u8ba1\u91cf.<\/p>\n

    \u56de\u5fc6, \u505a\u76f4\u65b9\u56fe\u65f6\u8fd8\u9700\u8981\u5206\u7ec4, \u7136\u540e\u8ba1\u7b97\u6bcf\u7ec4\u6709\u591a\u5c11\u4e2a\u6570\u636e(\u5373\u9891\u6570), \u7136\u540e\u624d\u662f\u4f5c\u56fe. \u5206\u7ec4\u9996\u5148\u9700\u8981\u786e\u5b9a\u7ec4\u6570, \u5373\u5230\u5e95\u8981\u5206\u591a\u5c11\u7ec4. \u8fd9\u4e2a\u4e8b\u5b9e\u4e0a\u662f\u975e\u5e38\u91cd\u8981\u7684, \u5206\u7ec4\u8fc7\u5c11, \u6570\u636e\u5c31\u975e\u5e38\u96c6\u4e2d; \u5206\u7ec4\u8fc7\u591a, \u6570\u636e\u5c31\u975e\u5e38\u5206\u6563, \u8fd9\u90fd\u4f1a\u63a9\u76d6\u5206\u5e03\u7684\u7279\u5f81.<\/p>\n

    \u5173\u4e8e\u7ec4\u6570\u7684\u591a\u5c11, \u6211\u67e5\u4e86\u4e0bwiki<\/a>, \u603b\u7ed3\u8d77\u6765, \u5176\u65b9\u6cd5\u6709\u5982\u4e0b\u51e0\u79cd, \u8fd9\u91cc\u5047\u8bbe$n=50$\u4e3a\u6837\u672c\u603b\u6570:<\/p>\n

      \n
    1. \u65b9\u6839<\/strong>: \u6570\u636e\u4e2a\u6570\u7684\u5e73\u65b9\u6839\u5e76\u53d6\u6574, Excel\u516c\u5f0f:=INT(SQRT(n))<\/code>, \u8fd9\u91cc\u7ed3\u679c\u4e3a7<\/li>\n
    2. Sturges \u516c\u5f0f<\/strong>:\u6570\u636e\u4e2a\u6570\u5173\u4e8e$2$\u7684\u5bf9\u6570\u53d6\u6574\u52a0$1$, Excel\u516c\u5f0f:=INT(LOG(n,2))+1<\/code>, \u8fd9\u91cc\u7ed3\u679c\u4e3a6<\/li>\n
    3. Rice \u51c6\u5219<\/strong>: \u6570\u636e\u4e2a\u6570\u7684\u4e09\u6b21\u65b9\u6839\u7684\u4e8c\u500d\u53d6\u6574, Excel\u516c\u5f0f=INT(2*n^(1\/3))<\/code>, \u8fd9\u91cc\u7ed3\u679c\u4e3a6<\/li>\n
    4. Doane \u516c\u5f0f<\/strong>: \u662fSturges\u516c\u5f0f\u7684\u4fee\u6b63, \u5bf9\u5904\u7406\u5f02\u5e38\u6570\u636e\u6709\u6548. \u8ba1\u7b97\u516c\u5f0f\u4e3a:
      \n$$
      \n1 + \\log_2( n ) + \\log_2 \\left( 1 + \\frac { |g_1| }{\\sigma_{g_1}} \\right) ,
      \n$$
      \n\u5176\u4e2d
      \n$$
      \n\\sigma_{g_1} = \\sqrt { \\frac { 6(n-2) }{ (n+1)(n+3) } }
      \n$$
      \n\u800c$g_1$\u4e3a\u8be5\u5206\u5e03\u7684\u4e09\u9636\u77e9\u504f\u5ea6\u4f30\u8ba1<\/strong>. \u5177\u4f53\u7684\u8ba1\u7b97\u53ef\u4ee5\u5728      \u8fd9\u4e2a\u7f51\u9875<\/a>\u627e\u5230. \u53ea\u9700\u628a\u4f60\u7684\u6570\u636e(\u8fd9\u91cc, \u4f8b\u5982\u53d6\u7b2c\u4e00\u5217) \u7c98\u8d34\u5230\u7f51\u9875\u76841 Copy&Paste your data<\/strong>\u4e0b\u9762\u7684\u8f93\u5165\u6846, \u7136\u540e\u5355\u51fb 2. Please click here to start java applet<\/strong> \u4ee5\u52a0\u8f7djava, \u6700\u540e\u70b9\u51fb 3.Press Here to calculate the optimal bin size<\/strong> \u6211\u4eec\u5c31\u5f97\u5230\u4f18\u5316\u540e\u7684\u76f4\u65b9\u56fe. \u5728\u56fe\u4e0a\u53ef\u4ee5\u770b\u5230# of bins 10<\/strong>\u8868\u793a\u6b64\u65f6\u6211\u4eec\u4f18\u5316\u540e\u7684\u7ec4\u6570\u662f10<\/strong>, \u540e\u9762\u4e00\u4e2aBin width:0.286<\/strong>\u8868\u793a\u7684\u662f\u7ec4\u8ddd.<\/li>\n<\/ol>\n

      wiki\u4e0a\u8fd8\u6709\u51e0\u79cd\u529e\u6cd5, \u6211\u8fd9\u91cc\u76f4\u63a5\u8df3\u8fc7. \u56e0\u4e3a\u57fa\u672c\u4e0a\u5229\u7528\u7b2c\u56db\u79cd\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6bd4\u8f83\u6709\u6548\u7684\u7ec4\u6570<\/strong>.<\/p>\n

      \u7b2c\u56db\u4e2d\u529e\u6cd5\u7684\u7ed3\u679c\u5982\u4e0b\u56fe(\u76f8\u5e94\u4e8e\u7b2c\u4e00\u5217\u6570\u636e):
      \n\"\"<\/p>\n

      \u6700\u540e, \u82e5\u4f60\u8fd8\u4e0d\u6ee1\u610f, \u53ef\u4ee5\u8c03\u6574\u4e0b\u9762\u7684\u6ed1\u5757, \u6765\u589e\u52a0\u6216\u8005\u51cf\u5c11\u7ec4\u6570.<\/p>\n

