```{r setup, include=FALSE}
knitr::opts_chunk$set(echo=TRUE, fig.align="center")
```

#### Statistics for Laboratory Scientists ( 140.615 )

## Analysis of Variance - Nested Models - Advanced

#### Example from class: mosquitos

```{r}
library(SPH.140.615)
summary(mosq)
```

The nested ANOVA.

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

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

```{r}
aves <- tapply(mosq$length, list(mosq$individual, mosq$cage), mean)
aves
aves <- as.numeric(aves) 
aves
cage <- factor(rep(c("A","B","C"), each=4))
cage
anova(aov(aves ~ cage))
```

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

```{r}
ind <- factor(paste(as.character(mosq$cage), as.character(mosq$ind), sep=":"))
ind
anova(aov(mosq$length ~ ind))
```

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

```{r}
anova(aov(length ~ cage, data=mosq))
```
