{"id":1793,"date":"2025-11-24T05:32:41","date_gmt":"2025-11-23T21:32:41","guid":{"rendered":"https:\/\/muma.my\/?p=1793"},"modified":"2025-11-24T05:32:41","modified_gmt":"2025-11-23T21:32:41","slug":"%e8%87%aa%e5%ad%a6%e7%bb%9f%e8%ae%a1%e5%ad%a6teach-yourself%ef%bc%9astatistics","status":"publish","type":"post","link":"https:\/\/muma.my\/?p=1793","title":{"rendered":"\u81ea\u5b66\u7edf\u8ba1\u5b66Teach Yourself\uff1aStatistics"},"content":{"rendered":"

\n\t\n<\/p>\n

\n\t\u4e25\u5143\u7ae0\u85cf\u4e66<\/span>0233 <\/span>\n<\/p>\n

\n\t <\/span>\n<\/p>\n

\n\t\u81ea\u5b66\u7edf\u8ba1\u5b66<\/u><\/strong><\/span><\/b>Teach Yourself<\/u><\/strong><\/span>\uff1a<\/u><\/strong><\/span>Statistics<\/u><\/strong><\/span>\n<\/p>\n

\n\t <\/span>\n<\/p>\n

\n\t\"\"
\n<\/span>\n<\/p>\n

\n\t
\n<\/span>\n<\/p>\n

\n\t\u7406\u67e5\u5fb7<\/span>\u00b7<\/span>\u53e4\u5fb7\u66fc\uff08<\/span>Richard Goodman<\/span>\uff09\u64b0\u5199\u7684\u300a<\/span>\u81ea\u5b66\u7edf\u8ba1\u5b66<\/span><\/b>\u300b\u4e00\u4e66\uff0c\u8be5\u4e66\u5c5e\u4e8e<\/span>\u201c<\/span>\u81ea\u5b66\u4e1b\u4e66<\/span>\u201d<\/span>\u7cfb\u5217\uff0c<\/span>\u4e8e<\/span>1957<\/span>\u5e74\u9996\u6b21\u51fa\u7248<\/span><\/b>\u3002\u5185\u5bb9\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u7edf\u8ba1\u5b66\u7684<\/span>\u57fa\u672c\u6982\u5ff5\u548c\u7406\u8bba\u6a21\u578b<\/span><\/b>\uff0c\u5305\u62ec\u5bf9<\/span>\u201c<\/span>\u7edf\u8ba1\u5b66<\/span>\u201d<\/span>\u4e00\u8bcd\u7684\u4e24\u79cd\u7528\u6cd5\u3001<\/span>\u968f\u673a\u62bd\u6837<\/span><\/b>\u7684\u539f\u7406\uff0c\u4ee5\u53ca\u5982\u4f55\u4ece\u6837\u672c\u63a8\u65ad\u603b\u4f53\u6027\u8d28\u3002\u4e66\u4e2d\u8be6\u7ec6\u89e3\u91ca\u4e86<\/span>\u6982\u7387\u5206\u5e03\u6a21\u578b<\/span><\/b>\uff0c\u5982\u4e8c\u9879\u5206\u5e03\u3001\u6cca\u677e\u5206\u5e03\u548c\u6b63\u6001\u5206\u5e03\uff0c\u5e76\u6df1\u5165\u63a2\u8ba8\u4e86<\/span>\u53cc\u53d8\u91cf\u5206\u5e03\u3001\u56de\u5f52\u5206\u6790\u548c\u76f8\u5173\u6027<\/span><\/b>\u3002\u6b64\u5916\uff0c\u6587\u672c\u7684\u5f88\u5927\u4e00\u90e8\u5206\u81f4\u529b\u4e8e<\/span>\u62bd\u6837\u7406\u8bba<\/span><\/b>\uff08\u5305\u62ec<\/span>t<\/span>\u68c0\u9a8c\u548c<\/span>F<\/span>\u68c0\u9a8c\uff09\u4ee5\u53ca<\/span>\u65b9\u5dee\u5206\u6790<\/span><\/b>\uff08<\/span>ANOVA<\/span>\uff09\u6280\u672f\uff0c\u65e8\u5728\u5206\u79bb\u548c\u68c0\u9a8c\u4e0d\u540c\u5206\u7c7b\u56e0\u7d20\u5bf9\u53d8\u5f02\u7684\u5f71\u54cd\u3002<\/span><\/span>\n<\/p>\n

\n\t <\/span>\n<\/p>\n

\n\t\u672c\u4e66\u65e8\u5728\u5e2e\u52a9\u90a3\u4e9b\u9700\u8981\u81ea\u5b66\u7edf\u8ba1\u5b66\u3001\u4f46\u5f80\u5f80\u7f3a\u4e4f\u6570\u5b66\u8bad\u7ec3\u7684\u4eba\uff0c\u4f7f\u5176\u80fd\u591f\u7406\u89e3\u4e00\u4e9b<\/span>\u57fa\u672c\u6982\u5ff5\u548c\u6240\u6d89\u53ca\u7684\u6570\u5b66\u77e5\u8bc6<\/span><\/b>\u3002\u4f5c\u8005\u6307\u51fa\uff0c\u7edf\u8ba1\u5b66\u662f\u5e94\u7528\u6570\u5b66\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u56e0\u6b64\u5373\u4f7f\u662f\u521d\u6b65\u7684\u5904\u7406\u4e5f\u9700\u8981\u4e00\u4e9b\u6570\u5b66\u77e5\u8bc6\u3002\u672c\u4e66\u5c06\u91cd\u70b9\u653e\u5728<\/span>\u57fa\u672c\u539f\u7406<\/span><\/b>\u4e0a\uff0c\u56e0\u6b64\u6ca1\u6709\u5c1d\u8bd5\u5904\u7406\u8d28\u91cf\u63a7\u5236\u3001\u6982\u7387\u5206\u6790\uff08<\/span>probit analysis<\/span>\uff09\u7b49\u5e94\u7528\u4e3b\u9898\u3002<\/span><\/span>\n<\/p>\n

\n\t <\/span>\n<\/p>\n

\n\t\u4e66\u4e2d\u5047\u8bbe\u7684\u6570\u5b66\u6c34\u5e73\u4e0d\u9ad8\u3002\u4f5c\u8005\u5f3a\u70c8\u5efa\u8bae\u8bfb\u8005\u8ddf\u8fdb\u8be5\u7cfb\u5217\u4e1b\u4e66\u4e2d\u963f\u535a\u7279\u5148\u751f\uff08<\/span>Mr.
\nAbbott<\/span>\uff09\u7684\u8457\u4f5c\uff0c\u5c24\u5176\u662f\u300a\u81ea\u5b66\u5fae\u79ef\u5206\u300b\uff08<\/span>Teach Yourself Calculus<\/span>\uff09\u3002\u9664\u4e86\u7b2c\u4e00\u7ae0\u5916\uff0c\u6bcf\u7ae0\u672b\u5c3e\u90fd\u9644\u6709\u4e00\u5957\u7ec3\u4e60\u9898\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u8be6\u7ec6\u7ae0\u8282\u8bc4\u8ff0<\/span><\/span>
\n<\/h2>\n

