Calculate the standard error from the effect size and p-value
se.from.p.Rd
This function calculates the standard error of an effect size provided the exact \(p\)-value and (continuous) effect size according to the formula by Altman and Bland (2011).
Arguments
- effect.size
Numeric vector or single number. The effect size, such as the standardized mean difference, Hedges' \(g\) or other continuous effect size.
- p
Numeric vector or single number. The exact \(p\)-value corresponding to the effect size.
- N
Numeric vector or single number. The total number of samples used to calculate the effect size/\(p\)-value.
- effect.size.type
The type of effect sizes provided in
effect.size
. For effect sizes based on differences (e.g., mean differences), this parameter has to be set to"difference"
. For effect sizes based on ratios (e.g., risk ratio, odds ratio), this parameter has to be set to"ratio"
.- calculate.g
Logical. Calculates the standardized mean difference corrected for small sample bias (Hedges' \(g\)).
FALSE
by default.
Value
A dataframe containing the following columns:
(log)EffectSize
: The input effect size. Log-transformed ifeffect.size.type
is"ratio"
.Hedges.g
: The calculated Hedges' g values (only ifcalculate.g=TRUE
).(log)StandardError
: The standard error (SE) for the effect size. Log-transformed ifeffect.size.type
is"ratio"
.(log)LLCI
and(log)ULCI
: The lower and upper 95% confidence interval of the effect size. Log-transformed ifeffect.size.type="ratio"
.
Details
This function calculates the standard error, standard deviation and 95% confidence interval of an effect size given the effect size and exact \(p\)-value. The function can be used for:
effect sizes based on differences (e.g., mean differences) by setting
effect.size.type
to"difference"
, oreffect sizes based on ratios (e.g. risk ratios, odds ratios or hazard ratios) by setting
effect.size.type
to"ratio"
. When ratios are used, the function returns the log-transformed effect sizes, standard error, standard deviation and confidence interval, which can be used for meta-analytic pooling using themetagen
function, along with the original effect size and confidence interval.
References
Altman D.G. & Bland J.M. (2011) How to obtain the confidence interval of a p value. BMJ 343:d2090.
Examples
# Example 1: one single effect size
se.from.p(effect.size = 0.71, p = 0.013, N = 75,
effect.size.type= "difference", calculate.g = TRUE)
#> Hedges.g StandardError StandardDeviation LLCI ULCI
#> 1 0.7026804 0.2830974 2.451696 0.1478196 1.257541
# Example 2: vector of effect sizes (Odds Ratio)
effect.size = c(0.91, 1.01, 0.72, 0.43)
p = c(0.05, 0.031, 0.001, 0.09)
N = c(120, 86, 450, 123)
se.from.p(effect.size = effect.size, p = p, N = N,
effect.size.type = "ratio")
#> logEffectSize logStandardError logStandardDeviation logLLCI
#> 1 -0.094310679 0.048200284 0.52800765 -0.1887814995
#> 2 0.009950331 0.004620291 0.04284681 0.0008947275
#> 3 -0.328504067 0.099448976 2.10963136 -0.5234204779
#> 4 -0.843970070 0.498293938 5.52634711 -1.8206082430
#> logULCI EffectSize LLCI ULCI
#> 1 0.0001601406 0.91 0.8279674 1.0001602
#> 2 0.0190059342 1.01 1.0008951 1.0191877
#> 3 -0.1335876560 0.72 0.5924905 0.8749508
#> 4 0.1326681024 0.43 0.1619272 1.1418710