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Confidence interval for an average correlation of any type

Source: R/meta_ave.R
meta.ave.cor.gen.Rd

Computes the estimate, standard error, and confidence interval for an average correlation. Any type of correlation can be used (e.g., Pearson, Spearman, semipartial, factor correlation, gamma coefficient, Somers d coefficient, tetrachoric, point-biserial, biserial, correlation between latent factors, etc.). Each study should have the same type of correlation. If different types of correlations are used, they are assumed to be compatible.

For more details, see Chapter 2 of Bonett (2021, Volume 5).

Usage

meta.ave.cor.gen(alpha, cor, se, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

cor

vector of estimated correlations

se

vector of standard errors

bystudy

logical to also return each study estimate (TRUE) or not

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

  • Estimate - estimated effect size

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2008). “Meta-analytic interval estimation for bivariate correlations.” Psychological Methods, 13(3), 173–181. ISSN 1939-1463, doi:10.1037/a0012868 .

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

cor <- c(.396, .454, .409, .502, .350)
se <- c(.104, .064, .058, .107, .086)
meta.ave.cor.gen(.05, cor, se, bystudy = TRUE)
#>         Estimate      SE     LL     UL
#> Average   0.4222 0.03853 0.3439 0.4947
#> Study 1   0.3960 0.10400 0.1753 0.5788
#> Study 2   0.4540 0.06400 0.3201 0.5701
#> Study 3   0.4090 0.05800 0.2894 0.5160
#> Study 4   0.5020 0.10700 0.2651 0.6817
#> Study 5   0.3500 0.08600 0.1716 0.5061

# Should return:
#         Estimate      SE     LL     UL
# Average   0.4222 0.03853 0.3439 0.4947
# Study 1   0.3960 0.10400 0.1753 0.5788
# Study 2   0.4540 0.06400 0.3201 0.5701
# Study 3   0.4090 0.05800 0.2894 0.5160
# Study 4   0.5020 0.10700 0.2651 0.6817
# Study 5   0.3500 0.08600 0.1716 0.5061