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Estimate a meta-analytic mean across multiple single-group studies.

Source: R/meta_mean.R
meta_mean.Rd

meta_mean is suitable for synthesizing across multiple single-group studies with a continuous outcome variable when all studies are measured on the same scale.

Usage

meta_mean(
  data,
  means,
  sds,
  ns,
  labels = NULL,
  moderator = NULL,
  contrast = NULL,
  effect_label = "My effect",
  reference_mean = 0,
  reported_effect_size = c("mean_difference", "smd_unbiased", "smd"),
  random_effects = TRUE,
  conf_level = 0.95
)

Arguments

data

A dataframe or tibble

means

A collection of study means, 1 per study

sds

A collection of study standard deviations, 1 per study, all >0

ns

A collection of sample sizes, 1 per study, all integers > 2

labels

An optional collection of study labels

moderator

An optional factor to analyze as a categorical moderator, must have k > 2 per groups

contrast

An optional contrast to estimate between moderator levels; express as a vector of contrast weights with 1 weight per moderator level.

effect_label

Optional character giving a human-friendly name of the effect being synthesized

reference_mean

Optional reference mean, defaults to 0

reported_effect_size

Character specifying effect size to return; Must be one of 'mean_difference', 'smd_unbiased' (to return an unbiased Cohen's d1) or 'smd' (to return Cohen's d1 without correction for bias)

random_effects

TRUE for random effect model; FALSE for fixed effects

conf_level

The confidence level for the confidence interval. Given in decimal form. Defaults to 0.95.

Value

An esci-estimate object; a list of data frames and properties. Returned tables include:

  • es_meta - A data frame of meta-analytic effect sizes. If a moderator was defined, there is an additional row for each level of the moderator.

    • effect_label - Study label

    • effect_size - Effect size

    • LL - Lower bound of conf_level% confidence interval

    • UL - Upper bound of conf_level% confidence interval

    • SE - Expected standard error

    • k - Number of studies

    • diamond_ratio - ratio of random to fixed effects meta-analytic effect sizes

    • diamond_ratio_LL - lower bound of conf_level% confidence interval for diamond ratio

    • diamond_ratio_UL - upper bound of conf_level% confidence interval for diamond ratio

    • I2 - I2 measure of heterogeneity

    • I2_LL - Lower bound of conf_level% confidence interval for I2

    • I2_UL - upper bound of conf_level% confidence interval for I2

    • PI_LL - lower bound of conf_level% of prediction interval

    • PI_UL - upper bound of conf_level% of prediction interval

    • p - p value for the meta-analytic effect size, based on null of exactly 0

    • *width - width of the effect-size confidence interval

    • FE_effect_size - effect size of the fixed-effects model (regardless of if fixed effects was selected

    • RE_effect_size - effect size of the random-effects model (regardless of if random effects was selected

    • FE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio

    • RE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio

  • es_heterogeneity - A data frame of of heterogeneity values and conf_level% CIs for the meta-analytic effect size. If a moderator was defined also reports heterogeneity estimates for each level of the moderator.

    • effect_label - study label

    • moderator_variable_name - if moderator passed, gives name of the moderator

    • moderator_level - 'Overall' and each level of moderator, if passed

    • measure - Name of the measure of heterogeneity

    • estimate - Value of the heterogeneity estimate

    • LL - lower bound of conf_level% confidence interval

    • UL - upper bound of conf_level% confidence interval

  • raw_data - A data from with one row for each study that was passed

    • label - study label

    • effect_size - effect size

    • weight - study weight in the meta analysis

    • sample_variance - expected level of sampling variation

    • SE - expected standard error

    • LL - lower bound of conf_level% confidence interval

    • UL - upper bound of conf_level% confidence interval

    • mean - used to calculate study p value; this is the d value entered for the study

    • sd - use to calculate study p value; set to 1 for each study

    • n - study sample size

    • p - p value for the study, based on null of exactly 0

Details

The meta-analytic effect size, confidence interval and heterogeneity estimates all come from metafor::rma().

The diamond ratio and its confidence interval come from CI_diamond_ratio().

If reported_effect_size is smd_unbiased or smd the conversion to d1 is handled by CI_smd_one().

Examples

# Data set -- see Introduction to the New Statistics, 2nd edition
data("data_mccabemichael_brain")

# Fixed effect, 95% CI
estimate <- esci::meta_mean(
  data = esci::data_mccabemichael_brain,
  means = "M Brain",
  sds = "s Brain",
  ns = "n Brain",
  labels = "Study name",
  random_effects = FALSE
)

myplot_forest <- esci::plot_meta(estimate)


# Add a moderator, report cohen's d1
estimate_moderator_d <- esci::meta_mean(
  data = esci::data_mccabemichael_brain,
  means = "M Brain",
  sds = "s Brain",
  ns = "n Brain",
  labels = "Study name",
  moderator = "Research group",
  reported_effect_size = "smd_unbiased",
  random_effects = FALSE
)

# Forest plot
myplot_forest_moderator_d <- esci::plot_meta(estimate_moderator_d)
#> Scale for x is already present.
#> Adding another scale for x, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.