[教育]應(yīng)用統(tǒng)計(jì)方法第一章數(shù)理統(tǒng)計(jì)基本概念

1、2024/3/26,1,應(yīng)用統(tǒng)計(jì)方法電子教案,開(kāi)課系：數(shù)理系對(duì)象：工科研究生學(xué)時(shí)：48授課教師：李曉童Email：moonlane2009@126.com電話(huà)：89734591,2024/3/26,2,參考書(shū):,吳翊等 國(guó)防大學(xué)出版社1995高惠璇,北京大學(xué)出版社 2001梅長(zhǎng)林等 西安交通大學(xué)出版社 2002,2024/3/26,3,考核方式,閉卷考試(50%)+課程論文(40%)+考勤（10%）,2024/3/26,4

2、,主要內(nèi)容,數(shù)理統(tǒng)計(jì)基礎(chǔ)--抽樣分布,參數(shù)估計(jì),假設(shè)檢驗(yàn)回歸分析方差分析多元分析的基本概念多元正態(tài)的參數(shù)估計(jì)與假設(shè)檢驗(yàn)主成分分析判別分析聚類(lèi)分析因子分析,2024/3/26,5,chapter1 數(shù)理統(tǒng)計(jì)基本概念 (Basic Concept of Mathematical Statistics),2024/3/26,6,數(shù)理統(tǒng)計(jì)學(xué)是數(shù)學(xué)的重要分支．它研究怎樣有效得收集，整理和分析帶有隨機(jī)性的數(shù)據(jù)，以對(duì)所考察的

3、問(wèn)題作出推斷和預(yù)測(cè)，直到采取一定的決策和行動(dòng)提供依據(jù)和建議．統(tǒng)計(jì)學(xué)：去掉帶有隨機(jī)性．也是數(shù)據(jù)科學(xué)數(shù)理統(tǒng)計(jì)和統(tǒng)計(jì)學(xué)的區(qū)別：,2024/3/26,7,那里有受隨機(jī)性影響的數(shù)據(jù),那里就有數(shù)理統(tǒng)計(jì)的問(wèn)題,教育學(xué)醫(yī)學(xué)環(huán)境科學(xué)氣象，地質(zhì)，考古，服裝工業(yè)經(jīng)濟(jì)學(xué)社會(huì)學(xué),心理學(xué)農(nóng)業(yè)文學(xué)．．．．．,2024/3/26,8,例１如何估計(jì)產(chǎn)品的壽命？－－工業(yè)管理極重要的問(wèn)題，因?yàn)閴勖鼘?shí)驗(yàn)是破壞性的，只能抽取少量產(chǎn)品做試驗(yàn)．為評(píng)價(jià)這批電子產(chǎn)品的

4、使用壽命，隨機(jī)抽?。保概_(tái)作試驗(yàn)，測(cè)得壽命數(shù)據(jù)為（小時(shí)）：?。保罚。玻?，５０，６８，１００，１３０，１４０，?。玻罚?，２８０，３４０，４１０，４５０，５２０，?。叮玻?，１９０，２１０，８００，１１００．　問(wèn)整批電子設(shè)備中壽命超過(guò)２００小時(shí)的占多大比例？?。▍?shù)估計(jì)問(wèn)題）,2024/3/26,9,例２　某針織廠(chǎng)進(jìn)行技術(shù)革新，漂白工藝過(guò)程中，要考慮溫度對(duì)針織品斷裂強(qiáng)力（主要質(zhì)量指標(biāo)）的影響，為了比較70°C,80

5、6;C 影響有無(wú)差異，在兩個(gè)溫度下做了８次試驗(yàn)：70:20.5,18.8,19.8,20.9,21.5,19.5,21.0,21.280:17.7,20.3,20.0,18.8,19.0,20.1,20.2,19.1.問(wèn)這兩種溫度下強(qiáng)力有無(wú)差別?(假設(shè)檢驗(yàn)問(wèn)題),這1公斤差別是由什么引起?隨機(jī)誤差?溫度的不同?,2024/3/26,10,例3.為探討吸煙與慢性支氣管炎是否有關(guān),調(diào)查了339人問(wèn)從這批數(shù)據(jù)能否判定

6、患慢性支氣管炎與吸煙有關(guān)?(列聯(lián)表的獨(dú)立性),2024/3/26,11,§1.1 樣本和總體(Sample and Population)§1.2 直方圖與經(jīng)驗(yàn)分布函數(shù)(Histogram and Empirical Distribution Function)§1.3 統(tǒng)計(jì)量及其分布(Statistic and Distribution),2024/3/26,12,§1.1 樣本

