统计学原理第七抽章样调查ppt课件

1、1,第七章,抽样调查,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,2,第一节 抽样调查的基本概念及理论依据,一、估计量和估计值 二、全及总体和抽样总体 三、全及指标和样本指标

2、四、抽样方式和样本可能数目 五、抽样理论依据,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,3,一、估计量和估计值,1. 估计量：是指用于估计相关的总体参数的统计量。样本均值、样

3、本比例（样本成数）和样本方差都是估计量，估计量是随机的。 2. 估计值：是指估计量的具体数值。根据具体样本数据，按照估计量的计算公式，计算出的样本均值、样本比例和样本方差的具体数值就是估计值。是抽样推断的基础。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0

4、.0. Copyright 2004-2011 Aspose Pty Ltd.,4,二、全及总体和抽样总体,1. 全及总体（总体）：是指所要认识对象的全体，是同一性质的许多个体的集合体。有变量总体与属性总体之分，全及总体是惟一的、确定的但却是未知的，常用“N”表示。 2. 抽样总体（样本）：是从全及总体中随机抽取出来一部分单位的集合体。有大样本和小样本之分，以30个样本单位为划分依据。 样本总体是随机的、已知的，常用“n”表示。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Co

5、pyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,5,三、全及指标和样本指标,（一） 全及指标 根据全体总体各个单位的标志值或标志特征计算的、反映总体某种属性的综合指标。全及指标也是惟一确定的，但也是未知的。 1. 总体平均数：根据变量总体的标志值计算的。,Evaluation only. Created with Aspose.Slides f

6、or .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,6,2. 总体成数（总体比例）：常用“P”表示,是指总体中具有某种标志的单位数在总体中所占的比重。变量总体也可以计算成数。,具有某种属性的单位数,总体单位总数,总体成数,不具有某种属性的单位数,不具有某种属性的单位数所占的

7、比重,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,7,3. 总体标准差和总体方差2,都是测量总体标志值分散程度的指标。,（二）抽样指标 是指根据抽样总体各个标志值或标志特征计算

8、的综合指标。与全及指标相对应也有抽样平均数、抽样成数、样本标准差和样本方差等估计量。抽样指标是随机的。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,8,1. 样本平均数：,2.

9、 样本成数数：,3. 样本标准差 和样本方差：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,9,四、抽样方式和样本可能数目,（一）抽样方式 1. 重复抽样（放回抽样）：从总体N

10、中随机抽取n个单位，每次抽取均为独立试验。 2. 不重复抽样（不放回抽样）：每次抽中的单位不再放回总体中，为不独立试验。 3. 考虑顺序抽样：即考虑总体单位的性质，还考虑各单位排序的抽样。 4. 不考虑顺序抽样：只考虑总体单位的性质差异，而不考虑其排序的抽样。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET

11、 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,10,（二）样本可能数目,是指从既定的总体中可以抽取多少个样本，即样本总体的数量有多少。 1. 考虑顺序的不重复抽样可能数目 即不重复排列的可能样本数目。计算公式：,设：N=10，n=5，则： ANn =109876=30240个可能样本数目,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty L

12、td.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,11,2. 考虑顺序的重复抽样可能数目,即可重复排列的可能样本数目。公式： BNn=Nn =105 =100000个可能样本数目 3. 不考虑顺序的不重复抽样可能数目 即不重复组合。计算公式：,!,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .

