第7章-离散型数据的χ2检验-.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第,7,章离散型数据的,2,检验,7.1,一般原理,一、,2,分布,设,X,N,(0,1),，又设,X,1,X,2,X,n,是,X,的一个样本，它的平方和记作,称,2,服从参数为,n,的,2,分布，记为,2,2,(,n,),如果,二、,Pearson,定理,设,k,为离散型数据的分组数目，,O,i,表示第,i,组的观察数,(,频数,),，,T,i,表示第,i,组理论数，,p,i,表示第,i,组的理论频率，,n,为总观察数 则有,随着,n,的增加，下式,近似地服从自由度为,k,-1,的,2,分布。,说明,1,k,组数据只有,k,-1,项是独立的,7.2,拟合优度检验,1,遗传杂交试验：实验数据是否符合理论分离比例,【,例,7.1】,P,黄,满,绿,皱,F,1,黄,满,(,自交,),F,2,黄,满,黄,皱,绿,满,绿,皱,315 101 108 32,Y_R_,Y_rr,yyR,_,yyrr,1,遗传杂交试验：实验数据是否符合理论分离比例,【7.1,解,】N,558,F,2,表型,Y_R_,Y_rr,yyR,_,yyrr,实际观察数,O,315 101 108 32,理论频率,p,9/16 3/16,3/16,1/16,理论预期数,T,312.75 104.25,104.25,34.75,0.016 0.101 0.135 0.218,2,0.016+0.101+0.135+0.218,0.470,说明,2,H,0,:,O,i,-,T,i,=0,单尾检验，时拒绝,H,0,df,4,1,3,，,结论：接受,H,0,1,遗传杂交试验：实验数据是否符合理论分离比例,说明,3,当,df,=1,时，应做连续性矫正,【,例,7.2】,F,2,表型 正常翅,残翅,实际观察数,O,311 81,理论预期数,T,294 98,0.926 2.778,2,0.926+2.778,3.704,df,2,1,1,，,结论：接受,H,0,说明,4,O,i,，,T,i,分别为实际频数和理论频数，而不是频率和理论频率说明,5,注意“,n,要足够大，以及,np,i,不太小”这两个条件,实际计算时，,n50,，,np,i,T,i,5,，,T,i,10,说明,6,当总体参数未知，需估计理论参数时，应做自由度矫正,如果被估计的总体参数为,r,个，则,df,=k-r-1,2,检验实验数据是否服从二项分布或,Poisson,分布,【,例,】,调查到幼儿园接小孩的家长性别，以,10,人为一组，记录每组女性人数，共调查,100,组数据,女性家长分布类型的推断,女性人数,观测数,理论频率,理论数,（,x,i,）,（,O,i,）,0,0,1,0,2,0,3,4,4,14,5,22,6,27,7,19,8,9,9,5,10,0,女性家长分布类型的推断,女性人数,观测数,理论频率,理论数,（,x,i,）,（,O,i,）,p(x,i,),T,i,Np(x,i,),0,0,0.0001,0.01,1,0,0.0019,0.19,0.810,2,0,0.0125,1.25,3,4,0.0480,4.80,4,14,0.1209,12.09,0.302,5,22,0.2087,20.87,0.061,6,27,0.2503,25.03,0.155,7,19,0.2058,20.58,0.121,8,9,0.1111,11.11,9,5,0.0355,3.55,0.090,10,0,0.0051,0.51,4,6.25,1415.17,女性家长分布类型的推断,女性人数,观测数,理论频率,理论数,（,x,i,）,（,O,i,）,p(x,i,),T,i,Np(x,i,),0,0,0.0001,0.01,1,0,0.0019,0.19,0.810,2,0,0.0125,1.25,3,4,0.0480,4.80,4,14,0.1209,12.09,0.302,5,22,0.2087,20.87,0.061,6,27,0.2503,25.03,0.155,7,19,0.2058,20.58,0.121,8,9,0.1111,11.11,9,5,0.0355,3.55,0.090,10,0,0.0051,0.51,5,6.25,14,15.17,3,对连续型数据的吻合度检验,表,1-2“,三尺三株高测量结果,155,153,159,155,150,159,157,159,151,152,159,158,153,153,144,156,150,157,160,150,150,150,160,156,160,155,160,151,157,155,159,161,156,141,156,145,156,153,158,161,157,149,153,153,155,162,154,152,162,155,161,159,161,156,162,151,152,154,157,162,158,155,153,151,157,156,153,147,158,155,148,163,156,163,154,158,152,163,158,154,164,155,156,158,164,148,164,154,157,165,158,166,154,154,157,167,157,159,170,158,表,1-3“,三尺三株高的频数分布统计,组 