      \u9891\u6570\u7684\u7edf\u8ba1<\/h6>\n

      \u5728Excel\u4e2d\u4f5c\u76f4\u65b9\u56fe, \u6211\u4eec\u9700\u8981\u5efa\u7acb\u4ed3\u5e93(bins), \u5373\u6bcf\u7ec4\u7684\u5206\u70b9. \u660e\u663e\u6211\u4eec\u53ea\u9700\u628a\u6570\u636e\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u4e4b\u95f4\u7684\u533a\u95f4\u5206\u4e3a\u5982\u4e0a\u6240\u8ba1\u7b97\u7684\u7ec4\u6570(\u8fd9\u91cc\u662f10<\/strong>), \u5e76\u6c42\u5176\u5206\u70b9\u5373\u53ef. \u5177\u4f53\u5730, \u5728Excel\u4e2d\u64cd\u4f5c\u5982\u4e0b(\u4e3a\u4e86\u5177\u6709\u4e00\u822c\u6027, 10\u5728\u4e0b\u9762\u6362\u4e3an<\/strong>):<\/p>\n

        \n
      1. \u53c2\u8003\u7b2c\u4e00\u4e2a\u56fe, \u5728H1\u4e2d\u8f93\u5165:=E12<\/code>, \u5e76\u6309F4\u5207\u6362\u5230\u7edd\u5bf9\u5f15\u7528, \u8fd9\u662f\u56e0\u4e3aA\u5217\u7684\u7b2c\u4e00\u4e2a\u5206\u70b9\u5c31\u662f\u6700\u5c0f\u503c.<\/li>\n
      2. \u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u7528\u6570\u636e\u586b\u5145\u7684\u529e\u6cd5\u8ba1\u7b97\u540e\u9762\u7684\u503c, \u4e8e\u662f\u53ea\u9700\u8bbe\u8ba1\u597d\u7b2c\u4e8c\u4e2a\u516c\u5f0f, \u5728H2\u4e2d\u4e2d\u8f93\u5165:=H2+$E$11\/10<\/code>, \u610f\u601d\u5f88\u660e\u663e, \u5c31\u662f\u524d\u4e00\u4e2a\u6570\u636e(H2)\u52a0\u4e0a\u7ec4\u8ddd, \u8fd9\u91cc\u7ec4\u8ddd\u7b49\u4e8e\u533a\u57df<\/strong>(E11)\u9664\u4ee5\u7ec4\u657010. \u6ce8\u610f\u7531\u4e8e\u7ec4\u6570\u5728\u4e0b\u9762\u586b\u5145\u4e2d\u662f\u4e0d\u52a8\u7684, \u56e0\u6b64\u662f\u7edd\u5bf9\u5f15\u7528.<\/li>\n
      3. \u586b\u5145\u76f4\u5230\u4e00\u5171\u670911\u4e2a\u6570\u4e3a\u6b62(10\u4e2a\u533a\u95f4, 11\u4e2a\u5206\u70b9,\u5475\u5475~~), \u8fd9\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6700\u540e\u4e00\u4e2a\u503c\u5e94\u8be5\u662f\u6700\u5927\u503c3.1(E13\u5355\u5143\u683c\u7ed9\u51fa)\u5224\u65ad.<\/li>\n
      4. \u81f3\u6b64, A\u5217\u6570\u636e\u7684\u4ed3\u5e93\u5c31\u505a\u597d\u4e86, \u5b8c\u5168\u7c7b\u4f3c\u7684\u505aB\u5217\u6570\u636e\u7684. \u6ce8\u610f\u8fd9\u91cc\u7ec4\u6570\u662f\u9700\u8981\u4ece\u65b0\u8ba1\u7b97\u7684, \u8fd9\u91cc\u5229\u7528\u7ec4\u6570\u8ba1\u7b97\u7684\u65b9\u6cd54\u7ed3\u679c\u6709\u4e9b\u5947\u8469, \u7adf\u7136\u7ec4\u6570\u662f2, \u9700\u8981\u6539\u8fdb, \u4e00\u822c5-8\u6bd4\u8f83\u6b63\u5e38, \u8fd9\u91cc\u9009\u62e96, \u56e0\u4e3a\u524d\u9762\u4e09\u79cd\u7684\u8ba1\u7b97\u6709\u4e24\u79cd\u662f6, \u4e00\u79cd\u7ed3\u679c\u662f7.<\/li>\n<\/ol>\n

        \u505a\u597d\u540e\u7684\u6548\u679c\u5982\u4e0b\u56fe(\u4e00\u5982\u65e2\u5f80\u5730, \u6570\u636e\u53ea\u4fdd\u7559\u4e24\u4f4d\u5c0f\u6570):
        \n\"\"<\/p>\n

        \u76f4\u65b9\u56fe\u7684\u4f5c\u6cd5<\/h6>\n

        \u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u5f00\u59cb\u4f5c\u76f4\u65b9\u56fe\u4e86. \u4e00\u822c\u6709\u4e24\u79cd\u529e\u6cd5, \u5229\u7528Excel\u7684FREQUENCY<\/code>\u624b\u52a8\u8ba1\u7b97\u9891\u6570, \u7136\u540e\u6dfb\u52a0\u76f4\u65b9\u56fe. \u8fd9\u79cd\u4f5c\u6cd5\u7684\u597d\u5904\u662f\u7531\u4e8e\u662f\u6309\u7167\u516c\u5f0f\u6765\u8ba1\u7b97\u7684, \u56e0\u6b64\u6570\u636e\u6539\u53d8\u65f6\u76f4\u65b9\u56fe\u4f1a\u968f\u7740\u6539\u53d8. \u4e0d\u597d\u7684\u5730\u65b9\u662f\u4e0d\u591f\u81ea\u52a8\u5316, \u9700\u8981\u7684\u8ba1\u7b97\u6bd4\u8f83\u591a. \u56e0\u6b64\u6211\u53ea\u4ecb\u7ecd\u5982\u4f55\u8ba1\u7b97\u9891\u6570.<\/p>\n

