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

#### Statistics for Laboratory Scientists ( 140.615 )

## Analysis of Variance - Multiple Comparisons

#### Example from class: pea sections and sugar

The data.

```{r}
x <- c(75,67,70,75,65,71,67,67,76,68,
       57,58,60,59,62,60,60,57,59,61,
       58,61,56,58,57,56,61,60,57,58,
       58,59,58,61,57,56,58,57,57,59,
       62,66,65,63,64,62,65,65,62,67)
treat <- factor(rep(c("C","G","F","G+F","S"), rep(10,5)))
sugar <- data.frame(rsp=x, trt=treat)
head(sugar)
str(sugar)
summary(sugar)
```

Plot the data.

```{r}
set.seed(1)
par(las=1)
stripchart(sugar$rsp ~ sugar$trt, method="jitter", pch=1, xlab="response", ylab="group")
```

Analysis of variance.

```{r}
aov.out <- aov(rsp ~ trt, data=sugar)
summary(aov.out)
```

Tukey's HSD

```{r}
sugar.tukey <- TukeyHSD(aov.out)
par(las=1)
plot(sugar.tukey)
abline(v=0, lty=2, col="red")
sugar.tukey
```

Bonferroni corrected confidence intervals (a customized function), based on a pooled estimate of the within-group standard deviation. 

```{r}
library(devtools)
devtools::install_github("bllfrg/SPH.140.615",quiet=TRUE)
library(SPH.140.615)
sugar.bonf <- ci.bonf(sugar$rsp, sugar$trt)
sugar.bonf
```

An alternative built-in function to get Bonferroni corrected pairwise comparisons p-values, based on a pooled estimate of the within-group standard deviation. 

```{r}
pairwise.t.test(sugar$rsp, sugar$trt, p.adjust="bonf")
```

The Newman-Keuls procedure, using a customized function.

```{r}
newman.keuls(sugar$rsp, sugar$trt)
```