限,频数,P(LXU),理论数,139.5,-,142.5,1,0.00307,0.307,142.5,-,145.5,2,0.01320,1.320,145.5,-,148.5,3,0.04611,4.611,0.0090,148.5,-,151.5,10,0.11321,11.321,0.1541,151.5,-,154.5,19,0.19529,19.529,0.0144,154.5,-,157.5,27,0.23680,23.680,0.4655,157.5,-,160.5,20,0.20183,20.183,0.0017,160.5,-,163.5,11,0.12091,12.091,0.0984,163.5,-,166.5,5,0.05090,5.090,0.1321,166.5,-,169.5,1,0.01505,1.505,169.5,-,172.5,1,0.00363,0.363,总计,100,1.000,100,0.8751,6,7,6959,6.238,2=,表,1-3“,三尺三株高的频数分布统计,组 限,频数,P(LXU),理论数,139.5,-,142.5,1,0.00307,0.307,142.5,-,145.5,2,0.01320,1.320,145.5,-,148.5,3,0.04611,4.611,0.0090,148.5,-,151.5,10,0.11321,11.321,0.1541,151.5,-,154.5,19,0.19529,19.529,0.0144,154.5,-,157.5,27,0.23680,23.680,0.4655,157.5,-,160.5,20,0.20183,20.183,0.0017,160.5,-,163.5,11,0.12091,12.091,0.0984,163.5,-,166.5,5,0.05090,5.090,0.1321,166.5,-,169.5,1,0.01505,1.505,169.5,-,172.5,1,0.00363,0.363,总计,100,1.000,100,0.8751,6,7,6.959,6.238,2=,7.3,独立性检验,一、原理,例,7.3,不同给药方式与给药效果的,22,列联表,问题：,不同的处理（给药方式）的效果是否一样,给药方式,有效,(,A),无效,总数,有效率,口服,(B),58,40,98,59,.,2%,注射,6431,95,67,.,4%,总数,122,71,193,一、原理,不同的处理（给药方式）的效果一样,两个处理的有效率相等,A,和,B,相互独立,(,或称,A,和,B,无关联,),P(AB)=P(A)P(B),处理方式有差异,处理和疗效有关,A,和,B,不独立,给药,方式,有效,(,A),无效,总数,有效率,口服,(B),58,40,98,59,.,2%,注射,64,31,95,67,.,4%,总数,122,71,193,不同给药方式与给药效果的,22,列联表,二、,22,列联表,2,检验,给药方式,有效,(,A),无效,总数,口服,(B),O,1,=58,O,2,=40,98,注射,O,3,64,O,4,=31,95,总数,122,71,193,T,1,=61.95,T,2,=36.05,T,3,=60.05,T,4,=34.95,二、,22,列联表,2,检验,给药方式,有效,(,A),无效,总数,口服,(B),O,1,=58,O,2,=40,98,注射,O,3,=64,O,4,=31,95,总数,122,71,193,T,1,=61.95,T,2,=36.05,T,1,=60.05,T,1,=34.95,校正？,三、注意事项,1,rc,列联表,rc,k,组数,估计参数,(r-1)+(c-1),df,=rc-(r-1)+(c-1)-1,=rc-r+1-c+1-1,=r(c-1)-(c-1),=(c-1)(r-1),三、注意事项,2,理论频数不能小于,5,3,当,df,=1,时，值应矫正,4,解题步骤：,或,计算理论频数,求,求,结论,第,7,章 结 束,