          \n
        1. \u5728J1\u4e2d\u8f93\u5165A\u7684\u9891\u6570<\/code>\u4f5c\u4e3a\u6807\u9898<\/li>\n
        2. \u5728J2\u4e2d\u8f93\u5165\u9891\u6570\u8ba1\u7b97\u516c\u5f0f:=FREQUENCY(A2:A51,H2:H12)<\/code>\u9053\u7406\u662f\u5f88\u660e\u663e\u7684, A2:A51<\/code>\u8868\u793a\u5f85\u7edf\u8ba1\u7684\u6570\u636e, H2:H12<\/code>\u8868\u793a\u4ed3\u5e93\u5206\u7ec4, \u6b64\u65f6\u8fd4\u56de\u7684\u662f\u7b2c\u4e00\u4e2a\u4ed3\u5e93\u7684\u9891\u6570.<\/li>\n
        3. \u4e3a\u4e86\u8ba1\u7b97\u5176\u4ed6\u4ed3\u5e93\u7684\u9891\u6570, \u6211\u4eec\u53ea\u9700\u9009\u4e2dJ2:J12<\/code>, \u518d\u6309F2<\/code>, \u6700\u540e\u6309Ctrl+Shift+Enter<\/code>\u5373\u53ef\u5f97\u5230\u5176\u4ed6\u4ed3\u5e93\u7684\u9891\u6570.<\/li>\n<\/ol>\n

          \u4e0b\u9762\u6211\u4ecb\u7ecd\u5982\u4f55\u901a\u8fc7\u6570\u636e\u5206\u6790<\/strong>\u7684\u76f4\u65b9\u56fe\u5de5\u5177\u6765\u5feb\u6377\u7684\u751f\u6210\u76f4\u65b9\u56fe.<\/p>\n

            \n
          1. \u70b9\u51fb\u6570\u636e\u9762\u677f<\/strong>, \u70b9\u51fb\u6700\u540e\u7684\u6570\u636e\u5206\u6790<\/strong>, \u5728\u5f39\u51fa\u7684\u6570\u636e\u5206\u6790\u9009\u6846\u4e2d, \u9009\u62e9\u76f4\u65b9\u56fe<\/strong>\u5e76\u786e\u5b9a.<\/li>\n
          2. \u5728\u8f93\u5165\u533a\u57df<\/strong>\u4e2d\u9009\u62e9A\u5217\u6570\u636e$A$1:$A$51<\/code>, \u5728\u63a5\u6536\u533a\u57df<\/strong>\u4e2d\u9009\u62e9:$H$1:$H$12<\/code>, \u7531\u4e8e\u9009\u62e9\u7684\u6570\u636e\u4e2d\u6709\u8868\u5934<\/strong>, \u6211\u4eec\u9700\u8981\u52fe\u9009\u6807\u5fd7<\/strong>. \u5728\u8f93\u51fa\u9009\u9879<\/strong>\u4e2d\u9009\u62e9\u8f93\u51fa\u533a\u57df<\/strong>, \u6211\u4eec\u8fd9\u91cc\u8f93\u51fa\u5230\u5f53\u524d\u5de5\u4f5c\u8868\u7684$D$18<\/code>. \u6700\u540e\u52fe\u9009\u56fe\u8868\u8f93\u51fa<\/strong>. \u5e76\u786e\u5b9a<\/li>\n
          3. \u8bf7\u624b\u52a8\u8c03\u6574\u76f4\u65b9\u56fe\u7684\u5927\u5c0f<\/li>\n<\/ol>\n

            \u81f3\u6b64A\u5217\u6570\u636e\u7684\u76f4\u65b9\u56fe\u5df2\u7ecf\u4f5c\u597d. \u6548\u679c\u5982\u56fe\u6240\u793a:
            \n\"\u76f4\u65b9\u56fe\"<\/p>\n

            \u8d8b\u52bf\u7ebf\u7684\u6dfb\u52a0<\/h5>\n

            \u4e3a\u4e86\u5bf9\u6bd4\u4e0e\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u5173\u7cfb, \u6211\u4eec\u5728\u4e0a\u9762\u7684\u76f4\u65b9\u56fe\u4e2d\u6dfb\u52a0\u6b63\u6001\u5206\u5e03<\/strong>.<\/p>\n

            \u9996\u5148, \u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6b63\u6001\u5206\u5e03\u7684\u5bc6\u5ea6.<\/p>\n

              \n
            1. \u5728F18<\/code>\u4e2d\u8f93\u5165\u6b63\u6001\u56fe<\/strong>\u4f5c\u4e3a\u6807\u9898<\/li>\n
            2. \u5728F19<\/code>\u4e2d\u8f93\u5165\u516c\u5f0f:=NORM.DIST(D19:D29,$E$3,$E$7,FALSE)<\/code>\u8ba1\u7b97\u7b2c\u4e00\u4e2a\u5206\u70b9\u7684\u6b63\u6001\u5206\u5e03\u4e4b\u6982\u7387\u5bc6\u5ea6. \u5176\u4e2d\u4e4b\u6240\u4ee5\u9009\u62e9D19:D29<\/code>\u56e0\u4e3a\u6211\u4eec\u5f85\u4f1a\u8981\u7528\u6570\u7ec4\u8ba1\u7b97\u5f97\u5230\u540e\u9762\u5206\u70b9\u7684\u6982\u7387\u5bc6\u5ea6. \u800c$E$3<\/code>\u662fA\u5217\u6570\u636e\u7684\u5747\u503c, $E$7<\/code>\u662fA\u5217\u6570\u636e\u7684\u6807\u51c6\u5dee, \u6700\u540e\u7684FALSE<\/code>\u8868\u793a\u6211\u4eec\u8ba1\u7b97\u7684\u662f\u6982\u7387\u5bc6\u5ea6<\/strong>\u800c\u975e\u7d2f\u79ef\u5bc6\u5ea6<\/strong>.
              \n\u603b\u8d77\u6765\u8bf4, \u5c31\u662f\u8ba1\u7b97A\u5217\u6570\u636e\u4f5c\u4e3a\u6b63\u6001\u5206\u5e03\u5728\u7ed9\u5b9a\u5206\u70b9\u7684\u6982\u7387\u5bc6\u5ea6\u662f\u591a\u5c11<\/strong>. \u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u505a\u51faA\u5217\u6570\u636e\u7684\u6b63\u6001\u5206\u5e03\u5206\u5e03\u56fe\u4e86.<\/li>\n
            3. \u8ba1\u7b97\u5176\u4ed6\u5206\u70b9\u7684\u6982\u7387\u5bc6\u5ea6, \u8fd9\u53ef\u7531\u524d\u9762\u8bb2\u8fc7\u7684\u6570\u7ec4\u8ba1\u7b97\u516c\u5f0f\u5f97\u5230: \u9009\u4e2dF19:F29<\/code>, \u6309\u4e0bF2<\/code>, \u518d\u6309Ctrl+Shift+Enter<\/code>\u5373\u53ef<\/li>\n<\/ol>\n