13、 Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,12,4. 不考虑顺序的重复抽样可能数目,即可重复组合。计算公式： DNn=CnN+n-1,对于同一总体，采用四种不同的抽样组织形式，其样本可能数目也是不同的。按样本可能数目的多少排序依次是：考虑顺序的重复抽样考虑顺序的不重复抽样不考虑顺序的重复抽样不考虑顺序的不重复抽样,Evaluatio

14、n only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,13,五、抽样理论依据,抽样调查的理论依据是概率论的大数定律。 （一）大数定律 1. 独立同分布大数定律：证明当n足够大时，平均数具有稳定性，为用样本

15、平均数估计总体平均数提供了理论依据。 2. 贝努力大数定律：证明当n足够大时，频率具有稳定性，为用频率代替概率提供了理论依据。大数的重要意义P253,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose

16、Pty Ltd.,14,（二）中心极限定律,1. 独立同分布中心极限定理：证明不论变量总体服从何种分布，只要它的数学期望和方差存在，从中抽取容量为n 的样本，则这个样本的总和或平均数是个随机变量，当n 充分大时，样本的总和或平均数趋于正态分布. 2. 德莫佛-拉普拉斯中心极限定理：证明属性总体的样本成数和样本方差，在n足够大时，同样趋于正态分布。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluati

17、on only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,15,第二节 抽样平均误差,一、抽样平均误差的概念 二、影响抽样平均误差的因素 三、抽样平均误差的意义 四、抽样平均误差的计算,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation

18、 only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,16,一、抽样平均误差的概念,（一）抽样误差 是指样本指标和总体指标之间在数量上的差别，是随机性的代表性误差。是抽样推断的依据，不包括登记误差和可能产生的偏差。 （二）抽样平均误差 是指所有可能出现的样本指标的标准差，即所有可能出现的样本指标和总体指标的平均离差。抽样实际误差无法知道，而平均误差是可能计算的。,Evaluation only. Created with Aspose.

19、Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,17,二、影响抽样平均误差的因素,（一）总体标志的变动程度（x ） 总体标志的变动程度与抽样平均误差成同向变动关系。 （二）抽样单位数（n）的多少 在其他条件不变的情况下，抽样单位数与抽样平均误差成反向变动

20、关系。 （三）抽样组织方式 重复抽样方式的高于不重复抽样，分类抽样的低于机械抽样或整群抽样。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,18,三、抽样平均误差的意义,抽样平均

21、误差是一种标准差的概念，是所有可能样本指标与总体指标之间离差平方的平均数的平方根。它概括了一系列抽样可能结果所产生的所有抽样误差。它有三点意义： 1. 是衡量抽样指标对于总体指标代表性程度的一个尺度； 2. 是计算极限误差的依据； 3. 是确定抽样单位数多少的计算依据之一,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides fo

22、r .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,19, 四、抽样平均误差的计算,（一）抽样平均数的抽样平均误差x 是变量总体一系列抽样平均数对总体平均数的标准差。其理论计算公式：,平均数抽样平均误差,样本平均数（随机变量）,总体平均数（惟一确定的，但通常是未知的）,样本可能数目,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty L

23、td.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,20,1. 重复抽样抽样平均数的抽样平均误差x,根据数理统计理论，在重复抽样方式下，抽样平均误差与全及总体的标准差成正比关系，而与抽样总体单位数的平方根成反比关系，可推导出如下公式：,平均数抽样平均误差,全及总体的标准差,抽样单位数,抽样平均误差仅为全及总体标准差的,注意理解P259例题,重要,Evaluation only. Created with A

24、spose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,21,2. 不重复抽样抽样平均数的抽样平均误差x,不重复抽样与重复抽样相比，样本可能数目减少，且样本变量之间不是互相独立的。因此，在重复抽样的基础上考虑一个修正系数即可。证明过程见P261-26

25、2,总体单位总数,样本单位总数,抽样比例,总体标准差,重要,重要,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,22,（一）抽样成数的抽样平均误差p,属性总体的标志值是用文字表示

26、的，且标志只有两个取值，非此即彼，故将属性总体的标志称为“交替标志”或“是非标志”。 交替标志也可以计算平均数（即成数）和标准差。为了计算交替标志的平均数和标准差必须将交替变异的标志过渡到数量标志。 交替标志仍以x表示，设：x =1表示单位具有某一标志， x = 0表示单位不具有某一标志。具有某一标志的单位数用N1表示；,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Crea

27、ted with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,23,不具有某一标志的单位数用N0表示。,总体成数和标准差与样本成数和标准差的计算方法相同。只是总体指标用大写字母表示，样本指标用小写字母表示。例如： 具有某一标志的单位数占总体的比重：,总体成数,样本成数,不具有某一标志的单位数占总体的比重：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .

