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, ...)
cov_pooled(x, y = NULL, data = NULL, verbose = TRUE, ...)
```

## Arguments

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

`data`

. Any missing values (`NA`

s) are dropped from the resulting vector.`x`

can also be a formula (see`stats::t.test()`

), in which case`y`

is ignored.- data
An optional data frame containing the variables.

- verbose
Toggle warnings and messages on or off.

- ...
Arguments passed to or from other methods. When

`x`

is a formula, these can be`subset`

and`na.action`

.- 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] 4.52193
cov_pooled(mpg + hp + cyl ~ am, data = mtcars)
#> mpg hp cyl
#> mpg 24.029887 -269.13174 -5.991498
#> hp -269.131741 4570.24588 89.247233
#> cyl -5.991498 89.24723 2.395682
```