計算ANOVA用手

Question

我嘗試使用下面的代碼來計算SSB和SSW「手動」：

> data.soy  
protein amount 
1 cereal  5 
2 cereal  17 
3 cereal  12 
4 cereal  10 
5 cereal  4 
6 energy  19 
7 energy  10 
8 energy  9 
9 energy  7 
10 energy  5 
11 veggie  25 
12 veggie  15 
13 veggie  12 
14 veggie  9 
15 veggie  8 

> soy.fit<-lm(amount~protein, data=data.soy) 
> anova(soy.fit) 

Analysis of Variance Table 

Response: amount 
      Df Sum Sq Mean Sq F value Pr(>F) 
protein 3 55.53 18.511 0.4916 0.6953 
Residuals 11 414.20 37.655  
> n1<-length(cereal) 
> n1 
[1] 5 
> n2<-length(energy) 
> n2 
[1] 5 
> n3<-length(veggy) 
> n3 
[1] 5 
> m<-mean((cereal+energy)+(cereal+veggy)) 
> m 
[1] 43 
> s<-sd((cereal+energy)+(cereal+veggy)) 
> s 
[1] 15.11622 
> m1<-mean(cereal) 
> m1 
[1] 9.6 
> m2<-mean(energy) 

> m2 
[1] 10 
> m3<-mean(veggy) 
> m3 
[1] 13.8 
> overallm<-(((n1*m1)+(n2*m2)+(n3*m3))/(n1+n2+n3)) 
> overallm 
[1] 11.13333 
> SSB<-((n1*(m1-overallm)^2)+(n2*(m2-overallm)^2)+(n3*(m3-overallm)^2)) 
> SSB  
[1] 53.73333 

但是，當我使用anova()功能檢查了我的答案，它說55.53。我做錯了什麼，或者是一個四捨五入的問題或什麼？

Answer 1

anova不是，有趣的是，在爲R.方差分析的最簡單或者最直觀的功能你要aov，或者更可能的這種情況下，oneway.test：

使用oneway.test（默認情況下假定方差相等）：

> oneway.test(amount ~ protein, data=data.soy) 

     One-way analysis of means (not assuming equal variances) 

data: amount and protein 
F = 0.6117, num df = 2.000, denom df = 7.913, p-value = 0.5662 

使用aov：

> aov(amount ~ protein, data=data.soy) 
Call: 
    aov(formula = amount ~ protein, data = data.soy) 

Terms: 
       protein Residuals 
Sum of Squares 53.7333 416.0000 
Deg. of Freedom  2  12 

Residual standard error: 5.887841 
Estimated effects may be unbalanced 

> summary(aov(amount ~ protein, data=data.soy)) 
      Df Sum Sq Mean Sq F value Pr(>F) 
protein  2 53.7 26.87 0.775 0.482 
Residuals 12 416.0 34.67 

這是相同oneway.test設置var.equal=TRUE：

> oneway.test(amount ~ protein, data=data.soy, var.equal=TRUE) 

     One-way analysis of means 

data: amount and protein 
F = 0.775, num df = 2, denom df = 12, p-value = 0.4824 

或做你與lm和anova做的：

> anova(lm(amount ~ protein, data=data.soy)) 
Analysis of Variance Table 

Response: amount 
      Df Sum Sq Mean Sq F value Pr(>F) 
protein 2 53.73 26.867 0.775 0.4824 
Residuals 12 416.00 34.667