meta_analysis: Random-effects meta-analysis

In statsExpressions: Tidy Dataframes and Expressions with Statistical Details

Random-effects meta-analysis

Description

Parametric, robust, and Bayesian random-effects meta-analysis.

A non-parametric meta-analysis is not available, so type = "nonparametric" is not supported.

Usage

meta_analysis(
  data,
  type = "parametric",
  random = "mixture",
  digits = 2L,
  conf.level = 0.95,
  ...
)

Arguments

data	A data frame. It must contain columns named estimate (effect sizes or outcomes) and std.error (corresponding standard errors). These two columns will be used: as yi and sei arguments in metafor::rma() (for parametric test) as yi and sei arguments in metaplus::metaplus() (for robust test) as y and SE arguments in metaBMA::meta_random() (for Bayesian test)
type	A character specifying the type of statistical approach: "parametric" "nonparametric" "robust" "bayes" You can specify just the initial letter (e.g. "np" or "bf"). Matching is on the initial lowercase letter only, so any other value (including capitalized values such as "Bayes") falls back to "parametric" without a warning.
random	The type of random-effects distribution for the robust meta-analysis: "mixture" (default; mixture of normals), "normal", or "t-dist" (t-distribution). Passed to metaplus::metaplus() and only used when type = "robust".
digits	Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).
conf.level	Scalar between 0 and 1 (default: ⁠95%⁠ confidence/credible intervals, 0.95).
...	Additional arguments passed to the respective meta-analysis function.

Value

The returned object is a tibble data frame with the additional class "statsExpressions". The exact set of columns depends on the test and, for functions that accept a type argument, on the chosen analysis (parametric, non-parametric, robust, or Bayesian). Any given call therefore returns some (not all) of the columns below.

Hypothesis testing

• statistic: the numeric value of a statistic

• df: the numeric value of a parameter being modeled (often degrees of freedom for the test)

• df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)

• p.value: the p-value associated with the observed statistic (two-sided unless a one-sided alternative is requested, where supported)

• method: the name of the inferential statistical test

Effect size estimation

• effectsize: the name of the effect size

• estimate: estimated value of the effect size

• conf.level: the coverage level of the confidence/credible interval (e.g. 0.95); the interval itself spans conf.low to conf.high

• conf.low: lower bound for the effect size estimate

• conf.high: upper bound for the effect size estimate

• conf.method: method used to compute the confidence/credible interval

• conf.distribution: statistical distribution for the effect

Bayesian analysis (only when type = "bayes")

• bf10: Bayes factor for the alternative hypothesis relative to the null

• log_e_bf10: natural logarithm of the Bayes factor (present for most, but not all, Bayesian analyses)

• prior.distribution, prior.scale, prior.location: prior specification used to compute the Bayes factor and posterior estimates

Pairwise comparisons (for pairwise_comparisons() and pairwise_contingency_table())

• group1, group2: the two levels being compared

• p.adjust.method: the adjustment method used for multiple comparisons

• p.value.adj: the adjusted p-value; returned by pairwise_contingency_table(). Note that pairwise_comparisons() instead folds the adjusted value into p.value (and does not return a separate p.value.adj column)

Common columns

• n.obs: number of observations

• expression: a list-column of pre-formatted plotmath expressions; each element is a language object (not a character string) containing the statistical details, ready to be used in {ggplot2} (e.g. in labs() or annotate())

For a per-function, column-by-column breakdown of the output (and an explanation of the internal add_expression_col() engine that builds the expression column), see the Return value schema article. For more examples, see the data frame output vignette.

Random-effects meta-analysis

The table below provides summary about:

• statistical test carried out for inferential statistics

• type of effect size estimate and a measure of uncertainty for this estimate

• functions used internally to compute these details

Hypothesis testing and Effect size estimation

Type	Test	Effect size	CI available?	Function used
Parametric	Meta-analysis via random-effects models	beta	Yes	metafor::rma()
Robust	Meta-analysis via robust random-effects models	beta	Yes	metaplus::metaplus()
Bayesian	Meta-analysis via Bayesian random-effects models	beta	Yes	metaBMA::meta_random()

Citation

Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes and Expressions with Statistical Details. Journal of Open Source Software, 6(61), 3236, https://doi.org/10.21105/joss.03236

Note

Important: The function assumes that you have already downloaded the needed package ({metafor}, {metaplus}, or {metaBMA}) for meta-analysis. If they are not available, you will be asked to install them.

Examples

set.seed(123)
library(statsExpressions)

# let's use `mag` dataset from `{metaplus}`
data(mag, package = "metaplus")
dat <- dplyr::rename(mag, estimate = yi, std.error = sei)

# ----------------------- parametric ----------------------------------------



meta_analysis(dat)



# ----------------------- robust --------------------------------------------

meta_analysis(dat, type = "robust", random = "normal")



# ----------------------- Bayesian ------------------------------------------

meta_analysis(dat, type = "bayes")

statsExpressions documentation built on Oct. 9, 2026, 5:06 p.m.