              \u81f3\u6b64, A\u5217\u6570\u636e\u7684\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u5c31\u8ba1\u7b97\u597d\u4e86. \u4e0b\u9762\u6211\u4eec\u5c06\u901a\u8fc7\u5b83\u505a\u51faA\u5217\u6570\u636e\u7684\u6b63\u6001\u5206\u5e03\u56fe, \u5e76\u5c06\u5176\u6dfb\u52a0\u5230\u539f\u6765\u7684\u76f4\u65b9\u56fe\u4e2d.<\/p>\n

                \n
              1. \u5728\u76f4\u65b9\u56fe\u7684\u7a7a\u767d\u5904\u5355\u51fb\u4ee5\u9009\u4e2d\u8be5\u76f4\u65b9\u56fe, \u6b64\u65f6\u4f1a\u770b\u5230\u8bbe\u8ba1\u9762\u677f<\/strong>, \u5355\u51fb\u4ee5\u5207\u6362\u5230\u8be5\u9762\u677f, \u7136\u540e\u5355\u51fb\u9009\u62e9\u6570\u636e<\/strong>, \u6211\u4eec\u60f3\u8981\u5c06\u6b63\u6001\u56fe\u7684\u6570\u636e\u6dfb\u52a0\u5230\u5f53\u524d\u56fe\u8868<\/li>\n
              2. \u5355\u51fb\u6dfb\u52a0(A)<\/strong>, \u5728\u7cfb\u5217\u540d\u79f0\u91cc\u9762\u8f93\u5165=Sheet1!$F$18<\/code>, \u5c31\u662f\u6b63\u6001\u56fe\u7684\u6807\u9898; \u5728\u7cfb\u5217\u503c\u91cc\u9009\u62e9=Sheet1!$F$19:$F$29<\/code>(\u8fd9\u91cc\u6570\u636e\u7684\u6dfb\u52a0\u90fd\u662f\u70b9\u51fb\u540e\u9762\u5e26\u989c\u8272\u7684\u5c0f\u6846\u6846, \u7136\u540e\u518d\u9009\u62e9\u6570\u636e\u8303\u56f4), \u5c31\u662f\u4e0a\u9762\u8ba1\u7b97\u7684\u6b63\u6001\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6.<\/li>\n
              3. \u4e24\u6b21\u786e\u5b9a, \u5373\u53ef\u5728\u56fe\u8868\u4e2d\u770b\u5230\u6dfb\u52a0\u8fdb\u6765\u7684\u6b63\u6001\u5206\u5e03\u56fe, \u4f46\u662f\u6b64\u65f6\u6bd4\u4f8b\u4e0d\u5bf9(\u662f\u6309\u7167\u5b9e\u9645\u6570\u636e\u7684\u503c\u6765\u4f5c\u56fe\u7684, \u5373\u4e00\u4e2a\u662f\u9891\u6570\u6700\u5927\u4e3a19, \u800c\u4e00\u4e2a\u4e3a\u6982\u7387\u5bc6\u5ea6, \u6700\u5927\u4e3a0.79), \u8fd9\u53ef\u4ee5\u901a\u8fc7\u8bbe\u7f6e\u6b21\u5750\u6807\u8f74<\/strong>\u6765\u8c03\u6574.<\/li>\n
              4. \u540c\u6837\u9009\u4e2d\u76f4\u65b9\u56fe(\u7a7a\u767d\u5904\u5355\u51fb), \u5207\u6362\u5230\u89c6\u56fe<\/strong>(\u4e8b\u5b9e\u4e0a\u5728\u56fe\u8868\u7a7a\u767d\u5904\u53cc\u51fb\u5373\u53ef\u5feb\u901f\u5207\u6362\u5230\u89c6\u56fe\u9762\u677f), \u5355\u51fb\u66f4\u6539\u56fe\u8868\u7c7b\u578b<\/strong>, \u5728\u6240\u6709\u56fe\u8868\u4e2d\u9009\u62e9\u7ec4\u5408<\/strong>, \u53ef\u4ee5\u770b\u5230\u9891\u7387<\/strong>\u7cfb\u5217\u9ed8\u8ba4\u7684\u662f\u7c07\u72b6\u67f1\u5f62\u56fe<\/strong>, \u8fd9\u4e2a\u4e0d\u7528\u4fee\u6539, \u5728\u6b63\u6001\u56fe<\/strong>\u7cfb\u5217, \u9ed8\u8ba4\u7684\u662f\u6298\u7ebf\u56fe<\/strong>, \u6211\u4eec\u5c06\u5176\u4fee\u6539\u4e3aX Y(\u6563\u70b9\u56fe)<\/strong>\u7684\u7b2c\u4e09\u4e2a\u5e26\u5e73\u6ed1\u7ebf\u7684\u6563\u70b9\u56fe<\/strong>, \u5e76\u52fe\u9009\u540e\u9762\u7684\u6b21\u5750\u6807\u8f74<\/strong>, \u786e\u5b9a\u5373\u53ef\u5f97\u5230\u5e26\u6b63\u6001\u5206\u5e03\u7684\u76f4\u65b9\u56fe.<\/li>\n<\/ol>\n