\n\t<\/a>\u7b2c<\/span> I <\/span>\u7ae0\uff1a\u521d\u6b65\u4e86\u89e3<\/span> (A FIRST LOOK AROUND)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u4f5c\u4e3a\u5f15\u8a00\u90e8\u5206\uff0c\u63a2\u8ba8\u4e86\u7edf\u8ba1\u5b66\u7684\u5b9a\u4e49\u3001\u8303\u7574\u4ee5\u53ca\u6838\u5fc3\u6982\u5ff5\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7edf\u8ba1\u5b66\u548c\u7edf\u8ba1\u6570\u636e\uff08<\/span>Statistics and Statistics<\/span><\/b>\uff09\uff1a<\/span><\/b> \u533a\u5206\u4e86<\/span>\u201c<\/span>\u7edf\u8ba1\u6570\u636e<\/span>\u201d<\/span>\uff08<\/span>Statistics<\/span>\uff0c\u590d\u6570\u7528\u6cd5\uff09\u4f5c\u4e3a\u6570\u503c\u6570\u636e\u7684\u7cfb\u7edf\u96c6\u5408\uff0c\u548c<\/span>\u201c<\/span>\u7edf\u8ba1\u5b66<\/span>\u201d<\/span>\uff08<\/span>Statistics<\/span>\uff0c\u5355\u6570\u7528\u6cd5\uff09\u4f5c\u4e3a\u6d89\u53ca\u6536\u96c6\u3001\u6574\u7406\u3001\u5206\u6790\u548c\u89e3\u91ca\u6b64\u7c7b\u6570\u636e\u4ee5\u53ca\u76f8\u5173\u4e00\u822c\u539f\u7406\u7684\u4e13\u95e8\u4eba\u7c7b\u6d3b\u52a8\u6216\u79d1\u5b66\u5206\u652f\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7edf\u8ba1\u5b66\u7684\u6f14\u53d8\uff1a<\/span><\/b> \u5f15\u7528\u4e86<\/span> A. J. Wickens <\/span>\u7684\u89c2\u70b9\uff0c\u6307\u51fa\u7edf\u8ba1\u5b66\u7684\u91cd\u70b9\u5df2\u4ece\u63cf\u8ff0\u8fc7\u53bb\uff08\u63cf\u8ff0\u6027\u7edf\u8ba1\uff0c<\/span>Descriptive
\nStatistics<\/span>\uff09\u8f6c\u53d8\u4e3a\u7528\u4e8e\u89e3\u51b3\u95ee\u9898\u548c\u5236\u5b9a\u884c\u52a8\u65b9\u6848\uff08\u4f8b\u5982\u79c1\u8425\u4f01\u4e1a\u7684\u8d28\u91cf\u63a7\u5236\u6d4b\u8bd5\u3001\u79d1\u5b66\u5b9e\u9a8c\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u53d8\u91cf\u7684\u7c7b\u578b\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u79bb\u6563\u6216\u4e0d\u8fde\u7eed\u53d8\u91cf\uff08<\/span>Discrete or Discontinuous Variable<\/span>\uff0c\u5982\u677f\u7403\u5f97\u5206\uff09\u548c\u8fde\u7eed\u53d8\u91cf\uff08<\/span>Continuous
\nVariable<\/span>\uff0c\u5982\u8dd1\u6b65\u8ddd\u79bb\uff09\u7684\u6982\u5ff5\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u63cf\u8ff0\u6027\u7edf\u8ba1\uff1a<\/span><\/b> \u8ba8\u8bba\u4e86\u6574\u7406\u548c\u603b\u7ed3\u6570\u636e\u7684\u65b9\u6cd5\uff0c\u5305\u62ec\u5217\u8868\u3001\u56fe\u8868\u5c55\u793a\uff0c\u4ee5\u53ca\u4f7f\u7528\u5355\u4e2a\u6570\u5b57\u6216\u4e00\u7ec4\u6570\u5b57\uff08\u5982\u5e73\u5747\u503c\u3001\u6700\u9ad8\u5206\uff09\u6765\u6982\u62ec\u4fe1\u606f\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u6837\u672c\u4e0e\u603b\u4f53\uff08<\/span>Samples and Populations<\/span><\/b>\uff09\uff1a<\/span><\/b> \u8fd9\u662f\u7edf\u8ba1\u5b66\u79d1\u5b66\u7684\u4e2d\u5fc3\u601d\u60f3\u4e4b\u4e00\u3002\u5b9a\u4e49\u4e86\u603b\u4f53\uff08<\/span>Population\/Universe<\/span>\uff0c\u5373\u6240\u6709\u9879\u76ee<\/span>\/<\/span>\u89c2\u6d4b\u503c\u7684\u603b\u96c6\uff09\u548c\u6837\u672c\uff08<\/span>Sample<\/span>\uff0c\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6\u51fa\u7684\u6709\u9650\u9879\u76ee\u96c6\uff09\u3002\u91cd\u70b9\u5f3a\u8c03<\/span>\u968f\u673a\u6837\u672c<\/span><\/b>\uff08<\/span>Random Sample<\/span>\uff09\u7684\u5b9a\u4e49\uff0c\u4ee5\u53ca<\/span>\u201c<\/span>\u968f\u673a<\/span>\u201d<\/span>\u4e00\u8bcd\u662f\u9650\u5b9a<\/span>\u9009\u62e9\u65b9\u6cd5<\/span><\/b>\u800c\u975e\u6837\u672c\u672c\u8eab\u7684\u7279\u6027\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7edf\u8ba1\u63a8\u65ad\uff08<\/span>Statistical Inference<\/span><\/b>\uff09\u4e0e\u6982\u7387\uff1a<\/span><\/b> \u9610\u660e\u4e86\u4ece\u6837\u672c\u6570\u636e\u5f97\u51fa\u603b\u4f53\u7ed3\u8bba\u7684\u8fc7\u7a0b\uff08\u5373\u7edf\u8ba1\u63a8\u65ad\uff09\u3002\u6307\u51fa\u6982\u7387\u6982\u5ff5\u662f\u6240\u6709\u975e\u7eaf\u7cb9\u63cf\u8ff0\u6027\u7edf\u8ba1\u7406\u8bba\u7684\u57fa\u7840\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7edf\u8ba1\u6a21\u578b\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u7edf\u8ba1\u5b66\u5bb6\u8bbe\u5b9a\u7406\u60f3\u5206\u5e03\uff08\u5982\u6807\u51c6\u5206\u5e03\uff09\u4f5c\u4e3a\u6a21\u578b\u6765\u4ee3\u8868\u603b\u4f53\u53d8\u91cf\u5206\u5e03\u7684\u8d8b\u52bf\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u663e\u8457\u6027\u68c0\u9a8c\uff08<\/span>Tests of Significance<\/span><\/b>\uff09\uff1a<\/span><\/b> \u8ba8\u8bba\u4e86\u5982\u4f55\u68c0\u9a8c\u5173\u4e8e\u603b\u4f53\u7684\u5047\u8bbe\u662f\u5426\u7ad9\u5f97\u4f4f\u811a\u3002\u6838\u5fc3\u662f<\/span>\u96f6\u5047\u8bbe<\/span><\/b>\uff08<\/span>Null Hypothesis<\/span>\uff09\uff0c\u5982\u679c\u968f\u673a\u62bd\u6837\u63d0\u4f9b\u7684\u8bc1\u636e<\/span>\u201c<\/span>\u4e0d\u5229\u4e8e<\/span>\u201d<\/span>\u8be5\u5047\u8bbe\uff0c\u5219\u5c06\u5176\u5426\u5b9a\u3002\u68c0\u9a8c\u7684\u4e25\u82db\u7a0b\u5ea6\u53d6\u51b3\u4e8e\u6240\u9009\u7684<\/span>\u663e\u8457\u6027\u6c34\u5e73<\/span><\/b>\uff08<\/span>Level of Significance<\/span>\uff09\uff0c\u901a\u5e38\u662f<\/span> 0.05 <\/span>\u6216<\/span> 0.01 <\/span>\u6c34\u5e73\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> II <\/span>\u7ae0\uff1a\u9891\u7387\u4e0e\u6982\u7387<\/span> (FREQUENCIES AND PROBABILITIES)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u6df1\u5165\u63a2\u8ba8\u4e86\u5982\u4f55\u63cf\u8ff0\u548c\u603b\u7ed3\u9891\u7387\u5206\u5e03\uff0c\u5e76\u5960\u5b9a\u4e86\u6982\u7387\u8bba\u4f5c\u4e3a\u7edf\u8ba1\u5206\u6790\u57fa\u7840\u7684\u5730\u4f4d\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u9891\u7387\u5206\u5e03\u7684\u5c55\u793a\uff1a<\/span><\/b> \u8be6\u7ec6\u4ecb\u7ecd\u4e86\u9891\u7387\u8868\uff08<\/span>Frequency Tables<\/span>\uff09\u7684\u8bbe\u7f6e\uff0c\u4ee5\u53ca\u7528\u76f4\u65b9\u56fe\uff08<\/span>Histograms<\/span>\uff09\u548c\u9891\u7387\u591a\u8fb9\u5f62\uff08<\/span>Frequency Polygons<\/span>\uff09\u8fdb\u884c\u56fe\u793a\u7684\u65b9\u6cd5\u3002\u76f4\u65b9\u56fe\u5f3a\u8c03\u5355\u5143\u683c\u7684\u9762\u79ef\u6d4b\u91cf\u9891\u7387\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7d2f\u79ef\u9891\u7387\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u7d2f\u79ef\u9891\u7387\u56fe\uff08<\/span>Cumulative Frequency Diagrams<\/span>\uff09\u548c\u7d2f\u79ef\u9891\u7387\u591a\u8fb9\u5f62\uff08<\/span>Cumulative
\nFrequency Polygon<\/span>\uff09\uff0c\u7528\u4e8e\u663e\u793a\u53d8\u91cf\u53d6\u503c\u7b49\u4e8e\u6216\u5c0f\u4e8e\u67d0\u4e00\u7ed9\u5b9a\u503c\u7684\u9891\u7387\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u4f4d\u7f6e\u7edf\u8ba1\u91cf\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u63cf\u8ff0\u5206\u5e03\u96c6\u4e2d\u8d8b\u52bf\u7684\u7edf\u8ba1\u91cf\uff1a<\/span>\u4f17\u6570<\/span><\/b>\uff08<\/span>Mode<\/span>\uff0c\u9891\u7387\u6700\u5927\u503c\uff09\u548c<\/span>\u4e2d\u4f4d\u6570<\/span><\/b>\uff08<\/span>Median<\/span>\uff0c\u5c06\u603b\u9891\u7387\u5206\u6210\u4e24\u7b49\u4efd\u7684\u503c\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u5747\u503c\uff08<\/span>The Mean<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5f3a\u8c03\u4e86\u7b97\u672f\u5e73\u5747\u503c\uff08<\/span>Mean<\/span>\uff09\u7684\u91cd\u8981\u6027\uff0c\u5e76\u89e3\u91ca\u4e86\u5b83\u5728\u76f4\u65b9\u56fe\u51e0\u4f55\u610f\u4e49\u4e0a\u662f\u8d28\u5fc3\uff08<\/span>centroid<\/span>\uff09\u7684\u6a2a\u5750\u6807\uff08<\/span>x-co-ordinate<\/span>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u79bb\u6563\u5ea6\u91cf\uff08<\/span>Measures of Spread<\/span><\/b>\uff09\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u8303\u56f4\uff08<\/span>Range<\/span>\uff09\u3001\u56db\u5206\u4f4d\u6570\uff08<\/span>Quartiles<\/span>\uff09\u3001\u56db\u5206\u4f4d\u8ddd\uff08<\/span>inter-quartile range<\/span>\uff09\u548c<\/span>\u65b9\u5dee<\/span><\/b>\uff08<\/span>Variance<\/span>\uff0c<\/span><\/span>s<\/span><\/i>2<\/span><\/i>\n<\/p>\n

