单因素方差分析的MATLAB实现

单因素均衡数据的实现

单因素非均衡数据方差分析

p192 8.22

 X=[85,80,90,88,87,94,56,62,55,48,92,99,95,91,75,72,81];group=[ones(1,3),2*ones(1,4),3*ones(1,2),4*ones(1,2),5*ones(1,4),6*ones(1,3)];anova1(X,group);

从箱线图可以看到第2个第五个离盒子中心线较远，效果较为突出

按计算公式计算得

 close all;clear all;clc x1=[87,85,80];x2=[90,88,87,94];x3=[56,62];x4=[55,48];x5=[92,99,95,91];x6=[75,72,81];X=[x1,x2,x3,x4,x5,x6];ni=[length(x1),length(x2),length(x3),length(x4),length(x5),length(x6)];
%  length(X)ti=[sum(x1),sum(x2),sum(x3),sum(x4),sum(x5),sum(x6)]; q1=sum(ti);a=6;n=length(X);q2=sum(X.^2);st=q2-q1^2/n;sa=sum(ti.^2./ni)-q1^2/n;se=st-sa;

 

p214 8

 close all;clear all;clc x=[21.8,21.9,21.7,21.6,21.7,21.7,21.4,21.5,21.4,22.9,22.8,22.8,22.6,22.5,21.9,21.7,21.8,21.4];group=[ones(1,5),2*ones(1,4),3*ones(1,5),4*ones(1,4)];[p,table,stats]=anova1(x,group)p =5.4118e-08table =4×6 cell 数组'Source'    'SS'        'df'    'MS'        'F'          'Prob>F'    'Groups'    [4.2450]    [ 3]    [1.4150]    [55.0278]    [5.4118e-08]'Error'     [0.3600]    [14]    [0.0257]           []              []'Total'     [4.6050]    [17]          []           []              []stats = 包含以下字段的 struct:gnames: {4×1 cell}n: [5 4 5 4]source: 'anova1'means: [21.7400 21.5000 22.7200 21.7000]df: 14s: 0.1604

 d=multcompare(stats)d =组序号'    '组序号'  '置信下限' '置信上限'  '组均值差' '置信上限'   1.0000    2.0000   -0.0727    0.2400    0.5527    0.16261.0000    3.0000   -1.2748   -0.9800   -0.6852    0.00001.0000    4.0000   -0.2727    0.0400    0.3527    0.98172.0000    3.0000   -1.5327   -1.2200   -0.9073    0.00002.0000    4.0000   -0.5296   -0.2000    0.1296    0.33003.0000    4.0000    0.7073    1.0200    1.3327    0.0000

可以看出第三组和第四组 【0.7073,1.0200】区间不包括0，说明在显著性水平0.05下，两组间均值的差异是显著的 

这篇文章也介绍的很详细https://blog.csdn.net/matlab_matlab/article/details/57076854