# biserial.cor: Point-Biserial Correlation In ltm: Latent Trait Models under IRT

 biserial.cor R Documentation

## Point-Biserial Correlation

### Description

Computes the point-biserial correlation between a dichotomous and a continuous variable.

### Usage

```
biserial.cor(x, y, use = c("all.obs", "complete.obs"), level = 1)

```

### Arguments

 `x` a numeric vector representing the continuous variable. `y` a factor or a numeric vector (that will be converted to a factor) representing the dichotomous variable. `use` If `use` is "all.obs", then the presence of missing observations will produce an error. If `use` is "complete.obs" then missing values are handled by casewise deletion. `level` which level of `y` to use.

### Details

The point biserial correlation computed by `biserial.cor()` is defined as follows

(X1.bar - X0.bar) * sqrt(pi * (1 - pi)) / S_x,

where X1.bar and X0.bar denote the sample means of the X-values corresponding to the first and second level of Y, respectively, S_x is the sample standard deviation of X, and pi is the sample proportion for Y = 1. The first level of Y is defined by the `level` argument; see Examples.

### Value

the (numeric) value of the point-biserial correlation.

### Note

Changing the order of the levels for `y` will produce a different result. By default, the first level is used as a reference level

### Author(s)

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

### Examples

```
# the point-biserial correlation between
# the total score and the first item, using
# '0' as the reference level
biserial.cor(rowSums(LSAT), LSAT[[1]])

# and using '1' as the reference level
biserial.cor(rowSums(LSAT), LSAT[[1]], level = 2)

```

ltm documentation built on March 18, 2022, 6:36 p.m.