Statistics for Laboratory Scientists ( 140.615 )

Analysis of Variance - Nested Models - Advanced

Example from class: mosquitos

library(SPH.140.615)
summary(mosq)

##      length      individual cage 
##  Min.   :49.30   1:6        A:8  
##  1st Qu.:58.25   2:6        B:8  
##  Median :67.05   3:6        C:8  
##  Mean   :66.63   4:6             
##  3rd Qu.:72.03                   
##  Max.   :84.00

The nested ANOVA.

mosq.aov <- aov(length ~ cage / individual, data=mosq)
nested.anova(mosq.aov)

## Analysis of Variance Table
## 
## Response: length
##                 Df  Sum Sq Mean Sq  F value    Pr(>F)    
## cage             2  665.68  332.84   1.7409    0.2295    
## cage:individual  9 1720.68  191.19 146.8781 6.981e-11 ***
## Residuals       12   15.62    1.30                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

What happens when we use the average of the two measurements for each mosquito?

aves <- tapply(mosq$length, list(mosq$individual, mosq$cage), mean)
aves

##       A     B     C
## 1 59.00 69.80 57.05
## 2 79.35 55.25 78.50
## 3 83.80 50.00 69.55
## 4 69.20 64.80 63.30

aves <- as.numeric(aves) 
aves

##  [1] 59.00 79.35 83.80 69.20 69.80 55.25 50.00 64.80 57.05 78.50 69.55 63.30

cage <- factor(rep(c("A","B","C"), each=4))
cage

##  [1] A A A A B B B B C C C C
## Levels: A B C

anova(aov(aves ~ cage))

## Analysis of Variance Table
## 
## Response: aves
##           Df Sum Sq Mean Sq F value Pr(>F)
## cage       2 332.84 166.419  1.7409 0.2295
## Residuals  9 860.34  95.593

What happens when we ignore the cages, and just do the ANOVA with individual mosquitos as the groups?

ind <- factor(paste(as.character(mosq$cage), as.character(mosq$ind), sep=":"))
ind

##  [1] A:1 A:1 A:2 A:2 A:3 A:3 A:4 A:4 B:1 B:1 B:2 B:2 B:3 B:3 B:4 B:4 C:1 C:1 C:2 C:2 C:3 C:3 C:4 C:4
## Levels: A:1 A:2 A:3 A:4 B:1 B:2 B:3 B:4 C:1 C:2 C:3 C:4

anova(aov(mosq$length ~ ind))

## Analysis of Variance Table
## 
## Response: mosq$length
##           Df  Sum Sq Mean Sq F value    Pr(>F)    
## ind       11 2386.35 216.941  166.66 2.329e-11 ***
## Residuals 12   15.62   1.302                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

What happens when we ignore the individual mosquitoes, and just do the ANOVA with the cages as the groups?

anova(aov(length ~ cage, data=mosq))

## Analysis of Variance Table
## 
## Response: length
##           Df  Sum Sq Mean Sq F value  Pr(>F)  
## cage       2  665.68  332.84  4.0256 0.03312 *
## Residuals 21 1736.30   82.68                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1