                \u6700\u7ec8\u6548\u679c\u5982\u56fe\u6240\u793a:
                \n\"\u5e26\u6b63\u6001\u5206\u5e03\u56fe\u7684\u76f4\u65b9\u56fe\"<\/p>\n

                \u4f5c\u4e3a\u7ec3\u4e60, \u8bf7\u81ea\u884c\u5bf9B\u5217\u6570\u636e\u4f5c\u51fa\u5e26\u6b63\u6001\u56fe\u7684\u76f4\u65b9\u56fe. \u53ef\u4ee5\u53c2\u8003\u6211\u6700\u7ec8\u7684Example.xlsx<\/a>\u6587\u4ef6.<\/p>\n

                \u81f3\u6b64, \u6211\u4eec\u5b8c\u6210\u4e86\u975e\u53c2\u6570\u68c0\u9a8c\u7684\u7b2c\u4e00\u6b65: \u901a\u8fc7\u76f4\u65b9\u56fe\u5927\u81f4\u5224\u65ad\u662f\u5426\u7b26\u5408\u6b63\u6001\u5206\u5e03.<\/p>\n

                \u7ed3\u8bba\u662f(\u5bf9A\u5217\u6570\u636e): \u53ef\u4ee5\u770b\u5230\u5927\u81f4\u8fd8\u662f\u7b26\u5408\u6b63\u6001\u5206\u5e03\u7684, \u53ea\u662f\u56fe\u5f62\u4e0d\u5bf9\u79f0, \u53f3\u8fb9\u6709\u4e2a\u957f\u5c3e(\u53f3\u504f\u6001\u5206\u5e03), \u9700\u8981\u53cd\u601d\u5b9e\u9a8c\u65f6\u662f\u4ec0\u4e48\u9020\u6210\u4e86\u4f4e\u503c<\/strong>\u7684\u7f3a\u5931. (\u5f53\u7136\u8fd9\u53ef\u80fd\u4e0d\u662f\u5b9e\u9a8c\u624b\u6bb5\u9020\u6210\u7684, \u6709\u53ef\u80fd\u8fd9\u6b63\u597d\u662f\u4f60\u7684\u5b9e\u9a8c\u672c\u8eab\u9700\u8981\u6570\u636e\u53cd\u6620\u7684\u60c5\u51b5).<\/p>\n

                $\\chi^2$\u62df\u5408\u68c0\u9a8c<\/h5>\n

                $\\chi^2$\u62df\u5408\u68c0\u9a8c\u5e76\u4e0d\u53ea\u662f\u9488\u5bf9\u6b63\u6001\u5206\u5e03\u6765\u68c0\u9a8c\u7684. \u4e8b\u5b9e\u4e0a, \u89c2\u5bdf\u4e0a\u56fe(\u76f4\u65b9\u56fe\u7684\u5de6\u8fb9), \u6211\u4eec\u77e5\u9053A\u5217\u6570\u636e\u5728\u6bcf\u4e2a\u4ed3\u5e93\u7684\u9891\u6570, \u4f8b\u5982: D19=0.24, E19=1<\/code>, \u8868\u793a\u7684\u662fA\u5217\u6570\u636e\u4e2d\u5c0f\u4e8e\u7b49\u4e8e0.24\u7684\u67091\u4e2a, D20=0.53,E20=13<\/code>\u8868\u793a\u5927\u4e8e0.24\u5c0f\u4e8e\u7b49\u4e8e0.53\u7684\u6570\u636e\u670913\u4e2a, \u4e0e\u6b64\u7c7b\u63a8, \u6700\u540e\u7684D30=\u5176\u4ed6, E30=1<\/code>\u8868\u793a, \u5927\u4e8e3.10\u7684\u67091\u4e2a.<\/p>\n

                \u73b0\u5728, \u5047\u8bbeA\u5217\u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684<\/strong>, \u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u5404\u4e2a\u4ed3\u5e93\u7684\u7406\u8bba\u9891\u6570np_i<\/strong>. \u800c\u82f1\u56fd\u7edf\u8ba1\u5b66\u5bb6K.Pearson\u8bc1\u660e\u4e86\u7edf\u8ba1\u91cf<\/p>\n

                $$\\begin{equation}
                \n\\chi^2=\\sum_{i=1}^k\\frac{(v_i-np_i)^2}{np_i},
                \n\\label{eq1}
                \n\\end{equation}$$
                \n\u5728\u6837\u672c\u5bb9\u91cf\u5145\u5206\u5927\u65f6\u662f\u8fd1\u4f3c\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a$k-1$\u7684$\\chi^2$\u5206\u5e03. \u8fd9\u91cc, $v_i$\u5c31\u662f\u5b9e\u9645\u7684\u9891\u6570, \u4e0a\u8868\u7684F19:F29<\/code>, \u800c$n$\u662f\u4ed3\u5e93\u603b\u6570, \u5373\u7ec4\u6570, $p_i$\u662f\u968f\u673a\u4f4d\u4e8e\u8be5\u4ed3\u5e93\u7684\u6982\u7387, \u8fd9\u662f\u9700\u8981\u6839\u636e\u5047\u8bbe\u7684\u5206\u5e03(\u4e0d\u4e00\u5b9a\u5c31\u662f\u6b63\u6001\u5206\u5e03)\u7684\u5bc6\u5ea6\u51fd\u6570\u6765\u8ba1\u7b97\u7684.<\/strong><\/p>\n