28、Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,24,交替标志的平均数和标准差计算表P265,样本成数,属性总体抽样平均误差的计算也有重复抽样和不重复抽样之分：,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright

29、 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,25,1. 重复抽样抽样成数的抽样平均误差,2. 不重复抽样抽样成数的抽样平均误差,样本成数,样本单位数,总体单位总数,抽样比例,解决未知的总体指标的4点办法：P263,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile

30、 . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,26,1. 用过去调查所得到的资料。如果有几个不同的总体方差，应该用数值较大的。 谨慎性要求。2越大，说明总体的离散程度越高，要抽取更多的样本单位（n）才具有代表性。 2. 用样本方差代替总体方差2（） 3. 用小规模调查资料计算的方差代替2 4. 用估计材料计算的方差代替

31、2,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,27,（三）抽样平均误差计算实例P266,Evaluation only. Created with Aspose.Slides

32、 for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,28,样本平均数,样本成数,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004

33、-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,29,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slid

34、es for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,30,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Asp

35、ose Pty Ltd.,31,第三节 全及指标的推断,一、全及指标的点估计 二、全及指标的区间估计,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,32,一、全及指标的点估计,（

36、一）点估计的概念 点估计又称定值估计，它是直接以样本指标作为相应总体指标的估计量。 例如，以样本平均数直接估计总体平均数，即：x=X。例如，某地区根据样本资料计算的粮食亩产量为600公斤，就以600公斤作为全地区粮食亩产水平的估计值。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client P

37、rofile . Copyright 2004-2011 Aspose Pty Ltd.,33,（二）点估计的优缺点,1. 优点：点估计能够提供总体指标的具体数值，可以作为行动决策的数量依据。例如，企业的市场部门对产品销量的预测直接决定着生产部门和采购部门的作业计划。 2. 缺点：任何点估计的结果不是对就是错，并不能提供误差情况和误差程度等相关的信息。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd

38、.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,34,（三）点估计量的评价标准,估计一个总体指标可以用多种样本统计量，例如估计总体平均数，可以用样本平均数，也可以用样本中位数、样本众数等。具体应以哪一个统计量来估计总体平均数才是最优的，就涉及估计量的评价标准问题。 一个优良的估计量应该符合以下三个标准：,Evaluation only. Created with Aspose.Slides for .NET

39、 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,35,1. 无偏性。即样本统计量的期望值（平均数）等于被估计的总体平均数。 2. 一致性。即当样本单位数n充分大时，样本统计量也充分靠近总体参数（指标）。 3. 有效性。即作为优良估计量的方差应该比其他估计量的方差小。 同时具备上述条件

40、的估计量就是优良的,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,36, 二、全及指标的区间估计,（一）区间估计的概念 区间估计是在点估计的基础上，给出在一定的置信程度下，确定总

41、体指标取值区间的方法和过程。 （二）置信区间（抽样极限误差） 是根据概率理论，以一定的可靠程度保证抽样误差不超过某一事先给定的范围。这一范围是抽样指标与全及指标之间离差的可能范围。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2

42、004-2011 Aspose Pty Ltd.,37,设：x 与p分别表示抽样平均数与抽样成数的置信区间（抽样极限误差），则：,将上式中的绝对值符合去掉并进行变换：,抽样调查的目的是用样本指标来估计总体指标，而不是用总体指标来估计样本指标,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Clien

