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Confidence interval for an average mean difference from 2-group studies

Source: R/meta_ave.R
meta.ave.mean2.Rd

Computes the estimate, standard error, and confidence interval for an average mean difference from two or more 2-group studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence intervals. Equality of variances within or across studies is not assumed.

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

Usage

meta.ave.mean2(alpha, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

m1

vector of estimated means for group 1

m2

vector of estimated means for group 2

sd1

vector of estimated SDs for group 1

sd2

vector of estimated SDs for group 2

n1

vector of group 1 sample sizes

n2

vector of group 2 sample sizes

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

  • df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619 .

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

Examples

m1 <- c(7.4, 6.9)
m2 <- c(6.3, 5.7)
sd1 <- c(1.72, 1.53)
sd2 <- c(2.35, 2.04)
n1 <- c(40, 60)
n2 <- c(40, 60)
meta.ave.mean2(.05, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)
#>         Estimate        SE        LL       UL        df
#> Average     1.15 0.2830183 0.5904369 1.709563 139.41000
#> Study 1     1.10 0.4604590 0.1819748 2.018025  71.46729
#> Study 2     1.20 0.3292036 0.5475574 1.852443 109.42136

# Should return:
#         Estimate        SE        LL       UL     df
# Average     1.15 0.2830183 0.5904369 1.709563 139.41
# Study 1     1.10 0.4604590 0.1819748 2.018025  71.47
# Study 2     1.20 0.3292036 0.5475574 1.852443 109.42