                \u8fd9\u6837, \u6211\u4eec\u4e0d\u96be\u7406\u89e3, $\\chi$\u68c0\u9a8c\u5c31\u662f\u68c0\u9a8c\u4e0a\u9762\u8fd9\u4e2a\u5047\u8bbe, \u5373\u5047\u8bbeA\u5217\u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684<\/strong>, \u662f\u5426\u6210\u7acb\u7684\u4e00\u4e2a\u6807\u51c6. \u6b64\u5916, \u5b83\u8fd8\u53ef\u4ee5\u7528\u6765\u505a\u72ec\u7acb\u6027\u68c0\u9a8c<\/strong>, \u8bf7\u5173\u6ce8\u6211\u53e6\u4e00\u7bc7\u6587\u7ae0\u5b9e\u9a8c\u6570\u636e\u72ec\u7acb\u6027\u68c0\u9a8c\u5c0f\u8bb0<\/a><\/em>.<\/p>\n

                \u4e0b\u9762, \u6211\u60f3\u901a\u8fc7Excel\u6765\u8ba1\u7b97$\\chi^2$\u68c0\u9a8c\u7684\u7ed3\u679c(\u6982\u7387\u503c).<\/p>\n

                  \n
                1. \u4e3a\u4e86\u65b9\u4fbf, \u5c06A\u5217\u6570\u636e\u7684\u5206\u7ec4\u4ee5\u53ca\u9891\u6570\u7edf\u8ba1\u8868(\u7531\u76f4\u65b9\u56fe\u7684\u4f5c\u6cd5\u81ea\u52a8\u751f\u6210, \u4f4d\u4e8e\u76f4\u65b9\u56fe\u7684\u5de6\u8fb9)\u4ee5\u53ca\u63cf\u8ff0\u7edf\u8ba1\u8868\u590d\u5236\u5230\u65b0\u7684\u5de5\u4f5c\u8868(\u8bf7\u53c2\u8003\u6700\u540e\u7684\u6548\u679c\u56fe)<\/li>\n
                2. \u8ba1\u7b97\u5404\u4e2a\u4ed3\u5e93\u7684\u7406\u8bba\u9891\u6570, \u8fd9\u9700\u8981\u7279\u522b\u5904\u7406\u7b2c\u4e00\u4e2a\u4ed3\u5e93\u548c\u6700\u540e\u4e00\u4e2a\u4ed3\u5e93(\u5176\u4ed6<\/strong>\u7684\u54ea\u4e00\u4e2a), \u9996\u5148\u6765\u770b\u7b2c\u4e00\u4e2a\u7684\u7406\u8bba\u9891\u6570\u8ba1\u7b97\u516c\u5f0f, \u5728C3\u4e2d\u8f93\u5165:=$G$16*NORM.DIST(A3,$G$4,$G$8,TRUE)<\/code>, \u5176\u4e2dG16<\/code>\u5c31\u662f\u6570\u636e\u603b\u6570, \u5b83\u540e\u9762\u4e58\u7684\u662f\u6b63\u6001\u5206\u5e03\u4e0b\u7b2c\u4e00\u4e2a\u4ed3\u5e93\u7684\u6982\u7387(\u8fd8\u8bb0\u5f97\u5417? \u7b2c\u4e00\u4e2a\u4ed3\u5e93\u8868\u793a\u5c0f\u4e8e\u7b49\u4e8e\u8be5\u503c), \u6211\u60f3, \u53ea\u9700\u89e3\u91ca\u4e0b\u6700\u540e\u4e00\u4e2a\u53c2\u6570(\u524d\u9762\u7684\u53c2\u6570\u5df2\u7ecf\u8bf4\u8fc7), \u8fd9\u91cc\u7684TRUE<\/code>\u8868\u793a\u8ba1\u7b97\u7684\u662f\u7d2f\u79ef\u5206\u5e03\u5bc6\u5ea6<\/strong>, \u8fd9\u662f\u5f53\u7136\u7684, \u56e0\u4e3a\u8be5\u4ed3\u5e93\u8868\u793a\u7684\u662f\u5c0f\u4e8e\u7b49\u4e8e0.24\u7684\u6570\u636e.<\/li>\n
                3. \u8ba1\u7b97\u6700\u540e\u4e00\u4e2a\u4ed3\u5e93\u7684\u7406\u8bba\u5bc6\u5ea6, \u7531\u4e8e\u6700\u540e\u4e00\u4e2a\u4ed3\u5e93\u8868\u793a\u7684\u662f\u5927\u4e8e\u8be5\u503c\u7684\u6570\u636e\u4e2a\u6570, \u56e0\u6b64\u5b83\u5bf9\u5e94\u7684\u6982\u7387\u5bc6\u5ea6\u662f1(\u5bc6\u5ea6\u4e4b\u548c\u4e3a1\u54e6)\u51cf\u53bb\u8be5\u6570\u503c\u7684\u7d2f\u79ef\u5206\u5e03\u5bc6\u5ea6<\/strong>. \u8fd9\u6837\u6211\u4eec\u5728C14<\/code>\u4e2d\u8f93\u5165:=$G$16*(1-NORM.DIST($A$13,$G$4,$G$8,TRUE))<\/code><\/li>\n
                4. \u8ba1\u7b97\u4e2d\u95f4\u4ed3\u5e93\u7684\u7406\u8bba\u9891\u6570, \u5728C4<\/code>\u4e2d\u8f93\u5165:=$G$16*(NORM.DIST(A4,$G$4,$G$8,TRUE)-NORM.DIST(A3,$G$4,$G$8,TRUE))<\/code>, \u9053\u7406\u662f\u5f88\u6e05\u695a\u7684, \u65e2\u7136\u6211\u4eec\u8ba1\u7b97\u7684\u662f\u4ecb\u4e8eA3<\/code>\u4e0eA4<\/code>\u7684\u9891\u6570, \u5f53\u7136\u5c31\u662f\u6837\u672c\u5bb9\u91cf(G16<\/code>)\u4e58\u4ee5A4<\/code>\u4e0eA3<\/code>\u7684\u7d2f\u79ef\u5206\u5e03\u5bc6\u5ea6\u4e4b\u5dee.<\/li>\n
                5. \u81f3\u6b64, \u6211\u4eec\u5f97\u5230\u4e86\u7406\u8bba\u9891\u6570(\u4e0d\u4e00\u5b9a\u662f\u6574\u6570), \u6700\u540e\u6211\u4eec\u53ea\u9700\u5229\u7528Excel\u63d0\u4f9b\u7684$\\chi^2$\u6982\u7387\u7684\u8ba1\u7b97\u51fd\u6570CHISQ.TEST<\/code>\u6765\u8ba1\u7b97$\\chi^2$\u68c0\u9a8c\u7684\u7ed3\u679c: \u5728A16<\/code>\u8f93\u5165\u516c\u5f0f:=CHISQ.TEST(B3:B14,C3:C14)<\/code>, \u8fd9\u91ccB3:B14<\/code>\u662f\u5b9e\u9645\u9891\u6570, C3:C14<\/code>\u662f\u7406\u8bba\u9891\u6570, \u8fd9\u6837Excel\u5c31\u4f1a\u6839\u636e\\eqref{eq1}\u6765\u8ba1\u7b97\u7ed3\u679c($\\chi^2$\u5206\u5e03\u7684\u6982\u7387\u503c$p$).<\/li>\n<\/ol>\n