\n\t\u25cf     <\/span>\u77e9\uff08<\/span>Moments<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5b9a\u4e49\u4e86\u5206\u5e03\u7684<\/span>r<\/span><\/i> <\/span>\u9636\u77e9\uff08<\/span>rth moment<\/span>\uff09\u548c<\/span>r<\/span><\/i> <\/span>\u9636\u5747\u503c\u77e9\uff08<\/span>rth mean-moment<\/span>\uff0c<\/span><\/span>m<\/span><\/i>r<\/span><\/i>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u76f8\u5bf9\u9891\u7387\u4e0e\u6982\u7387\uff1a<\/span><\/b> \u63a2\u8ba8\u4e86\u6982\u7387\u6982\u5ff5\u5982\u4f55\u6e90\u4e8e\u76f8\u5bf9\u9891\u7387\uff08<\/span>Relative Frequencies<\/span>\uff09\uff0c\u5373\u968f\u7740\u62bd\u6837\u7ee7\u7eed\uff0c\u4e8b\u4ef6\u53d1\u751f\u7684\u76f8\u5bf9\u9891\u7387\u8d8b\u4e8e\u4e00\u4e2a\u552f\u4e00\u6781\u9650\u3002\u6307\u51fa\u4e86<\/span>\u201c<\/span>\u968f\u673a<\/span>\/<\/span>\u5747\u7b49\u53ef\u80fd<\/span>\u201d<\/span>\uff08<\/span>equi-probable<\/span>\uff09\u6982\u5ff5\u5728\u6982\u7387\u5b9a\u4e49\u4e2d\u7684\u5faa\u73af\u6027\u56f0\u96be\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u6982\u7387\u7684\u57fa\u672c\u6570\u5b66\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u4e92\u8865\u4e8b\u4ef6\uff08<\/span>Complementary Events<\/span>\uff09\u3001\u4e92\u65a5\u4e8b\u4ef6\uff08<\/span>Mutually Exclusive Events<\/span>\uff09\u548c\u72ec\u7acb\u4e8b\u4ef6\uff08<\/span>Independent Events<\/span>\uff09\u7684\u6982\u7387\u8ba1\u7b97\u89c4\u5219\uff08\u52a0\u6cd5\u5b9a\u7406\u548c\u4e58\u6cd5\u5b9a\u7406\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u8fde\u7eed\u5206\u5e03\uff1a<\/span><\/b> \u5f15\u5165\u4e86\u8fde\u7eed\u53d8\u91cf\u7684<\/span>\u6982\u7387\u5bc6\u5ea6<\/span><\/b>\uff08<\/span>Probability Density<\/span>\uff09<\/span>\u03d5(x)<\/span><\/i>\uff0c\u4ee5\u53ca\u6982\u7387\u7684\u8ba1\u7b97\u6d89\u53ca\u79ef\u5206\uff08<\/span>Probability <\/span>P(alexleb)
\n =<\/span><\/i><\/span>\u222b<\/span><\/i>a<\/span><\/i>b<\/span><\/i>\u03d5(x)dx<\/span><\/i>\uff09\u3002\u5bf9\u4e8e\u8fde\u7eed\u53d8\u91cf\uff0c\u8c08\u8bba\u5b83\u53d6\u7279\u5b9a\u503c\u7684\u6982\u7387\u662f\u65e0\u610f\u4e49\u7684\uff0c\u53ea\u80fd\u8c08\u8bba\u5176\u5728\u67d0\u4e00\u533a\u95f4\u5185\u7684\u6982\u7387\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u8fde\u7eed\u6982\u7387\u5206\u5e03\u7684\u77e9\uff1a<\/span><\/b> \u5b9a\u4e49\u4e86\u8fde\u7eed\u5206\u5e03\u7684\u603b\u4f53\u53c2\u6570\uff0c\u5982\u5747\u503c<\/span>\u03bc’<\/span><\/i>\u3001\u65b9\u5dee<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i>\u3001\u504f\u5ea6<\/span><\/span>\u03bc<\/span><\/i>3<\/span><\/i>\uff08\u7528\u4e8e\u8861\u91cf\u4e0d\u5bf9\u79f0\u6027\uff09\u548c\u5cf0\u5ea6<\/span><\/span>\u03bc<\/span><\/i>4<\/span><\/i>\uff08\u7528\u4e8e\u8861\u91cf\u4e2d\u5fc3\u6241\u5e73\u7a0b\u5ea6\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u671f\u671b\uff08<\/span>Expectation<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5b9a\u4e49\u4e86\u53d8\u91cf<\/span>x<\/span><\/i> <\/span>\u7684\u671f\u671b<\/span>mathscr(x)<\/span><\/i>\uff0c\u662f\u79bb\u6563\u53d8\u91cf<\/span><\/span>x<\/span><\/i>i<\/span><\/i> <\/span>\u4e58\u4ee5\u5176\u76f8\u5e94\u6982\u7387<\/span>p(<\/span><\/i><\/span>x<\/span><\/i>i<\/span><\/i>)<\/span><\/i> <\/span>\u7684\u603b\u548c\uff0c\u4ee5\u53ca\u8fde\u7eed\u53d8\u91cf\u7684\u76f8\u5e94\u79ef\u5206\u5f62\u5f0f\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6982\u7387\u751f\u6210\u51fd\u6570\uff08<\/span>p.g.f.<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5b9a\u4e49\u4e86\u51fd\u6570<\/span>G(t)
\n =mathscr(<\/span><\/i><\/span>t<\/span><\/i>x<\/span><\/i>)<\/span><\/i>\uff0c\u5176\u6cf0\u52d2\u5c55\u5f00\u5f0f\u7684\u7cfb\u6570\u662f\u53d8\u91cf<\/span>x<\/span><\/i> <\/span>\u53d6\u7279\u5b9a\u503c\u7684\u6982\u7387\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> III <\/span>\u7ae0\uff1a\u7edf\u8ba1\u6a21\u578b<\/span> I<\/span>\uff1a\u4e8c\u9879\u5206\u5e03<\/span> (STATISTICAL MODELS. I: THE BINOMIAL
\nDISTRIBUTION)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5904\u7406\u79bb\u6563\u4e8b\u4ef6\u7684\u4e8c\u9879\u5206\u5e03\u6a21\u578b\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6a21\u578b\u57fa\u7840\uff1a<\/span><\/b> \u63a2\u8ba8\u4e86\u5728<\/span>n<\/span><\/i> <\/span>\u6b21\u72ec\u7acb\u8bd5\u9a8c\u4e2d\uff0c\u4e8b\u4ef6<\/span>E<\/span><\/i> <\/span>\u53d1\u751f<\/span>x<\/span><\/i> <\/span>\u6b21\u7684\u6982\u7387\uff0c\u5176\u4e2d<\/span>E<\/span><\/i> <\/span>\u7684\u53d1\u751f\u6982\u7387<\/span>p<\/span><\/i> <\/span>\u4fdd\u6301\u4e0d\u53d8\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u751f\u6210\u51fd\u6570\uff1a<\/span><\/b> \u8bc1\u660e\u4e86\u4e8c\u9879\u5206\u5e03\u7684\u6982\u7387\u751f\u6210\u51fd\u6570\u662f<\/span>(q+pt<\/span><\/i><\/span>)<\/span><\/i>n<\/span><\/i>\uff0c\u5176\u4e2d<\/span>q=1-p<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6027\u8d28\uff1a<\/span><\/b> \u8ba8\u8bba\u4e86\u4e8c\u9879\u5206\u5e03\u7684\u9012\u63a8\u516c\u5f0f\uff08<\/span>Recursion Formula<\/span>\uff09\u3002\u6307\u51fa\u5f53<\/span>p=q=1\/2<\/span><\/i> <\/span>\u65f6\u5206\u5e03\u5bf9\u79f0\uff0c\u5426\u5219\u504f\u659c\uff0c\u4f46\u504f\u659c\u5ea6\u968f<\/span>n<\/span><\/i> <\/span>\u589e\u52a0\u800c\u51cf\u5c0f\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u77e9\u751f\u6210\u51fd\u6570\uff08<\/span>M.G.F.<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5f15\u5165\u4e86\u77e9\u751f\u6210\u51fd\u6570<\/span>M(t)
\n =G(<\/span><\/i><\/span>e<\/span><\/i>t<\/span><\/i>)<\/span><\/i>\uff0c\u901a\u8fc7\u5bf9<\/span>M(t)<\/span><\/i> <\/span>\u6c42\u5bfc\uff0c\u63a8\u5bfc\u4e86\u4e8c\u9879\u5206\u5e03\u7684\u5747\u503c\u4e3a<\/span>\u03bc’=np<\/span><\/i>\uff0c<\/span>\u65b9\u5dee\u4e3a<\/span><\/b> <\/b><\/span>\u03bc<\/span><\/i>2<\/span><\/i>=npq<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u62df\u5408\uff1a<\/span><\/b> \u89e3\u91ca\u4e86\u5728\u7f3a\u4e4f\u5148\u9a8c<\/span>p<\/span><\/i> <\/span>\u503c\u65f6\uff0c\u5982\u4f55\u901a\u8fc7\u8ba1\u7b97\u89c2\u6d4b\u5206\u5e03\u7684\u5e73\u5747\u503c\u6765\u4f30\u8ba1<\/span>p<\/span><\/i> <\/span>\u5e76\u62df\u5408\u4e8c\u9879\u5206\u5e03\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u7d2f\u8ba1\u6982\u7387\uff1a<\/span><\/b> \u8ba8\u8bba\u4e86\u8ba1\u7b97<\/span>\u201c<\/span>\u81f3\u5c11<\/span>k<\/span><\/i> <\/span>\u6b21\u53d1\u751f<\/span>\u201d<\/span>\u7684\u6982\u7387<\/span><\/span>P<\/span><\/i>n<\/span><\/i>(xgek)<\/span><\/i>\uff0c\u5e76\u63d0\u5230\u4e86\u5f53<\/span>k<\/span><\/i> <\/span>\u548c<\/span>n<\/span><\/i> <\/span>\u8f83\u5927\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e0d\u5b8c\u5168<\/span> Beta <\/span>\u51fd\u6570\u6bd4\u7387\uff08<\/span>Incomplete Beta Function Ratio<\/span>\uff09\u8fdb\u884c\u8fd1\u4f3c\u8ba1\u7b97\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> IV <\/span>\u7ae0\uff1a\u7edf\u8ba1\u6a21\u578b<\/span> II<\/span>\uff1a\u6cca\u677e\u5206\u5e03\uff1a\u7edf\u8ba1\u7a00\u6709\u6027<\/span> (STATISTICAL MODELS. II: THE
