1、【例2】整群抽样也整群抽样也是多阶段抽样的前提和基是多阶段抽样的前提和基础。础。ijYijyiMMMMMN.21NiiMM10MijiYY1jMjijiyy1MYYiiMyyiiNiiNYY1niinyy1MYY Myy 2110211NiMjijYYMS211122111NiiNiMjibYYNMYYNS211211NiiijMjwYYMNS211211NiijMjyynMs2121niibyynMs211211niiijMjwyyMns总体ANOVA（方差分析）表-群规模相等的整群抽样NiijYYSSB121NiiijjYYSSW121NiijMjYYSST121)1(122MNSSWSN
2、SSBSwb12NMSSTSniiniMjijynnMyy1111yyYYMYyE)(y2121)(111)(bNiiSnMfYYNnfyVyMy yVMNYYnfyVNii2121)(1)(1)(1)(122NYYnMfyVNii)1()(112NMYYnMfNii21bSnMfYNMY)()()()()(2222yvMNYvyVMNyNMVYVyNMY)(yV21)(bsnMfyv2)()(YYEYYYYEijikij分子可写成:2)1()(1MNMYYYYNiMkjikij2MNC2121)(SMNNMNMyYNiMkjij21)1)(1()(2SNMMYYYYNiMkjikijy)1(
3、11)1(1)1(11111)(111)(1)(22221122122 MSnMfMSNMNMnfYYNMnfYYNnMfyVMyVNiMjijNii（当N-1=N，NM-1=NM时）)1(11111222211221121 MSNMSMNMSNMYYYYYYYYYYNiMjMkjikijijNiMjijNiiy21)(SnMfyVsrs)1(1)()(MyVyVdeffsrs)1(1 M2wS2bS2222)1(wbwbsMsss21)1)(1()(2SNMMYYYYNiMkjikij212)1(1NiibYYNMS)1(11221MSNMYYNii22)1()1()1(1SNMSNMMb2
4、22)1)(1()1()1(SNMMSNMSNMb（1）222)1(SMSSb211211NiMjijYYNMS2221112211211)1(wbNiMjiijNiiNiMjijSMNSNYYYYMYYSNM（2）（3）总离差的分解群间方差群内方差)1(11222NSMNSNMSwb22221)1(1SSSNMNMSww（4）2221111wbSMNSNNMS（5）2bS2bs2wS2ws22222111111wbwbsMsMsMNsNNMS N很大时 （6）2222)1(wbwbsMsss10iY11M1,11M 当当 1时，时，deffM 当当 0时，时，deff1 当当 为负时，为负时
5、，deff1 群内方差为群内方差为0 0群间方差为群间方差为0 0群内方差大于群内方差大于总体方差相等总体方差相等ijyYiy2is)(17.98833.93.897511元niiyny6648.928)17.9833.93(.)17.9875(186122212NiibyynMs3423.4)()(8558.186648.928680254.011)(2yvyssnMfyvb置信区间:68.10666.89)3423.4(96.117.98，即79.220)87.527.6.2336.125(811)(11111122112112 niiMjiijniniiijMjwsnyyMnyyMns3
6、48256.079.220)16(6648.92879.2206648.928)1(2222wbwbsMsss1874.268deffnMnsrsiyiy18.14186)38.21838.258()38.218188(1128)(1)(38.2181238.2585.1801881221221niibniiyynMsyny元013.123.144)()(3.14418.141868120235.011)(2yvyssnMfyvb元元，93.24183.194)013.12(96.138.218Y18.141862bs68.1431)52.4398.1719.27(121)(1)(111)()
7、1(1222112211122见表最后一列MjniiiijniniMjiijwsnyyMnyyMns527.068.1431)18(18.1418668.143118.14186)1(2222wbwbsMsss689.4527.0)18(1)1(1Mdeffsrsn)(207.4128户deffMnnsrsY)(11111 niMjiijniiiMynynyY的方差估计为:niiyynnfyv12)()1(11)(当群Mi规模不等时，有不同的抽取方法和估计方法此法特点1.估计量 是有偏的2.操作简便，易于掌握和使用3.适用条件，群之间的规模差异不大时yiyyNMMNii1y0111MYNMNy
8、MyyMnMnyMyniiniii如果总体平均规模 未知,可以用样本平均规模 代替.MnMmnii1yMY00MniiynNY11)()1()(122NYYnfNYVNii1)()1()(122nyynfNYvnii1)()1()(1)(1220220NYYnMfNYVMYVNiiYy与niiniiMyy11niiniiMyMyMY1100 NiiiRXYNXnfRV122111 111)(11222212NYYMMnfNMYYMnfyVNiiiNiii 111222NYYMnfNYVNiii对比 RVYy与iYiMiYiY YVyV与 的样本估计分别为：nininiiiiiniiiyMyMy
9、ynMnfnyMyMnfyv1112222122211111及 niiniiiniiniiiyMyMyynnfNnyMynfNYv1122122122211111iiiMyy iM平均每个村的产量为：)(262.1103882.1.4667.111万公斤niiynyyMY0=726*1.262=916.212（万公斤）（万公斤）万公斤1.31)()()(19.966110)262.13882.1.()262.14667.1(103310172611)1(222212020YvYsyynnfMyvMYvnii)(43.848)6.23.0.22(10331公斤niiynNY)(71.2511万公
10、斤niiyny)(9.1567657.2010)697.0(33112122万公斤nyynfNYvnii)(6.39)()(万公斤YvYs)(08.8932091.257726110万公斤niiniiMyMY)(8.687061.910697.033112122万公斤nyMynfNYvniii)(2.26)()(万公斤YvYsiMiYiYiX)(85.87789401.2573052511万公斤RXxyXYniiniiniiMyy2)()(84.12791578.1510697.033112122万公斤nxRynfNYvniii)(3.11)()(万公斤YvYsniixRy2)()(02.2)
11、320057901910416021004320(3111天niiynyiM（天）0356.0)()1(1)(21niiyynnyv378.002.20356.096.102.2若估计全企业因病假而损失的人日:则5970209)0356.0(12950)()(2615902.2129502200yvMYvyMY478926159597020996.126159pnyynii1其他具有某种性质,0,1iy总体比例的无偏估计:niiniiAnMpnp11111)(1)(12NPPnfpVNii其无偏估计为:niippnnfpv12)()1(1)(二二、群规模不等时的估计、群规模不等时的估计niin
12、iiMAP111)(11)(1)(1222122NPPMMnfNPMAMnfpVNiiiNiii1)2(11)(1)(12121222122nMApMpAMnfnpMAMnfpvniniiiiniiniii为总体中群的平均规模,若未知,可用样本值 替代.NiiMNM11m其中:477.01517211niiniiMAp04.62515111niiMnm046.0477.0125729.12)04.6(2594.011)2(1)(212121222nMApMpAmnfpvniniiiinii046.0477.000055.096.1477.000156.0)523.0)(477.0(115194
13、.0111)(pqnfpvsrs353.000156.000055.0)()(pvpvdeffsrs04.6M128.0353.0)104.6(1)1(1deffM2110211NiMjijYYMS211122111NiiNiMjibYYNMYYNS211211NiiijMjwYYMNSniiniMjijynnMyy111121)(bsnMfyv)1(1)()(MyVyVdeffsrs2222)1(wbwbsMsss)(11111niMjiijniiiMynynyniiyynnfyv12)()1(11)(0MYMyy1)()1()(122nyynfNYvniiniiniiMyy11 nininiiiiiniiiyMyMyynMnfnyMyMnfyv1112222122211111统计学
