Convert means and/or standard deviations of two independent groups into two effect measures (VR/CVR)
es_variab_from_means_sd (
mean_exp ,
mean_nexp ,
mean_sd_exp ,
mean_sd_nexp ,
n_exp ,
n_nexp ,
reverse_means_variability
)
Arguments
mean_exp: mean of participants in the experimental/exposed group.mean_nexp: mean of participants in the non-experimental/non-exposed group.mean_sd_exp: standard deviation of participants in the experimental/exposed group.mean_sd_nexp: standard deviation of participants in the non-experimental/non-exposed group.n_exp: number of participants in the experimental/exposed group.n_nexp: number of participants in the non-experimental/non-exposed group.reverse_means_variability: a logical value indicating whether the direction of the generated effect sizes should be flipped.
Returns
This function estimates VR and CVR
Details
This function converts the means and standard deviations of two independent groups into a log variability ratio (VR) and a log coefficient of variation ratio (CVR).
The formulas used to obtain the log VR are (formulas 5 and 15, Senior et al. 2020):
l o g v r = l o g ( m e a n _ s d _ e x p m e a n _ s d _ n e x p ) + 1 2 ∗ ( n _ e x p − 1 ) − 1 2 ∗ ( n _ n e x p − 1 ) logvr = log(\frac{mean\_sd\_exp}{mean\_sd\_nexp}) + \frac{1}{2 * (n\_exp - 1)} - \frac{1}{2 * (n\_nexp - 1)} l o gv r = l o g ( m e an _ s d _ n e x p m e an _ s d _ e x p ) + 2 ∗ ( n _ e x p − 1 ) 1 − 2 ∗ ( n _ n e x p − 1 ) 1 l o g v r _ s e = 1 2 ∗ ( n _ n e x p ( n _ n e x p − 1 ) 2 + n _ e x p ( n _ e x p − 1 ) 2 ) logvr\_se = \sqrt{\frac{1}{2} * (\frac{n\_nexp}{(n\_nexp - 1)^2} + \frac{n\_exp}{(n\_exp - 1)^2})} l o gv r _ se = 2 1 ∗ ( ( n _ n e x p − 1 ) 2 n _ n e x p + ( n _ e x p − 1 ) 2 n _ e x p ) l o g v r _ c i _ l o = l o g v r − q n o r m ( . 975 ) ∗ l o g v r _ s e logvr\_ci\_lo = logvr - qnorm(.975) * logvr\_se l o gv r _ c i _ l o = l o gv r − q n or m ( .975 ) ∗ l o gv r _ se l o g v r _ c i _ u p = l o g v r + q n o r m ( . 975 ) ∗ l o g v r _ s e logvr\_ci\_up = logvr + qnorm(.975) * logvr\_se l o gv r _ c i _ u p = l o gv r + q n or m ( .975 ) ∗ l o gv r _ se The formulas used to obtain the log CVR are (formulas 6 and 16, Senior et al. 2020):
c v t = m e a n _ s d _ e x p / m e a n _ e x p cvt = mean\_sd\_exp / mean\_exp c v t = m e an _ s d _ e x p / m e an _ e x p c v c = m e a n _ s d _ n e x p / m e a n _ n e x p cvc = mean\_sd\_nexp / mean\_nexp c v c = m e an _ s d _ n e x p / m e an _ n e x p l o g c v r = l o g ( c v t c v c ) + 1 2 ∗ ( 1 n _ e x p − 1 − 1 n _ n e x p − 1 ) + 1 2 ∗ ( m e a n _ s d _ n e x p 2 n _ n e x p ∗ m e a n _ n e x p 2 − m e a n _ s d _ e x p 2 n _ e x p ∗ m e a n _ e x p 2 ) logcvr = log(\frac{cvt}{cvc}) + \frac{1}{2} * (\frac{1}{n\_exp - 1} - \frac{1}{n\_nexp - 1}) + \frac{1}{2} * (\frac{mean\_sd\_nexp^2}{n\_nexp * mean\_nexp^2} - \frac{mean\_sd\_exp^2}{n\_exp * mean\_exp^2}) l o g c v r = l o g ( c v c c v t ) + 2 1 ∗ ( n _ e x p − 1 1 − n _ n e x p − 1 1 ) + 2 1 ∗ ( n _ n e x p ∗ m e an _ n e x p 2 m e an _ s d _ n e x p 2 − n _ e x p ∗ m e an _ e x p 2 m e an _ s d _ e x p 2 ) v t _ e x p = m e a n _ s d _ e x p 2 n _ e x p ∗ m e a n _ e x p 2 + m e a n _ s d _ e x p 4 2 ∗ n _ e x p 2 ∗ m e a n _ e x p 4 + n _ e x p ( n _ e x p − 1 ) 2 vt\_exp = \frac{mean\_sd\_exp^2}{n\_exp * mean\_exp^2} + \frac{mean\_sd\_exp^4}{2 * n\_exp^2 * mean\_exp^4} + \frac{n\_exp}{(n\_exp - 1)^2} v t _ e x p = n _ e x p ∗ m e an _ e x p 2 m e an _ s d _ e x p 2 + 2 ∗ n _ e x p 2 ∗ m e an _ e x p 4 m e an _ s d _ e x p 4 + ( n _ e x p − 1 ) 2 n _ e x p v t _ n e x p = m e a n _ s d _ n e x p 2 n _ n e x p ∗ m e a n _ n e x p 2 + m e a n _ s d _ n e x p 4 2 ∗ n _ n e x p 2 ∗ m e a n _ n e x p 4 + n _ n e x p ( n _ n e x p − 1 ) 2 vt\_nexp = \frac{mean\_sd\_nexp^2}{n\_nexp * mean\_nexp^2} + \frac{mean\_sd\_nexp^4}{2 * n\_nexp^2 * mean\_nexp^4} + \frac{n\_nexp}{(n\_nexp - 1)^2} v t _ n e x p = n _ n e x p ∗ m e an _ n e x p 2 m e an _ s d _ n e x p 2 + 2 ∗ n _ n e x p 2 ∗ m e an _ n e x p 4 m e an _ s d _ n e x p 4 + ( n _ n e x p − 1 ) 2 n _ n e x p l o g c v r _ s e = v t _ e x p + v t _ n e x p logcvr\_se = \sqrt{vt\_exp + vt\_nexp} l o g c v r _ se = v t _ e x p + v t _ n e x p l o g c v r _ c i _ l o = l o g c v r − q n o r m ( . 975 ) ∗ l o g c v r _ s e logcvr\_ci\_lo = logcvr - qnorm(.975) * logcvr\_se l o g c v r _ c i _ l o = l o g c v r − q n or m ( .975 ) ∗ l o g c v r _ se l o g c v r _ c i _ u p = l o g c v r + q n o r m ( . 975 ) ∗ l o g c v r _ s e logcvr\_ci\_up = logcvr + qnorm(.975) * logcvr\_se l o g c v r _ c i _ u p = l o g c v r + q n or m ( .975 ) ∗ l o g c v r _ se Examples
es_variab_from_means_sd (
n_exp = 55 , n_nexp = 55 ,
mean_exp = 2.3 , mean_sd_exp = 1.2 ,
mean_nexp = 1.9 , mean_sd_nexp = 0.9
)
References
Senior, A. M., Viechtbauer, W., & Nakagawa, S. (2020). Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio. Research Synthesis Methods, 11(4), 553-567. https://doi.org/10.1002/jrsm.1423