                  \u6700\u540e, \u6211\u6307\u51fa\u8be5\u7ed3\u679c\u7684\u610f\u4e49<\/strong>. \u9996\u5148\u6211\u4eec\u5fc5\u987b\u77e5\u9053\u4e24\u4e2a\u4e8b\u5b9e:<\/p>\n

                    \n
                  1. \u7edf\u8ba1\u63a8\u65ad(\u5047\u8bbe\u68c0\u9a8c)\u7684\u539f\u5047\u8bbe$H_0$\u662f\u5bf9\u60f3\u8981\u7684\u8bc1\u660e\u7684\u7ed3\u8bba\u7684\u5426\u5b9a<\/strong>, \u90a3\u4e48\u8fd9\u91cc$H_0$\u5c31\u662f: \u5b9e\u9a8c\u6570\u636e\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03.<\/li>\n
                  2. \u663e\u8457\u6027\u6c34\u5e73<\/a>\u662f\u6307\u5f53\u539f\u5047\u8bbe(\u5373$H_0$)\u5b9e\u9645\u4e0a\u662f\u6b63\u786e\u7684, \u4f46\u6839\u636e\u7edf\u8ba1\u63a8\u65ad, \u4eba\u4eec\u5374\u628a\u5b83\u62d2\u7edd\u4e86\u7684\u6982\u7387\u6216\u98ce\u9669.<\/li>\n<\/ol>\n

                    \u7531\u6b64\u53ef\u89c1, \u8fd9\u91cc\u8ba1\u7b97\u7684$p$\u503c\u8868\u793a: \u6211\u4eec\u63a5\u53d7\u5b9e\u9a8c\u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03(\u5373\u62d2\u7edd$H_0$), \u4f46\u662f\u5b9e\u9645\u4e0a\u5b9e\u9a8c\u6570\u636e\u5374\u4e0d\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\u6982\u7387. \u4e5f\u5373\u6211\u4eec\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u9519\u8bef\u7684\u6982\u7387<\/strong>. \\textcolor{red}{\u56e0\u6b64\u5f53$p$\u503c\u8d8a\u5c0f\u65f6, \u6211\u4eec\u8d8a\u6709\u7406\u7531\u76f8\u4fe1\u6211\u4eec\u7684\u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684}.<\/p>\n

                    \u5bf9\u4e8e\u5176\u4ed6\u7684\u5206\u5e03, \u552f\u4e00\u7684\u533a\u522b\u5c31\u662f\u5404\u4e2a\u4ed3\u5e93\u7684\u6982\u7387\u5bc6\u5ea6\u4e0d\u540c.<\/p>\n

                    \u6211\u6700\u540e\u8ba1\u7b97\u7684\u7ed3\u679c\u5982\u4e0b\u56fe:
                    \n\"\u5361\u65b9\u68c0\u9a8c\"<\/p>\n

                    \u5177\u4f53\u7684\u53ef\u4ee5\u53c2\u8003\u6211\u505a\u7684\u7684Example.xlsx<\/a>\u6587\u6863.<\/p>\n

                    \u66f4\u6b63<\/h5>\n

                    \u7531\u4e8eExcel\u7684\u5361\u65b9\u7edf\u8ba1\u4e8b\u5b9e\u4e0a\u53ea\u662f\u4e3a\u72ec\u7acb\u6027\u68c0\u9a8c\u800c\u8bbe\u8ba1\u7684, \u4ece\u5e2e\u52a9\u6587\u6863\u53ef\u4ee5\u770b\u5230\u5b83\u7684\u81ea\u7531\u5ea6\u5728\u8fd9\u91cc\u4e0d\u6b63\u786e, \u56e0\u4e3a\u6839\u636e\u5e2e\u52a9\u6587\u6863, \u81ea\u7531\u5ea6\u5f53$r=1$(\u5373\u884crow)\u81ea\u7531\u5ea6\u4e3a$c-1$, \u5373\u7edf\u8ba1\u7684\u5217\u6570\u51cf1, \u8fd9\u6837, \u8fd9\u91cc\u7684\u8ba1\u7b97\u662f11; \u4f46\u662f\u5b9e\u9645\u7684\u60c5\u51b5\u5374\u662f, \u7531\u4e8e\u6b63\u6001\u5206\u5e03\u4e2d\u5360\u4e86\u4e24\u4e2a\u81ea\u7531\u5ea6(\u5747\u503c\u548c\u6807\u51c6\u5dee), \u56e0\u6b64\u81ea\u7531\u5ea6\u5e94\u8be5\u662f$12-2-1=9$, \u8fd9\u6837, \u6211\u4eec\u5fc5\u987b\u91cd\u65b0\u8ba1\u7b97\u7edf\u8ba1\u91cf$\\chi^2$.<\/p>\n

