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

#### Statistics for Laboratory Scientists ( 140.615 )

## Correlation

#### Example from class: fathers' and daughters' heights

The Pearson & Lee (1906) data.

```{r}
library(SPH.140.615)
example(pear)
```

Plot the data.

```{r}
plot(pear)
```

Calculate the sample means and the sample standard deviations of the fathers' and daughters' heights.

```{r}
mes <- apply(pear, 2, mean)
mes
sds <- apply(pear, 2, sd)
sds
```

Calculate the Pearson correlation between the fathers' and daughters' heights.

```{r}
cor(pear) 
cor(pear)[1,2]
cor(pear$father, pear$daughter)
```

Spearman's rank correlation coefficient.

```{r}
cor(pear$father, pear$daughter, method="spearman")
```

Plot the ranks.

```{r}
plot(rank(pear$father), rank(pear$daughter), cex=0.5)
cor(rank(pear$father), rank(pear$daughter))
```

Test for association between the fathers' and daughters' heights.

```{r}
cor.test(pear$father, pear$daughter)
```