Pooled Indices of (Co)Deviation

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 (NAs) 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.

Value

Numeric, the pooled standard deviation. For cov_pooled() a matrix.

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: $$1.4826 \times Median(|\left\{x - Median_x,\,y - Median_y\right\}|)$$

See also

cohens_d(), mahalanobis_d()

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