双因素方差分析

1.双因素方差分析基本思想

双因素方差分析：顾名思义就是同时研究两个因素对实验结果影响是否显著的分析，分析的结果可能只有一个因素显著、也可能两个因素都显著或者都不显著。

双因素方差分析的前提同单因素方差分析一样，是建立在三项假定的基础上进行的：

1.样本数据符合正态分布；

2.样本数据满足方差齐性要求；

3.数据之间相互独立。

2.双因素方差分析R语言实例

data('ToothGrowth')
head(ToothGrowth)

##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5

table(ToothGrowth$supp,ToothGrowth$dose)

##     
##      0.5  1  2
##   OJ  10 10 10
##   VC  10 10 10

shapiro.test(ToothGrowth$len)

## 
##  Shapiro-Wilk normality test
## 
## data:  ToothGrowth$len
## W = 0.96743, p-value = 0.1091

attach(ToothGrowth)
fangcha <- aov(len~supp*dose)
summary(fangcha)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## supp         1  205.4   205.4  12.317 0.000894 ***
## dose         1 2224.3  2224.3 133.415  < 2e-16 ***
## supp:dose    1   88.9    88.9   5.333 0.024631 *  
## Residuals   56  933.6    16.7                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

结果可视化1

attach(ToothGrowth)

## The following objects are masked from ToothGrowth (pos = 3):
## 
##     dose, len, supp

interaction.plot(dose,supp,len)

结果可视化2

library(gplots) 

## 
## Attaching package: 'gplots'

## The following object is masked from 'package:stats':
## 
##     lowess

attach(ToothGrowth)

## The following objects are masked from ToothGrowth (pos = 4):
## 
##     dose, len, supp

## The following objects are masked from ToothGrowth (pos = 5):
## 
##     dose, len, supp

plotmeans(len ~ interaction(dose, supp, sep = ""))

结果可视化3

library(HH) 

## Loading required package: lattice

## Loading required package: grid

## Loading required package: latticeExtra

## Loading required package: multcomp

## Loading required package: mvtnorm

## Loading required package: survival

## Loading required package: TH.data

## Loading required package: MASS

## 
## Attaching package: 'TH.data'

## The following object is masked from 'package:MASS':
## 
##     geyser

## Loading required package: gridExtra

## 
## Attaching package: 'HH'

## The following object is masked from 'package:gplots':
## 
##     residplot

interaction2wt(len ~ dose*supp,data=ToothGrowth) 

4.参考文章

《R语言实战》（中文版），人民邮电出版社，2013.

视频《R语言与高级医学统计学》.