7、和總體 (Sample and Population),2024/3/26,13,2024/3/26,14,2024/3/26,15,2024/3/26,16,2024/3/26,17,2024/3/26,18,2024/3/26,19,2024/3/26,20,2024/3/26,21,2024/3/26,22,2024/3/26,23,2024/3/26,24,2024/3/26,25,2024/3/26,26,20

8、24/3/26,27,§1.2 直方圖與經(jīng)驗(yàn)分布函數(shù)Histogram and Empirical Distribution Function),2024/3/26,28,2024/3/26,29,2024/3/26,30,2024/3/26,31,2024/3/26,32,2024/3/26,33,2024/3/26,34,data wh100; input h w @@; if w50.3 and w54

9、.1 and w57.9 and w61.7 and w65.5 and w69.3 and w=73.2'; wgroup=int((w-46.5)*8/(77-46.5)-0.001)+1; cards;,2024/3/26,35,172.4 75.0 169.3 54.8 169.3 64.0 171.4 64.8 166.5 47.4 171.4 62.2168.2 66.9 165.1 52.0 16

10、8.8 62.2 167.8 65.0 165.8 62.2 167.8 65.0164.4 58.7 169.9 57.5 164.9 63.5 160.3 55.2 175.0 66.6 172.5 73.5172.0 64.0 168.4 57.0 155.0 57.0 175.5 63.9 172.3 69.0 168.6 58.0176.4 56.9 173.2 57.5 167.5 50.0 169.4 52.2 16

11、6.7 72.0 169.5 57.0165.7 55.4 161.2 48.5 172.8 57.0 175.1 75.5 157.5 50.5 169.8 62.9168.6 63.4 172.6 61.0 163.8 58.5 165.1 61.5 166.7 52.5 170.9 61.0166.1 69.5 166.2 62.5 172.4 52.6 172.8 60.0 177.8 63.9 162.7 56.816

12、8.8 54.0 169.1 66.2 177.5 60.0 177.0 66.2 169.9 55.9 167.4 54.4169.3 58.4 172.8 72.8 169.8 58.0 160.0 65.3 179.1 62.2 172.3 49.8163.3 46.5 172.9 66.7 165.4 58.0 175.8 63.2 162.3 52.2 165.4 65.7171.5 59.3 176.6 66.3 18

13、1.7 68.6 175.2 74.9 169.5 59.5 169.6 61.5169.1 63.1 185.5 77.0 173.9 65.5 162.5 50.0 171.5 58.5 175.6 59.8166.0 75.5 167.2 63.3 171.9 57.0 176.6 58.4 177.3 67.0 169.2 71.8166.2 49.8 181.7 63.0 175.8 68.3 172.3 55.5 17

14、2.7 58.5 174.3 64.0171.2 59.0 174.8 68.0 165.4 55.5 169.1 64.8 167.9 62.0 176.8 64.0183.5 69.9 165.5 48.6 171.0 70.5 170.3 58.5,2024/3/26,36,proc print data=wh100;run;proc freq data=wh100; tables wc ; /* tables w

15、group; */ title '100名學(xué)生的體重分為8個(gè)組的頻數(shù)表';run;proc chart data=wh100; vbar w / midpoints=48 to 76 by 4; title '對(duì)學(xué)生體重?cái)?shù)據(jù)使用選項(xiàng)MIDPOINT=產(chǎn)生的條形圖';run;proc chart data=wh100; vbar wgroup / discrete;

16、 /* vbar wc / discrete; */ title '把輸出1.2.1的頻數(shù)表用條形圖表示';run;proc univariate data=wh100 plot; var w;run;,2024/3/26,37,100名學(xué)生的體重分為8個(gè)組的頻數(shù)表 3

17、 12:45 Thursday, February 18, 2009 The FREQ Procedure Cumulative Cumulative

18、 wc Frequency Percent Frequency Percent -------------------------------------------------------------- =73.2 6 6.00

19、 100 100.00,2024/3/26,38,The UNIVARIATE Procedure Variable: w Stem Leaf # Boxplot

20、 76 0 1 | 74 9055 4 | 72 085

21、 3 | 70 58 2 | 68 036059

22、 6 | 66 2236790 7 | 64 00008800357 11 +- -- --+

23、 62 022225901234599 15 | | 60 000055 6 *- + --* 58 0004455

24、5570358 14 | | 56 890000055 9 +--- - -+ 54 04824559 8

25、 | 52 02256 5 | 50 005 3 |

26、 48 5688 4 | 46 54 2 | - ---+---

27、-+-- - -+--- -+,2024/3/26,39,五數(shù)概括與箱線(xiàn)圖----次序統(tǒng)計(jì)量的應(yīng)用之一,2024/3/26,40,做法,做法:1 畫(huà)一個(gè)箱子,其兩側(cè)恰為第一4分位數(shù)和第三4分位數(shù),在中位數(shù)位置上畫(huà)一豎線(xiàn),它在箱子內(nèi),這個(gè)箱子包含了樣本中50%的數(shù)據(jù).2 在箱子左右兩側(cè)各引一條水平線(xiàn),分別至最小值和最大值為止.個(gè)線(xiàn)段包含了樣本的25%的數(shù)據(jù).,2024/3/26,41,二 莖葉圖:每個(gè)數(shù)值分為兩部分,前面一部分(百位,