43、t Profile . Copyright 2004-2011 Aspose Pty Ltd.,38,全及指标X、P的区间估计公式：,（三）置信程度（可信赖程度或把握程度） 置信程度是用概率来表示的。极限误差与抽样平均误差是什么关系？是单位误差，极限误差是的若干倍。这里的倍数通常用 t来表示。t称概率度，它是以为尺度来衡量的相对误差范围，在数理统计中称为置信度,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty

44、 Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,39,置信程度（概率）与概率度是什么关系？,数理统计证明，概率与概率度是一种函数关系，即概率是概率度的函数。用P表示概率用以说明抽样估计的可靠程度，其函数关系式:,用占正态分布曲线面积的大小表示,3,0.6827 of Area,0.02275 of area,2,0.02275 of area,-1,1,-3,-2,0.9545 of Area,0.

45、9973 of Area,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,40,概率与概率度对照表,举例：教材P321，第1题。 （1）计算该厂全部灯泡平均耐用时间的取值范围（概率

46、保证程度0.9973）。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,41,Evaluation only. Created with Aspose.Slides for .N

47、ET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,42,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty L

48、td.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,43,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Cl

49、ient Profile . Copyright 2004-2011 Aspose Pty Ltd.,44,（2）检查500个灯泡中不合格产品占0.4%试在0.6827概率保证下，估计全部产品不合格率的取值范围。 已知：p = 0.4% , t = 1,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .

50、NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,45,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty

51、Ltd.,46,教材P323，第3题,不合格率=15250=6%，t=1，t=2,（1）t=1时，,（2）t=2时，,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,47,第四节

52、抽样组织形式,一、简单随机抽样 二、类型抽样 三、机械抽样 四、整群抽样,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,48,一、简单随机抽样（纯随机抽样）,是指对总体不作任何分

53、类、排队处理，从总体的全部单位中随机抽选样本单位的方法。 抽样方法：1. 直接抽选法； 2. 抽签法； 3. 随机数码表法（乱码表法）。 适用范围：1. 对调查对象了解很少； 2. 总体单位的排列没有秩序； 3. 抽到的单位比较分散时也不影 响调查工作。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.

54、5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,49,二、类型抽样（分类抽样）,是先对总体单位按一定标志进行分类，然后再从各类别中按照随机原则抽取一定比例的样本，由各类样本组成一个总样本的方法。 类型抽样有3方面作用： 1. 利用已知的信息提高抽样效率，增强样本对总体的代表性。 2. 便于组织、开展抽样工作。 3. 便于掌握总体中各个组成部分的情况。,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copy

55、right 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,50,（一）类型比例抽样法抽样单位数的确定,不考虑各类别间标志的差异程度，按照统一的抽样比例确定各类别要抽取的单位数。通常用各类别的单位数占总体单位数的比例来确定各类别应抽取的单位数。计算公式：,样本单位总数,各类别单位总数,总体单位总数,各类别抽取的单位数,例题见教材P279,Evaluation

56、only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,51,（二）类型适宜抽样法抽样单位数的确定,对于标志变动程度大的类别，抽取样本单位数的比例相应要大一些，反之，对于标志变动程度小的类别，抽取样本单位数的比

57、例相应要小一些。具体计算公式：,各类别抽取的单位数,样本单位总数,各类别单位总数,各类别标准差,例题见教材P280,各类别的全距,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,5

58、2,（三）类型比例抽样抽样误差的计算,类型比例抽样的方差由各类内部方差和类间方差构成，由于类型抽样的代表性很高，类间方差很小，可以忽略，因此，类型比例抽样的误差主要取决于各类内部方差的平均数的大小。 各类平均数内部方差的平均数,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profi

59、le . Copyright 2004-2011 Aspose Pty Ltd.,53,各类成数内部方差的平均数,各类别成数的内部方差,1. 重复抽样方式下类型抽样平均误差的计算,平均数抽样平均误差,成数抽样平均误差,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,54,2. 不重复抽样方式下类型抽样平均误差的计算,平均数抽样平均误差,成数抽样平均误差,Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.,Eva