The Pooled Standard Deviation is a weighted average of standard deviations
for two or more groups, *assumed to have equal variance*. It represents the
common deviation among the groups, around each of their respective means.

## Usage

```
sd_pooled(x, y = NULL, data = NULL, verbose = TRUE)
mad_pooled(x, y = NULL, data = NULL, constant = 1.4826, verbose = TRUE)
```

## Arguments

- x
A formula, a numeric vector, or a character name of one in

`data`

.- y
A numeric vector, a grouping (character / factor) vector, a or a character name of one in

`data`

. Ignored if`x`

is a formula.- data
An optional data frame containing the variables.

- verbose
Toggle warnings and messages on or off.

- constant
scale factor.

## Details

The standard version is calculated as: $$\sqrt{\frac{\sum (x_i - \bar{x})^2}{n_1 + n_2 - 2}}$$ The robust version is calculated as: $$1.4826 \times Median(|\left\{x - Median_x,\,y - Median_y\right\}|)$$

## Examples

```
sd_pooled(mpg ~ am, data = mtcars)
#> [1] 4.902029
mad_pooled(mtcars$mpg, factor(mtcars$am))
#> [1] 6.704213
```