\nPOISSON DISTRIBUTION: STATISTICAL RARITY)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u4ecb\u7ecd\u4e86\u5904\u7406\u7f55\u89c1\u4e8b\u4ef6\uff08<\/span>rare events<\/span>\uff09\u7684\u6cca\u677e\u5206\u5e03\u6a21\u578b\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u95ee\u9898\u80cc\u666f\uff1a<\/span><\/b> \u89e3\u51b3\u4e86\u50cf\u6392\u7248\u9519\u8bef\u6216\u653e\u5c04\u6027\u7c92\u5b50\u53d1\u5c04\u6b21\u6570\u8fd9\u7c7b\u95ee\u9898\uff0c\u5176\u4e2d\u4e8b\u4ef6\u53d1\u751f\u7684\u603b\u6b21\u6570<\/span>n<\/span><\/i> <\/span>\u7406\u8bba\u4e0a\u662f\u65e0\u9650\u7684\uff0c\u4f46\u5b9e\u9645\u53d1\u751f\u7684\u6b21\u6570\u662f\u6709\u9650\u7684\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6cca\u677e\u6a21\u578b\uff1a<\/span><\/b> \u6cca\u677e\u5206\u5e03\u662f\u4e8c\u9879\u5206\u5e03\u5728<\/span>n\u2192 \u221e<\/span><\/i> <\/span>\u4f46<\/span>np=m<\/span><\/i> <\/span>\u4fdd\u6301\u6709\u9650\uff08\u5373<\/span>p<\/span><\/i> <\/span>\u6781\u5c0f\uff0c\u4e8b\u4ef6\u7f55\u89c1\uff09\u65f6\u7684\u6781\u9650\u5f62\u5f0f\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6cca\u677e\u6982\u7387\uff1a<\/span><\/b> \u6cca\u677e\u5206\u5e03\u4e2d<\/span>x<\/span><\/i> <\/span>\u6b21\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u4e3a<\/span>p(x,m) =<\/span><\/i><\/span>e<\/span><\/i>-m<\/span><\/i><\/span>m<\/span><\/i>x<\/span><\/i>\/x!<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6027\u8d28\uff1a<\/span><\/b> \u63a8\u5bfc\u51fa\u6cca\u677e\u5206\u5e03\u7684<\/span>\u5747\u503c<\/span><\/b> <\/b>\u03bc=m<\/span><\/i> <\/span><\/b>\u548c\u65b9\u5dee <\/span><\/b><\/span>\u03c3<\/span><\/i>2<\/span><\/i>=m<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u8fd1\u4f3c\uff1a<\/span><\/b> \u6cca\u677e\u5206\u5e03\u53ef\u4f5c\u4e3a<\/span>p<\/span><\/i> <\/span>\u503c\u5f88\u5c0f\u4f46<\/span>n<\/span><\/i> <\/span>\u5f88\u5927\u7684\u4e8c\u9879\u5206\u5e03\u7684\u6709\u7528\u8fd1\u4f3c\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u6cca\u677e\u6982\u7387\u56fe\uff1a<\/span><\/b> \u63d0\u5230\u53ef\u4ee5\u4f7f\u7528\u6cca\u677e\u6982\u7387\u56fe\uff08<\/span>Poisson Probability Chart<\/span>\uff09\u6765\u907f\u514d\u8ba1\u7b97\u7d2f\u79ef\u6982\u7387<\/span>P(xgek,m)<\/span><\/i> <\/span>\u7684\u8fde\u7eed\u9879\u6c42\u548c\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u8d1f\u4e8c\u9879\u5206\u5e03\uff08<\/span>Negative Binomial Distribution<\/span><\/b>\uff09\uff1a<\/span><\/b> \u7b80\u8981\u63d0\u5230\u4e86\u5f53\u89c2\u6d4b\u5230\u7684\u9891\u7387\u5206\u5e03\u65b9\u5dee\u5927\u4e8e\u5e73\u5747\u503c\uff0c\u4e14<\/span>p<\/span><\/i> <\/span>\u5df2\u77e5\u4e0d\u662f\u5e38\u6570\u65f6\uff0c\u8d1f\u4e8c\u9879\u5206\u5e03\u53ef\u80fd\u63d0\u4f9b\u66f4\u597d\u7684\u62df\u5408\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> V <\/span>\u7ae0\uff1a\u7edf\u8ba1\u6a21\u578b<\/span> III<\/span>\uff1a\u6b63\u6001\u5206\u5e03<\/span> (STATISTICAL MODELS. III: THE
\nNORMAL DISTRIBUTION)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u4ecb\u7ecd\u4e86\u7edf\u8ba1\u5b66\u4e2d\u6700\u4e3a\u91cd\u8981\u7684\u8fde\u7eed\u5206\u5e03\u6a21\u578b\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u8fde\u7eed\u5206\u5e03\uff1a<\/span><\/b> \u6b63\u6001\u5206\u5e03\uff08<\/span>Normal Distribution<\/span>\uff09\u662f\u5bf9\u8fde\u7eed\u53d8\u91cf\uff08\u5982\u8eab\u9ad8\uff09\u7406\u60f3\u5316\u7684\u3001\u65e0\u9650\u603b\u4f53\u5206\u5e03\u7684\u8fd1\u4f3c\u63cf\u8ff0\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u5386\u53f2\u5730\u4f4d\uff1a<\/span><\/b> \u6b63\u6001\u5206\u5e03\u6700\u521d\u7531<\/span> de Moivre <\/span>\u53d1\u73b0\uff0c\u662f\u4e8c\u9879\u5206\u5e03\u7684\u6781\u9650\u5f62\u5f0f\u3002\u5b83\u5728\u89c2\u6d4b\u9886\u57df\u7684\u91cd\u8981\u6027\u6709\u6240\u4e0b\u964d\uff0c\u4f46\u5728<\/span>\u62bd\u6837\u7406\u8bba<\/span><\/b>\u7b49\u7406\u8bba\u9886\u57df\u7684\u91cd\u8981\u6027\u6709\u6240\u589e\u52a0\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u63a8\u5bfc\u4e0e\u51fd\u6570\uff1a<\/span><\/b> \u8be6\u7ec6\u6f14\u793a\u4e86\u6b63\u6001\u5206\u5e03\u662f\u5982\u4f55\u4ece\u4e8c\u9879\u5206\u5e03\u4e2d\u8fd1\u4f3c\u5bfc\u51fa\u7684\u3002\u6b63\u6001\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08<\/span>p.d.f.<\/span>\uff09\u4e3a<\/span>\u03d5(x)
\n =<\/span><\/i><\/span>1<\/span><\/i>\u03c3<\/span><\/i><\/span>2\u03c0<\/span><\/i>exp(-<\/span><\/i><\/span>(x-\u03bc<\/span><\/i><\/span>)<\/span><\/i>2<\/span><\/i>2<\/span><\/i><\/span>\u03c3<\/span><\/i>2<\/span><\/i>)<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6027\u8d28\uff1a<\/span><\/b> \u6b63\u6001\u5206\u5e03\u7684\u8303\u56f4\u662f<\/span>(-\u221e,
\n +\u221e)<\/span><\/i>\uff0c\u66f2\u7ebf\u662f\u5bf9\u79f0\u7684\uff08\u5747\u503c\u3001\u4e2d\u4f4d\u6570\u548c\u4f17\u6570\u91cd\u5408\uff09\uff0c\u5e76\u4e14\u6240\u6709\u5947\u6570\u9636\u7684\u5747\u503c\u77e9\u90fd\u4e3a\u96f6\u3002\u5076\u6570\u9636\u5747\u503c\u77e9<\/span><\/span>\u03bc<\/span><\/i>2r<\/span><\/i>=
\n 1 \u22c5 3 \u22c5 5dots(2r-1)<\/span><\/i><\/span>\u03c3<\/span><\/i>2r<\/span><\/i>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6982\u7387\u79ef\u5206\uff1a<\/span><\/b> \u8ba1\u7b97\u6982\u7387\u9700\u4f7f\u7528\u6982\u7387\u79ef\u5206\uff08<\/span>Probability Integral<\/span>\uff09\uff0c\u901a\u5e38\u5c06\u53d8\u91cf\u6807\u51c6\u5316\u4e3a<\/span>T=x\/\u03c3<\/span><\/i> <\/span>\u6765\u67e5\u8868\uff08\u5982\u8868<\/span> 5.4<\/span>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u79bb\u5dee\u8303\u56f4\uff1a<\/span><\/b> \u5f3a\u8c03\u4e86\u5728\u6b63\u6001\u5206\u5e03\u4e2d\uff0c\u53d8\u91cf\u504f\u79bb\u5747\u503c\u8d85\u8fc7<\/span>1\u03c3,
\n 2\u03c3, 3\u03c3<\/span><\/i> <\/span>\u7684\u6982\u7387\u5f88\u5c0f\uff0c\u4f8b\u5982\uff0c\u8d85\u8fc7<\/span>2\u03c3<\/span><\/i> <\/span>\u7684\u6982\u7387\u4ec5\u7ea6<\/span> 4.56%<\/span>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u62df\u5408\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u5982\u4f55\u901a\u8fc7\u8ba1\u7b97\u5747\u503c\u548c\u6807\u51c6\u5dee\u6765\u62df\u5408\u6b63\u6001\u66f2\u7ebf\uff0c\u4ee5\u53ca\u4f7f\u7528\u6982\u7387\u56fe\u7eb8\uff08<\/span>probability graph paper<\/span>\uff09\u6765\u786e\u5b9a\u5206\u5e03\u662f\u5426\u8fd1\u4f3c\u6b63\u6001\u5e76\u4f30\u8ba1\u53c2\u6570\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> VI <\/span>\u7ae0\uff1a\u591a\u4e8e\u4e00\u4e2a\u53d8\u91cf\uff1a\u4e8c\u5143\u5206\u5e03\u3001\u56de\u5f52\u548c\u76f8\u5173<\/span> (MORE VARIATES THAN ONE: BIVARIATE DISTRIBUTIONS, REGRESSION AND
\nCORRELATION)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u5f00\u59cb\u5904\u7406\u4e24\u4e2a\u6216\u591a\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u4e8c\u5143\u5206\u5e03\uff08<\/span>Bivariate Distributions<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5904\u7406\u4e24\u4e2a\u53d8\u91cf\uff08\u5982\u8eab\u9ad8\u548c\u4f53\u91cd\uff09\u7684\u8054\u5408\u5206\u5e03\u3002\u901a\u8fc7\u76f8\u5173\u8868\uff08<\/span>Correlation Tables<\/span>\uff09\u3001\u6563\u70b9\u56fe\uff08<\/span>Scatter Diagrams<\/span>\uff09\u3001\u7acb\u4f53\u56fe\uff08<\/span>Stereograms<\/span>\uff09\u548c\u9891\u7387\u7b49\u9ad8\u7ebf\u56fe\uff08<\/span>Frequency Contours<\/span>\uff09\u6765\u5c55\u793a\u6570\u636e\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u77e9\u548c\u534f\u65b9\u5dee\uff1a<\/span><\/b> \u5b9a\u4e49\u4e86\u4e8c\u5143\u5206\u5e03\u7684\u77e9<\/span>m<\/span><\/i><\/span>‘<\/span><\/i>rs<\/span><\/i>\uff0c\u5e76\u5f15\u5165\u4e86<\/span>\u534f\u65b9\u5dee<\/span><\/b>\uff08<\/span>Covariance<\/span>\uff0c<\/span><\/span>s<\/span><\/i>xy<\/span><\/i>\uff09\uff0c\u5b83\u8861\u91cf\u4e86<\/span>x<\/span><\/i> <\/span>\u548c<\/span>y<\/span><\/i> <\/span>\u7684\u5171\u540c\u53d8\u5316\u7a0b\u5ea6\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u56de\u5f52\uff08<\/span>Regression<\/span><\/b>\uff09\uff1a<\/span><\/b> \u63a2\u7a76\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u8054\u6027\uff0c\u7279\u522b\u662f\u5f53\u6563\u70b9\u56fe\u663e\u793a\u6570\u636e\u56f4\u7ed5\u67d0\u6761\u66f2\u7ebf\u805a\u96c6\u65f6\uff0c\u53ef\u80fd\u5b58\u5728\u51fd\u6570\u5173\u7cfb\u6216\u968f\u673a\u5173\u7cfb\uff08<\/span>stochastically