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

Source: R/meta_ave.R
meta.ave.stdmean2.Rd

Computes the estimate, standard error, and confidence interval for an average standardized mean difference from two or more 2-group studies. Square root unweighted variances, square root weighted variances, and single group standard deviation are options for the standardizer. Equality of variances within or across studies is not assumed.

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

Usage

meta.ave.stdmean2(alpha, m1, m2, sd1, sd2, n1, n2, stdzr, 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

stdzr

  • set to 0 for square root unweighted average variance standardizer

  • set to 1 for group 1 SD standardizer

  • set to 2 for group 2 SD standardizer

  • set to 3 for square root weighted average variance standardizer

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 (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(21.9, 23.1, 19.8)
m2 <- c(16.1, 17.4, 15.0)
sd1 <- c(3.82, 3.95, 3.67)
sd2 <- c(3.21, 3.30, 3.02)
n1 <- c(40, 30, 24)
n2 <- c(40, 28, 25)
meta.ave.stdmean2(.05, m1, m2, sd1, sd2, n1, n2, 0, bystudy = TRUE)
#>         Estimate      SE     LL     UL
#> Average   1.5261 0.17343 1.1862 1.8661
#> Study 1   1.6439 0.26290 1.1286 2.1592
#> Study 2   1.5661 0.30563 0.9671 2.1652
#> Study 3   1.4283 0.32892 0.7836 2.0729

# Should return: 
#         Estimate      SE     LL     UL
# Average   1.5261 0.17343 1.1862 1.8661
# Study 1   1.6439 0.26290 1.1286 2.1592
# Study 2   1.5661 0.30563 0.9671 2.1652
# Study 3   1.4283 0.32892 0.7836 2.0729

m1 <- c(41.2, 43.2, 49.1, 40.8)
m2 <- c(36.4, 37.1, 35.9, 31.4)
sd1 <- c(4.92, 4.75, 4.87, 5.01)
sd2 <- c(4.35, 4.24, 4.12, 4.87)
n1 <- c(42, 58, 62, 39)
n2 <- c(67, 70, 84, 45)
meta.ave.stdmean2(.05, m1, m2, sd1, sd2, n1, n2, 3, bystudy = FALSE)
#>         Estimate      SE     LL     UL
#> Average   1.8078 0.11648 1.5795 2.0361

# Should return: 
#         Estimate      SE     LL     UL
# Average   1.8078 0.11648 1.5795 2.0361