在Matlab中实现Levene方差齐性检验

在Matlab中实现Levene方差齐性检验盛经纬[e-mail]方差齐性检验在SPSS的独立样本t检验中作为方差齐性的检验方法，该模型由Levene在1960年提出。其统计值得计算方法为：212111ikiiiNkijiijNkNZZWkZZ其中k为样本组数，iN为第i组的样本含量，N为全部各组样本之和，ijZ为将原始数据转换后的新的变量的对应值，iZ为第i组的样本组内均值，Z为全部各组的总平均值。在SPSS中ijZ的计算方法为ijijiZYY在组间样本数不等的情况下编写的双样本Levene方差检验Matlab函数leven_test2程序：function[h,p,ci]=levene_test2(x,y)[e-mail]2013.11.24%toShawna%useageformat[h,p,ci]=levene_test2(x,y)%LeveveVarianceTestbyLevenein1960%usedinSPSSindependentttest%kisthenumberofgroups%xandyshouldbecolumnvector%xandycouldnotbethesamesize%thenullhypothesisisthatthevarianceishomogeneousk=2;%numberofgroupsalpha=0.05;%confidencedim=1;%tail=-1;%defaultleft-tailedtest:whenvarianceofxislessthanvarianceofy[mx,nx]=size(x);[my,ny]=size(y);NN=mx+my;N=[mx;my];clearmxmynxnyxmean=mean(x);ymean=mean(y);z1=abs(x-xmean);%newgroupxz2=abs(y-ymean);%newgroupyz1mean=mean(z1);z2mean=mean(z2);z_ave=(sum(z1)+sum(z2))/NN;SS1=N(1)*(z1mean-z_ave)^2+N(2)*(z2mean-z_ave)^2;%acrossgroupsSS2=var(z1,0,1)*(N(1)-1)+var(z2,0,1)*(N(2)-1);%innergroupsW=((NN-k)*SS1)/((k-1)*SS2);df1=k-1;df2=NN-k;%DOFp=fcdf(W,df1,df2);%iftail==-1%left-tailedtestp=1-p;%ifthisp0.05,thennormaltwosamplet-testcannotbeappliedh=cast(p=0.05,class(p));ci=cat(dim,zeros(size(W)),...W./finv(alpha,df1,df2));clearz1z2SS1SS2z_aveNNNxmeanymeanz1meanz2meanxyalphak%%iftail==0%two-tailedtest%p=2*min(fcdf(F,df1,df2),fpval(F,df1,df2));%ci=cat(dim,F.*finv(alpha/2,df2,df1),...%==F./finv(1-alpha/2,df1,df2)%F./finv(alpha/2,df1,df2));%end%%iftail==1%rightone-tailedtest%p=fpval(F,df1,df2);%ci=cat(dim,F.*finv(alpha,df2,df1),...%==F./finv(1-alpha,df1,df2)%Inf(size(F)));%endend鉴于检查方差齐性只是看组间方差小于组内方差的显著性，故默认使用left-tailedtest。如有相关需要也可在程序中直接修改。