meta_analysis {statsExpressions}

Random-effects meta-analysis

Description

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

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) or 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.

random

The type of random effects distribution. One of "normal", "t-dist", "mixture", for standard normal, t-distribution or mixture of normals respectively.

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). If NULL, no confidence intervals will be computed.

...

Additional arguments passed to the respective meta-analysis function.

Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

• 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 two-sided p-value associated with the observed statistic

• method: the name of the inferential statistical test

• estimate: estimated value of the effect size

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

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

• conf.level: width of the confidence interval

• conf.method: method used to compute confidence interval

• conf.distribution: statistical distribution for the effect

• effectsize: the name of the effect size

• n.obs: number of observations

• expression: pre-formatted expression containing statistical details

For examples, see 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	CI available?	Function used
Parametric	Pearson's correlation coefficient	Yes	correlation::correlation()
Non-parametric	Spearman's rank correlation coefficient	Yes	correlation::correlation()
Robust	Winsorized Pearson's correlation coefficient	Yes	correlation::correlation()
Bayesian	Bayesian Pearson's correlation coefficient	Yes	correlation::correlation()

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

# setup
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 = "random", random = "normal")



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

meta_analysis(dat, type = "bayes")