                      \n
                    1. \u5728D3<\/code>\u4e2d\u8f93\u5165\u516c\u5f0f:=(B3-C3)^2\/C3<\/code>, \u8ba1\u7b97\u7b2c\u4e00\u4e2a\u4ed3\u5e93\u7684\u9891\u7387\u4e0e\u671f\u671b\u4e4b\u5dee\u7684\u5e73\u65b9\u9664\u4ee5\u671f\u671b<\/li>\n
                    2. \u5411\u4e0b\u586b\u5145\u5230D14<\/code>, \u8fd9\u5c31\u8ba1\u7b97\u597d\u4e86\u5361\u65b9\u7edf\u8ba1\u91cf\u4e2d\u7684\u6bcf\u4e00\u9879<\/li>\n
                    3. \u6c42\u548c, \u5728B16\u4e2d\u6c42\u5f97\u5361\u65b9\u7edf\u8ba1\u91cf\u7684\u503c:=SUM(D3:D14)<\/code><\/li>\n
                    4. \u5728D16<\/code>\u4e2d\u6c42\u5f97\u81ea\u7531\u5ea6, =COUNT(B3:B14)-2-1<\/code><\/li>\n
                    5. \u5728B17\u4e2d\u8bbe\u5b9a\u663e\u8457\u6c34\u5e73<\/strong>, \u4f8b\u5982\u6211\u4eec\u60f3\u77e5\u9053\u5728\u663e\u8457\u6c34\u5e73\u4e3a$0.05$\u65f6, \u5047\u8bbe($H_0$)\u662f\u5426\u6210\u7acb, \u5219\u5728B17\u4e2d\u8f93\u51650.05<\/code><\/li>\n
                    6. \u5728B18<\/code>\u4e2d\u8ba1\u7b97\u6307\u5b9a\u663e\u8457\u6c34\u5e73\u4e0b\u7684\u4e34\u754c\u503c<\/strong>, \u8ba1\u7b97\u516c\u5f0f\u4e3a:=CHISQ.INV(1-B17,D16)<\/code>, \u8fd9\u91cc\u516c\u5f0f\u8fd4\u56de\u7684\u662f\u5f53$\\chi^2$\u7684\u7d2f\u79ef\u6982\u7387\u5bc6\u5ea6\u8fbe\u5230$1-0.05$\u65f6\u7684\u503c, \u540e\u9762\u7684D16<\/code>\u8868\u793a\u7684\u662f\u81ea\u7531\u5ea6, \u56e0\u4e3a\u8fd9\u4e0d\u662fExcel\u9ed8\u8ba4\u7684, \u6240\u6709\u9700\u8981\u624b\u52a8\u8ba1\u7b97<\/li>\n
                    7. \u6bd4\u8f83\u5361\u65b9\u7edf\u8ba1\u91cf\u548c\u4e34\u754c\u503c\u7684\u5927\u5c0f, \u56e0\u4e3a\u7406\u60f3\u60c5\u51b5\u4e0b(\u5373\u5047\u8bbe\u662f\u6b63\u6001\u5206\u5e03\u65f6), \u5361\u65b9\u7edf\u8ba1\u91cf\u5e94\u8be5\u4e3a$0$(\u671f\u671b\u9891\u6570\u548c\u5b9e\u9645\u9891\u6570\u76f8\u7b49\u4e86), \u6240\u4ee5\u5982\u679c\u5361\u65b9\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c\u5219\u63a5\u53d7\u539f\u5047\u8bbe$H_0$(\u4e0d\u662f\u6b63\u6001\u5206\u5e03, \u6ce8\u610f\u6982\u7387\u63a8\u65ad\u601d\u60f3\u662f\u4ece\u6982\u7387\u4e0a\u53cd\u8bc1, \u56e0\u6b64\u6211\u4eec\u539f\u5047\u8bbe\u662f:\u6570\u636e\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03, \u5373\u5426\u5b9a\u60f3\u8981\u8bc1\u660e\u7684\u547d\u9898: \u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684), \u5426\u5219\u62d2\u7edd\u539f\u5047\u8bbe(\u662f\u6b63\u6001\u5206\u5e03), \u56e0\u6b64\u6211\u4eec\u5728B19<\/code>\u4e2d\u7528\u4e00\u4e2aIF<\/code>\u6765\u5224\u65ad\u662f\u5426\u63a5\u53d7\u539f\u5047\u8bbe:=IF(B16<B18,\"\u662f\",\"\u5426\")<\/code><\/li>\n<\/ol>\n

                      \u8fd9\u6837, \u6211\u4eec\u5f97\u5230\u7684\u7ed3\u679c\u662f\u5426<\/strong>, \u56e0\u4e3a\u5361\u65b9\u7edf\u8ba1\u91cf\u8981\u5927\u4e8e\u4e34\u754c\u503c. \u4ece\u800c\u6839\u636e\u7edf\u8ba1\u63a8\u65ad(\u5728\u7ed9\u5b9a\u7684\u663e\u8457\u6027\u6c34\u5e73\u4e0b), \u6570\u636e\u662f\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684.<\/p>\n

                      \u6548\u679c\u5982\u56fe\u6240\u793a:
                      \n\"\u5361\u65b9\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\"<\/p>\n

                      \u6700\u7ec8\u7684Excel\u6587\u6863, Example.xlsx<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

                      \u5047\u8bbe\u68c0\u9a8c\u7684\u57fa\u672c\u77e5\u8bc6 \u5f80\u5f80\uff0c \u6211\u4eec\u6839\u636e\u5047\u8bbe\uff0c \u63d0\u51fa\u539f\u7406\u3002 \u800c\u8981\u9a8c\u8bc1\u8fd9\u4e00\u5047\u8bbe\u662f\u5426\u6210\u7acb …<\/p>\n

                      \u5b9e\u9a8c\u6570\u636e\u7684\u5047\u8bbe\u68c0\u9a8c\u5c0f\u8bb0<\/span> \u9605\u8bfb\u66f4\u591a »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[45,49,731,348,382],"class_list":["post-3705","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-45","tag-49","tag-731","tag-348","tag-382"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3705","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3705"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3705\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}