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).

se.from.p(effect.size, p, N, effect.size.type = 'difference', calculate.g = FALSE)

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 |

calculate.g | Logical. Calculates the standardized mean difference
corrected for small sample bias (Hedges' \(g\)). |

A dataframe containing the following columns:

`(log)EffectSize`

: The input effect size. Log-transformed if`effect.size.type`

is`"ratio"`

.`Hedges.g`

: The calculated Hedges' g values (only if`calculate.g=TRUE`

).`(log)StandardError`

: The standard error (SE) for the effect size. Log-transformed if`effect.size.type`

is`"ratio"`

.`(log)LLCI`

and`(log)ULCI`

: The lower and upper 95% confidence interval of the effect size. Log-transformed if`effect.size.type="ratio"`

.

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 the`metagen`

function, along with the original effect size and confidence interval.

Altman D.G. & Bland J.M. (2011) How to obtain the confidence interval
of a *p* value. *BMJ 343*:d2090.

# 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