Description Usage Arguments Details Value References See Also
This function is for internal package use only. See smd
for usage.
1 2 3 | compute_smd_pairwise(smd_parts)
compute_smd(D, S)
|
smd_parts |
a |
D |
vector of differences for each level of a factor (will be length 1 for numeric values) |
S |
the covariance matrix |
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)).
a single numeric value
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)
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