related<\/span>\uff09\u3002\u56de\u5f52\u66f2\u7ebf\uff08<\/span>Regression Curves<\/span>\uff09\u63cf\u7ed8\u4e86\u4e00\u4e2a\u53d8\u91cf\u7684\u5e73\u5747\u503c\u968f\u53e6\u4e00\u4e2a\u53d8\u91cf\u53d8\u5316\u7684\u60c5\u51b5\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u7ebf\u6027\u56de\u5f52\u4e0e\u76f8\u5173\u7cfb\u6570\uff1a<\/span><\/b> \u5047\u5b9a\u56de\u5f52\u662f\u7ebf\u6027\u7684\uff0c\u4f7f\u7528<\/span>\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/span><\/b>\uff08<\/span>Method of Least Squares<\/span>\uff09\u6765\u786e\u5b9a\u6700\u4f73\u62df\u5408\u7684\u56de\u5f52\u7ebf\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6837\u672c\u79ef\u77e9\u76f8\u5173\u7cfb\u6570\uff08<\/span><\/b>r<\/span><\/i>\uff09\uff1a<\/span><\/b> r<\/span><\/i> <\/span>\u662f\u8861\u91cf\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u8d8b\u5411\u7ebf\u6027\u7684\u7a0b\u5ea6\u7684\u6307\u6807\u3002\u5f53<\/span>r= \u00b1 1<\/span><\/i> <\/span>\u65f6\uff0c\u4e3a\u5b8c\u5168\u76f8\u5173\uff08<\/span>perfectly correlated<\/span>\uff09\uff0c\u4e24\u6761\u56de\u5f52\u7ebf\u91cd\u5408\uff1b\u5f53<\/span>r= 0<\/span><\/i> <\/span>\u65f6\uff0c\u53d8\u91cf\u4e0d\u76f8\u5173\uff08<\/span>uncorrelated<\/span>\uff09\uff0c\u56de\u5f52\u7ebf\u76f8\u4e92\u5782\u76f4\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u4f30\u8ba1\u7684\u6807\u51c6\u8bef\u5dee\uff08<\/span>Standard Error of Estimate<\/span><\/b>\uff09\uff1a<\/span><\/b> <\/span>S<\/span><\/i>y<\/span><\/i>2<\/span><\/i>=<\/span><\/i><\/span>s<\/span><\/i>y<\/span><\/i>2<\/span><\/i>(1
\n –<\/span><\/i><\/span>r<\/span><\/i>2<\/span><\/i>)<\/span><\/i> <\/span>\u8fdb\u4e00\u6b65\u8bc1\u660e\u4e86<\/span>r<\/span><\/i> <\/span>\u8d8a\u63a5\u8fd1<\/span>\u00b1
\n 1<\/span><\/i>\uff0c\u89c2\u6d4b\u503c\u8d8a\u7d27\u5bc6\u5730\u805a\u96c6\u5728\u56de\u5f52\u7ebf\u5468\u56f4\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u76f8\u5173\u6bd4\u7387\uff08<\/span>Correlation Ratios, <\/span><\/b><\/span>\u03b7<\/span><\/i>yx<\/span><\/i>\uff09\uff1a<\/span><\/b> \u5f53\u56de\u5f52\u662f\u975e\u7ebf\u6027\u65f6\uff0c\u76f8\u5173\u6bd4\u7387<\/span><\/span>\u03b7<\/span><\/i>yx<\/span><\/i> <\/span>\u662f\u66f4\u5408\u9002\u7684\u5173\u8054\u5ea6\u91cf\u3002\u5b83\u603b\u662f\u6ee1\u8db3<\/span><\/span>\u03b7<\/span><\/i>yx<\/span><\/i>2<\/span><\/i>ge<\/span><\/i><\/span>r<\/span><\/i>2<\/span><\/i>\uff0c\u5176\u5dee\u503c<\/span><\/span>\u03b7<\/span><\/i>yx<\/span><\/i>2<\/span><\/i>–<\/span><\/i><\/span>r<\/span><\/i>2<\/span><\/i> <\/span>\u53ef\u4f5c\u4e3a\u56de\u5f52\u504f\u79bb\u7ebf\u6027\u7684\u7a0b\u5ea6\u7684\u521d\u6b65\u5ea6\u91cf\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u79e9\u76f8\u5173\uff08<\/span>Rank Correlation<\/span><\/b>\uff09\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u65af\u76ae\u5c14\u66fc\uff08<\/span>Spearman’s<\/span>\uff09\u7684<\/span>R<\/span><\/i> <\/span>\u548c\u80af\u5fb7\u5c14\uff08<\/span>Kendall’s<\/span>\uff09\u7684<\/span>\u03c4<\/span><\/i> <\/span>\u4e24\u79cd\u7cfb\u6570\uff0c\u7528\u4e8e\u8861\u91cf\u6839\u636e\u67d0\u4e00\u7279\u5f81\u5bf9\u4e2a\u4f53\u8fdb\u884c\u6392\u5e8f\u540e\uff0c\u4e24\u4e2a\u6392\u540d\u7684\u76f8\u4f3c\u7a0b\u5ea6\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> VII <\/span>\u7ae0\uff1a\u6837\u672c\u4e0e\u603b\u4f53<\/span> I<\/span>\uff1a\u62bd\u6837\u7406\u8bba\u57fa\u7840<\/span> (SAMPLE AND POPULATION. I: SOME
\nFUNDAMENTALS OF SAMPLING THEORY)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u8f6c\u5411\u7edf\u8ba1\u63a8\u65ad\u7684\u6838\u5fc3\u95ee\u9898\uff0c\u5373\u5982\u4f55\u4ece\u6837\u672c\u4fe1\u606f\u63a8\u65ad\u603b\u4f53\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u968f\u673a\u6027\u7684\u6982\u5ff5\uff1a<\/span><\/b> \u518d\u6b21\u5f3a\u8c03\u968f\u673a\u6027\uff08<\/span>Randomness<\/span>\uff09\u6307\u9009\u62e9\u65b9\u6cd5\uff0c\u5e76\u8ba8\u8bba\u4e86\u5b9e\u9645\u603b\u4f53\u548c\u6982\u5ff5\u603b\u4f53\u7684\u7c7b\u578b\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u62bd\u6837\u65b9\u6cd5\uff1a<\/span><\/b> \u63d0\u5230\u4e86<\/span>\u8bb0\u53f7\u62bd\u6837<\/span><\/b>\uff08<\/span>Ticket Sampling<\/span>\uff09\u548c<\/span>\u968f\u673a\u62bd\u6837\u6570<\/span><\/b>\uff08<\/span>Random Sampling
\nNumbers<\/span>\uff0c\u5982\u4f7f\u7528<\/span> Rand Corporation <\/span>\u7b49\u51fa\u7248\u7684\u6570\u8868\uff09\u6765\u6d88\u9664\u4eba\u4e3a\u504f\u89c1\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6837\u672c\u5747\u503c\u7684\u5206\u5e03\uff1a<\/span><\/b> \u8bc1\u660e\u4e86\u4e0d\u8bba\u603b\u4f53\u5982\u4f55\u5206\u5e03\uff0c\u6837\u672c\u5747\u503c<\/span>barx<\/span><\/i> <\/span>\u7684\u671f\u671b\u503c<\/span>mathscr(barx)<\/span><\/i> <\/span>\u7b49\u4e8e\u603b\u4f53\u5747\u503c<\/span>\u03bc<\/span><\/i>\u3002\u6837\u672c\u5747\u503c\u5206\u5e03\u7684\u65b9\u5dee\u662f\u603b\u4f53\u65b9\u5dee\u7684<\/span>1\/n<\/span><\/i> <\/span>\u500d\uff08<\/span><\/span>\u03c3<\/span><\/i>barx<\/span><\/i>2<\/span><\/i>=<\/span><\/i><\/span>\u03c3<\/span><\/i>2<\/span><\/i>\/n<\/span><\/i>\uff09\uff0c\u5176\u6807\u51c6\u5dee\u88ab\u79f0\u4e3a<\/span>\u5747\u503c\u7684\u6807\u51c6\u8bef\u5dee<\/span><\/b>\uff08<\/span>Standard Error of the Mean<\/span>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u5e94\u7528\uff1a<\/span><\/b> \u6307\u51fa\u5f53\u6837\u672c\u5bb9\u91cf<\/span>n<\/span><\/i> <\/span>\u8f83\u5927\u65f6\uff0c\u5373\u4f7f\u603b\u4f53\u4e0d\u4e3a\u6b63\u6001\u5206\u5e03\uff0c<\/span>barx<\/span><\/i> <\/span>\u7684\u5206\u5e03\u4e5f\u8fd1\u4f3c\u4e8e\u6b63\u6001\u5206\u5e03\u3002\u82e5\u603b\u4f53\u672c\u8eab\u662f\u6b63\u6001\u5206\u5e03\uff0c\u5219<\/span>barx<\/span><\/i> <\/span>\u7684\u5206\u5e03\u4e5f\u7cbe\u786e\u5730\u662f\u6b63\u6001\u5206\u5e03\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u81ea\u7531\u5ea6\uff1a<\/span><\/b> \u5f15\u5165\u4e86<\/span>\u81ea\u7531\u5ea6<\/span><\/b>\uff08<\/span>Degrees of Freedom<\/span>\uff09\u7684\u6982\u5ff5\uff0c\u5f53\u5bf9\u6837\u672c\u65bd\u52a0\u7ebf\u6027\u7ea6\u675f\u65b9\u7a0b\uff08\u5982\u8ba1\u7b97\u6837\u672c\u5747\u503c\uff09\u65f6\uff0c\u81ea\u7531\u5ea6\u4f1a\u51cf\u5c11\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u6837\u672c\u65b9\u5dee\uff1a<\/span><\/b> \u8bc1\u660e\u4e86\u6837\u672c\u65b9\u5dee<\/span><\/span>s<\/span><\/i>2<\/span><\/i>=<\/span><\/i><\/span><\/span><\/i>(bar<\/span><\/i><\/span>x<\/span><\/i>i<\/span><\/i>-barx<\/span><\/i><\/span>)<\/span><\/i>2<\/span><\/i>\/n<\/span><\/i> <\/span>\u662f\u603b\u4f53\u65b9\u5dee<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i> <\/span>\u7684<\/span>\u6709\u504f\u4f30\u8ba1\u91cf<\/span><\/b>\uff08<\/span>biased estimator<\/span>\uff09\u3002\u800c<\/span><\/span><\/span><\/i>(bar<\/span><\/i><\/span>x<\/span><\/i>i<\/span><\/i>-barx<\/span><\/i><\/span>)<\/span><\/i>2<\/span><\/i>\/(n-1)<\/span><\/i> <\/span>\u662f<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i> <\/span>\u7684<\/span>\u65e0\u504f\u4f30\u8ba1\u91cf<\/span><\/b>\uff08<\/span>unbiased estimator<\/span>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> VIII <\/span>\u7ae0\uff1a\u6837\u672c\u4e0e\u603b\u4f53<\/span> II<\/span>\uff1a<\/span>t<\/span>\u3001<\/span>z <\/span>\u548c<\/span> F (SAMPLE AND POPULATION. II: t, z, AND F)<\/span><\/span>
\n<\/h3>\n

