# compute_smd: Compute the standardized mean difference In smd: Compute Standardized Mean Differences

## Description

This function is for internal package use only. See smd for usage.

## Usage

 1 2 3 compute_smd_pairwise(smd_parts) compute_smd(D, S) 

## Arguments

 smd_parts a list of components for from compute_smd_parts computing standardized mean differences D vector of differences for each level of a factor (will be length 1 for numeric values) S the covariance matrix

## Details

Computes:

d = √{D' S^{-1} D}

where D is a vector of differences between group 1 and 2 and S is the covariance matrix of these differences. If D is length 1, the result is multplied by sign(D).

In the case of a numeric or integer variable, this is equivalent to:

d = \frac{\bar{x}_1 - \bar{x}_2}{√{(s^2_1 + s^2_2)/2}}

where \bar{x}_g is the sample mean for group g and s^2_g is the sample variance.

For a logical or factor with only two levels, the equation above is \bar{x}_g = \hat{p}_g, i.e. the sample proportion and s^2_g = \hat{p}_g(1 - \hat{p}_g) (NOTE: interally smd uses the var function, which uses n-1 as the denominator. Hence, in small samples, s^2_g will not be precisely \hat{p}_g(1 - \hat{p}_g)).

## Value

a single numeric value

## References

Yang, D., & Dalton, J. E. (2012, April). A unified approach to measuring the effect size between two groups using SAS®. In SAS Global Forum (Vol. 335, pp. 1-6)

smd