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Confidence interval for an average standardized mean difference from paired-samples studies

Source: R/meta_ave.R
meta.ave.stdmean.ps.Rd

Computes the estimate, standard error, and confidence interval for an average standardized mean difference from two or more paired-samples studies. Squrare root unweighted variances and a single condition 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.stdmean.ps(alpha, m1, m2, sd1, sd2, cor, n, stdzr, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

m1

vector of estimated means for measurement 1

m2

vector of estimated means for measurement 2

sd1

vector of estimated SDs for measurement 1

sd2

vector of estimated SDs for measurement 2

cor

vector of estimated correlations for paired measurements

n

vector of sample sizes

stdzr

  • set to 0 for square root unweighted average variance standardizer

  • set to 1 for measurement 1 SD standardizer

  • set to 2 for measurement 2 SD 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(23.9, 24.1)
m2 <- c(25.1, 26.9)
sd1 <- c(1.76, 1.58)
sd2 <- c(2.01, 1.76)
cor <- c(.78, .84)
n <- c(25, 30)
meta.ave.stdmean.ps(.05, m1, m2, sd1, sd2, cor, n, 1, bystudy = TRUE)
#>         Estimate      SE      LL      UL
#> Average  -1.1931 0.15680 -1.5004 -0.8858
#> Study 1  -0.6818 0.17738 -1.0295 -0.3342
#> Study 2  -1.7722 0.25862 -2.2790 -1.2653

# Should return: 
#         Estimate      SE      LL      UL
# Average  -1.1931 0.15680 -1.5004 -0.8858
# Study 1  -0.6818 0.17738 -1.0295 -0.3342
# Study 2  -1.7722 0.25862 -2.2790 -1.2653

m1 <- c(23.9, 24.1)
m2 <- c(25.1, 26.9)
sd1 <- c(1.76, 1.58)
sd2 <- c(2.01, 1.76)
cor <- c(.78, .84)
n <- c(25, 30)
meta.ave.stdmean.ps(.05, m1, m2, sd1, sd2, cor, n, 0, bystudy = FALSE)
#>         Estimate      SE      LL      UL
#> Average  -1.1335 0.13996 -1.4078 -0.8591

# Should return: 
#         Estimate      SE      LL      UL
# Average  -1.1335 0.13996 -1.4078 -0.8591