\n\t\u672c\u7ae0\u5f15\u5165\u4e86\u8fdb\u884c\u7edf\u8ba1\u63a8\u65ad\u548c\u5047\u8bbe\u68c0\u9a8c\u7684\u4e09\u4e2a\u6838\u5fc3\u62bd\u6837\u5206\u5e03\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>t<\/span><\/i> <\/span><\/b>\u5206\u5e03\uff08<\/span>Student’s <\/span><\/b>t<\/span><\/i>\uff09\uff1a<\/span><\/b> \u89e3\u51b3\u4e86\u5728\u603b\u4f53\u65b9\u5dee<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i> <\/span>\u672a\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u68c0\u9a8c\u6837\u672c\u5747\u503c<\/span>barx<\/span><\/i> <\/span>\u662f\u5426\u7b26\u5408\u603b\u4f53\u5747\u503c<\/span>\u03bc<\/span><\/i> <\/span>\u7684\u95ee\u9898\u3002\u53d8\u91cf<\/span>t= (barx-\u03bc)<\/span><\/i><\/span>n-1<\/span><\/i>\/s<\/span><\/i> <\/span>\u7684\u5206\u5e03\u88ab\u79f0\u4e3a<\/span>t<\/span><\/i> <\/span>\u5206\u5e03\uff0c\u5b83\u4e0d\u4f9d\u8d56\u4e8e\u603b\u4f53\u65b9\u5dee<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i>\u3002\u968f\u7740\u81ea\u7531\u5ea6<\/span>\u03bd=n-1<\/span><\/i> <\/span>\u589e\u5927\uff0c<\/span>t<\/span><\/i> <\/span>\u5206\u5e03\u8d8b\u8fd1\u4e8e\u6b63\u6001\u5206\u5e03\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u7f6e\u4fe1\u533a\u95f4\uff08<\/span>Confidence Limits<\/span><\/b>\uff09\uff1a<\/span><\/b> \u4f7f\u7528<\/span>t<\/span><\/i> <\/span>\u5206\u5e03\u6765\u786e\u5b9a\u603b\u4f53\u5747\u503c<\/span>\u03bc<\/span><\/i> <\/span>\u5728\u7ed9\u5b9a\u6982\u7387\u4e0b\uff08\u5982<\/span> 95%<\/span>\uff09\u6240\u5904\u7684\u533a\u95f4\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>t<\/span><\/i> <\/span><\/b>\u5206\u5e03\u7684\u6269\u5c55\u5e94\u7528\uff1a<\/span><\/b> \u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528<\/span>t<\/span><\/i> <\/span>\u5206\u5e03\u6765\u68c0\u9a8c\u4e24\u4e2a\u72ec\u7acb\u6837\u672c\u7684\u5747\u503c\u662f\u5426\u5b58\u5728\u663e\u8457\u5dee\u5f02\uff08\u9700\u8981\u5148\u8ba1\u7b97\u8054\u5408\u65e0\u504f\u65b9\u5dee<\/span><\/span>\u03c3<\/span><\/i>2<\/span><\/i>\uff09\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf     <\/span>\u65b9\u5dee\u6bd4 <\/span><\/b>F<\/span><\/i> <\/span><\/b>\u68c0\u9a8c\uff08<\/span>The
\nVariance-ratio, <\/span><\/b>F<\/span><\/i>\uff09\uff1a<\/span><\/b> \u8ba8\u8bba\u4e86\u68c0\u9a8c\u4e24\u4e2a\u6837\u672c\u7684<\/span>\u65b9\u5dee<\/span><\/b>\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u663e\u8457\u5dee\u5f02\u7684\u91cd\u8981\u6027\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cb     <\/span>z<\/span><\/i> <\/span><\/b>\u5206\u5e03\uff1a<\/span><\/b> \u8d39\u5e0c\u5c14\uff08<\/span>Fisher<\/span>\uff09\u63d0\u51fa\u4e86<\/span>z=<\/span><\/i><\/span>1<\/span><\/i>2<\/span><\/i><\/span>log<\/span><\/i>e<\/span><\/i>(<\/span><\/i><\/span>\u03c3<\/span><\/i>1<\/span><\/i>2<\/span><\/i>\/<\/span><\/i><\/span>\u03c3<\/span><\/i>2<\/span><\/i>2<\/span><\/i>)<\/span><\/i> <\/span>\u7684\u5206\u5e03\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cb     <\/span>F<\/span><\/i> <\/span><\/b>\u5206\u5e03\uff1a<\/span><\/b> \u65af\u5185\u5fb7\u514b\uff08<\/span>Snedecor<\/span>\uff09\u4e3a\u4e86\u907f\u514d\u5bf9\u6570\u8ba1\u7b97\uff0c\u5c06\u65b9\u5dee\u6bd4<\/span><\/span>\u03c3<\/span><\/i>1<\/span><\/i>2<\/span><\/i>\/<\/span><\/i><\/span>\u03c3<\/span><\/i>2<\/span><\/i>2<\/span><\/i> <\/span>\u547d\u540d\u4e3a<\/span>F<\/span><\/i> <\/span>\u5206\u5e03\u3002<\/span>F<\/span><\/i> <\/span>\u5206\u5e03\u4e5f\u72ec\u7acb\u4e8e\u603b\u4f53\u65b9\u5dee\uff0c\u662f\u8fdb\u884c\u65b9\u5dee\u5206\u6790\u7684\u903b\u8f91\u57fa\u7840\u3002<\/span><\/span>\n<\/p>\n