28、十位)稱(chēng)為莖,后面部分(個(gè)位)稱(chēng)為葉. 如: 數(shù)值 分開(kāi) 莖 葉 112 12|2 11 2 然后畫(huà)一豎線(xiàn),在豎線(xiàn)的左側(cè)寫(xiě)上莖,右側(cè)寫(xiě)上葉.就形成了莖葉圖. 647 7024669 8012333566779 911233335667791000246678811224

29、68991223568133,,2024/3/26,42,要比較兩組樣本時(shí),可畫(huà)出它們的背靠背的莖葉圖.這是簡(jiǎn)單,直觀而有效的對(duì)比方法.例2.下面的數(shù)據(jù)是某廠(chǎng)車(chē)間某天40名員工生產(chǎn)的產(chǎn)品的數(shù)量. 甲車(chē)間 62056 乙車(chē)間 87775554211667788 8776644217224555

30、5666889 8766532801133344466778 73210922358 5300107,,,2024/3/26,43,2024/3/26,44,2024/3/26,45,2024/3/26,46,2024/3/26,47,2024/3/26,48,

31、7;1.3 統(tǒng)計(jì)量及其分布(Statistic and Distribution),2024/3/26,49,2024/3/26,50,data Money50;input w @@;cards;924 800 916 704 870 1040 824 690 574 490 972 988 1266 684 764 940 408 804 610 892 602 754 788 962 704 712 854 888

32、768 848 882 1192 820 878 614 846 746 828 792 872 696 644 926 808 1010 728 742 850 864 738;proc print data=Money50; var w;proc means data=Money50; var w;proc univariate data=Money50 plot;var w;run;,2024/3/26,5

33、1,The MEANS Procedure Analysis Variable : w N Mean Std Dev Minimum Maximum -------------------------------------

34、----------------------------- 50 810.3200000 156.1738226 408.0000000 1266.00 ------------------------------------------------------------------,Stem Leaf

35、 # Boxplot 12 7 1 0 12 11 9 1 0

36、 11 10 10 14 2 | 9 679 3 |

37、 9 2234 4 | 8 55556778899 11 +-----+ 8 001223 6 *--+--*

38、 7 556799 6 | | 7 0001344 7 +-----+ 6 89 2 |

39、 6 0114 4 | 5 7 1 | 5 |

40、 4 9 1 | 4 1 1 0 ----+----+----+----+ Mul

41、tiply Stem.Leaf by 10**+2,2024/3/26,52,,Stem Leaf # Boxplot 12 7 1 0 12

42、 11 9 1 0 11 10 10 14 2 |

43、 9 679 3 | 9 2234 4 | 8 55556778899 11 +-----+

44、 8 001223 6 *--+--* 7 556799 6 | | 7 0001344 7

45、+-----+ 6 89 2 | 6 0114 4 | 5 7

46、 1 | 5 | 4 9 1 |

47、 4 1 1 0 ----+----+----+----+ Multiply Stem.Leaf by 10**+2,2024/3/26,53,The SAS System 13:47 Saturday, February 20,

48、2009 22 The UNIVARIATE Procedure Variable: w Moments N

49、 50 Sum Weights 50 Mean 810.32 Sum Observations 40516 Std Deviation 156.173823 Variance 24390.2629

50、 Skewness 0.2322891 Kurtosis 1.40426379 Uncorrected SS 34026048 Corrected SS 1195122.88 Coeff Variation 19.2731048 Std Error Mean 22

51、.0863138 Basic Statistical Measures Location Variability Mean 810.3200 Std Deviation 156.17382

52、 Median 814.0000 Variance 24390 Mode 704.0000 Range 858.00000 Interquartile Range

53、176.00000,2024/3/26,54,2024/3/26,55,2024/3/26,56,2024/3/26,57,2024/3/26,58,2024/3/26,59,2024/3/26,60,2024/3/26,61,2024/3/26,62,2024/3/26,63,2024/3/26,64,2024/3/26,65,2024/3/26,66,2024/3/26,67,2024/3/26,68,2024/3/26,69,20