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

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

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

Usage

meta.ave.mean.ps(alpha, m1, m2, sd1, sd2, cor, n, 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

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 .

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.72, .78, .81, .85)
n <- c(30, 50, 30, 70)
meta.ave.mean.ps(.05, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)
#>         Estimate        SE        LL         UL      df
#> Average    -3.25 0.2340603 -3.713965 -2.7860352 107.657
#> Study 1    -2.00 0.5672507 -3.160158 -0.8398421  29.000
#> Study 2    -2.00 0.4227434 -2.849535 -1.1504653  49.000
#> Study 3    -5.00 0.5335104 -6.091151 -3.9088487  29.000
#> Study 4    -4.00 0.3023716 -4.603215 -3.3967852  69.000

# Should return:
#         Estimate        SE        LL         UL      df
# Average    -3.25 0.2340603 -3.713965 -2.7860352 107.657
# Study 1    -2.00 0.5672507 -3.160158 -0.8398421  29.000
# Study 2    -2.00 0.4227434 -2.849535 -1.1504653  49.000
# Study 3    -5.00 0.5335104 -6.091151 -3.9088487  29.000
# Study 4    -4.00 0.3023716 -4.603215 -3.3967852  69.000