\n\t<\/a>\u7b2c<\/span> IX <\/span>\u7ae0\uff1a\u65b9\u5dee\u5206\u6790<\/span> (ANALYSIS OF VARIANCE)<\/span><\/span>
\n<\/h3>\n

\n\t\u65b9\u5dee\u5206\u6790\uff08<\/span>ANOVA<\/span>\uff09\u662f\u4e00\u79cd\u91cd\u8981\u7684\u7edf\u8ba1\u6280\u672f\uff0c\u7528\u4e8e<\/span>\u5c06\u65b9\u5dee\u5f52\u56e0\u4e8e\u4e0d\u540c\u539f\u56e0\u7ec4<\/span><\/b>\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u95ee\u9898\u6838\u5fc3\uff1a<\/span><\/b> \u65e8\u5728\u5206\u89e3\u603b\u65b9\u5dee\uff0c\u4ee5\u68c0\u9a8c\u4e00\u4e2a\u6216\u591a\u4e2a\u5206\u7c7b\u56e0\u7d20\uff08\u5982\u725b\u7684\u54c1\u79cd\u3001\u9972\u6599\u79cd\u7c7b\uff09\u662f\u5426\u5bf9\u53d8\u91cf\u503c\uff08\u5982\u4ea7\u5976\u91cf\uff09\u6709\u663e\u8457\u5f71\u54cd\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u5355\u56e0\u7d20\u5206\u7c7b\uff08<\/span>One Criterion of Classification<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5c06\u603b\u53d8\u5f02\u5206\u89e3\u4e3a<\/span>\u7ec4\u95f4\u53d8\u5f02<\/span><\/b>\uff08<\/span>Variation between classes<\/span>\uff09\u548c<\/span>\u7ec4\u5185\u53d8\u5f02<\/span><\/b>\uff08<\/span>Variation
\nwithin classes<\/span>\uff09\u3002\u901a\u8fc7\u96f6\u5047\u8bbe\uff08\u5206\u7c7b\u56e0\u7d20\u65e0\u6548\uff09\u53ef\u4ee5\u4ece\u8fd9\u4e24\u4e2a\u53d8\u5f02\u6e90\u83b7\u5f97\u4e24\u4e2a\u72ec\u7acb\u7684\u3001\u65e0\u504f\u7684\u603b\u4f53\u65b9\u5dee\u4f30\u8ba1\u91cf\u3002\u5982\u679c\u7ec4\u95f4\u53d8\u5f02\u7684\u4f30\u8ba1\u91cf\u663e\u8457\u5927\u4e8e\u7ec4\u5185\u53d8\u5f02\u7684\u4f30\u8ba1\u91cf\uff08\u901a\u8fc7<\/span>F<\/span><\/i> <\/span>\u68c0\u9a8c\uff09\uff0c\u5219\u5426\u5b9a\u96f6\u5047\u8bbe\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u53cc\u56e0\u7d20\u5206\u7c7b\uff08<\/span>Two Criteria of Classification<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5c06\u53d8\u5f02\u5206\u89e3\u4e3a<\/span> A <\/span>\u56e0\u7d20\u95f4\u3001<\/span>B <\/span>\u56e0\u7d20\u95f4\u548c\u6b8b\u4f59\uff08<\/span>Residual<\/span>\uff09\u4e09\u4e2a\u90e8\u5206\u3002\u5206\u6790\u8868\u63d0\u4f9b\u4e86\u68c0\u9a8c<\/span><\/span>Q<\/span><\/i>A<\/span><\/i>\/<\/span><\/i><\/span>Q<\/span><\/i>residual<\/span><\/i> <\/span>\u548c<\/span><\/span>Q<\/span><\/i>B<\/span><\/i>\/<\/span><\/i><\/span>Q<\/span><\/i>residual<\/span><\/i> <\/span>\u7684<\/span>F<\/span><\/i> <\/span>\u68c0\u9a8c\u6b65\u9aa4\u3002<\/span><\/span>\n<\/p>\n

