# rcode16

## Correlation between numerical variables: R code for Chapter 16 examples

Click on a function argument for a short description of its meaning. The variable names are plucked from the examples further below.

Linear correlation:
`cor.test(, )`

Spearman rank correlation:
`cor.test(, , )`

### Example 16.1. Flipping Booby

Estimate a linear correlation between the number of non-parent adult visits experienced by boobies as chicks and the number of similar behaviors performed by the same birds when adult.

```booby <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter16/chap16e1FlippingBird.csv"))
```

Scatter plot.

```plot(futureBehavior ~ nVisitsNestling, data = booby)
```

For a fancier scatter plot using more options (Figure 16.1-4), see the commands .

Correlation coefficient. The `cor.test` function computes a number of useful quantities, which we save in the object `boobyCor`. The quantities can be extracted one at a time or shown all at once.

```boobyCor <- cor.test(booby\$futureBehavior, booby\$nVisitsNestling)
boobyCor
```

If only the estimated correlation and standard error are of interest, they can be obtained as follows. The calculation of standard error uses `nrow(booby)` to get the sample size for the correlation, but this will only be true if there are no missing values.

```r <- boobyCor\$estimate
r
SE <- sqrt( (1 - r^2)/(nrow(booby) - 3) )
unname(SE)
```

Confidence limit for a correlation coefficient. The 95% confidence interval for the correlation is included in the output of `cor.test`. If all you want is the confidence interval, it can be extracted from the `boobyCor` calculated in an earlier step.

```boobyCor\$conf.int
```

### Example 16.2. Inbreeding wolves

Test a linear correlation between inbreeding coefficients of litters of mated wolf pairs and the number of pups surviving their first winter.

```wolf <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter16/chap16e2InbreedingWolves.csv"))
```

Scatter plot.

```plot(nPups ~ inbreedCoef, data = wolf)
```

A fancier scatter plot with more options can be made with the commands .

Test of zero correlation. The results of the test are included in the output of `cor.test`.

```cor.test(wolf\$nPups, wolf\$inbreedCoef)
```

### Figure 16.4-1. Stream invertebrates

Effect of the range of the data on the correlation coefficient between population density of (log base 10 of number of individuals per square meter) and body mass (g) of different species of stream invertebrates.

```streamInvert <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter16/chap16f4_1StreamInvertebrates.csv"))
```

Scatter plot.

```plot(log10Density ~ log10Mass, data = streamInvert)
```

See for commands to make a scatter plot of these data with more options.

Effect of the range of the data on the correlation coefficient. Here is the correlation coefficient for the full range of the data. The command uses `cor.test` but we extract just the correlation coefficient for this exercise.

```cor.test(streamInvert\$log10Density, streamInvert\$log10Mass)\$estimate
```

Here is the correlation coefficient for the subset of the data corresponding to a log10Mass between 0 and 2.

```streamInvertReduced <- subset(streamInvert, log10Mass > 0 & log10Mass < 2)
cor.test(streamInvertReduced\$log10Density, streamInvertReduced\$log10Mass)\$estimate
```

### Example 16.5. Indian rope trick

Spearman rank correlation between impressiveness score of the Indian rope trick and the number of years elapsed bewteen the witnessing of the trick and the telling of it in writing.

```trick <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter16/chap16e5IndianRopeTrick.csv"))
```

Scatter plot.

```plot(impressivenessScore ~ years, data = trick)
```

See for commands to make a scatter plot of these data with more options.

Test of zero Spearman rank correlation. In this example, the variable "impressivenessScore" is a number score with lots of tied observations. Because of the ties, R will warn you that the P-value in the output is not exact.

```cor.test(trick\$years, trick\$impressivenessScore, method = "spearman")
```
The name of a numeric variable in data frame `booby`.
A second numeric variable from the same data frame, having the same number of elements as the first variable.
Name of a numeric variable in the data frame `trick`.
A second numeric variable in the same data frame.
An argument indicating the correlation method to use.

```plot(futureBehavior ~ nVisitsNestling, data = booby, pch = 16, col = "firebrick",
las = 1, bty = "l", cex = 1.2, xlab = "Events experienced as a nestling",
ylab = "Future behavior")
```

```plot(nPups ~ inbreedCoef, data = wolf, pch = 16, col = "firebrick",
las = 1, bty = "l", cex = 1.2, xlab = "Inbreeding coefficient",
ylab = "Number of pups")
```

```plot(log10Density ~ log10Mass, data = streamInvert, pch = 16, col = "firebrick",
las = 1, bty = "l", cex = 1.2, xlab = "Log population density",
ylab = "Log body mass")
```

```plot(impressivenessScore ~ years, data = trick, pch = 16, col = "firebrick",
las = 1, bty = "l", cex = 1.2, xlab = "Years elapsed",
ylab = "Impressiveness score")
```