\n\t\u25cf       <\/span>\u4ea4\u4e92\u4f5c\u7528\uff08<\/span>Interaction<\/span><\/b>\uff09\uff1a<\/span><\/b> \u5728\u4e09\u56e0\u7d20\u6216\u66f4\u591a\u56e0\u7d20\u5206\u7c7b\u4e2d\u5f15\u5165\u4e86<\/span>\u201c<\/span>\u4ea4\u4e92\u4f5c\u7528<\/span>\u201d<\/span>\u7684\u6982\u5ff5\u3002\u4ea4\u4e92\u4f5c\u7528\u6307\u7684\u662f\u4e24\u4e2a\u6216\u591a\u4e2a\u56e0\u7d20\u5171\u540c\u4f5c\u7528\u65f6\u5bf9\u53d8\u91cf\u503c\u7684\u5f71\u54cd\uff0c\u5373\u4f7f\u5355\u72ec\u7684\u56e0\u7d20\u53ef\u80fd\u6ca1\u6709\u5f71\u54cd\u3002\u5982\u679c\u4ea4\u4e92\u4f5c\u7528\u7684\u65b9\u5dee\u4f30\u8ba1\u91cf\u663e\u8457\uff0c\u5219\u6709\u7406\u7531\u6000\u7591\u96f6\u5047\u8bbe\u3002<\/span><\/span>\n<\/p>\n

\n\t <\/span>\n<\/p>\n

\n\t
\n<\/span>\n<\/p>\n

\n\t
\n<\/span>\n<\/p>\n

\n\t