Compares and combines paired-samples standardized mean differences in original and follow-up studies

Source: R/meta_rep.R

This function computes confidence intervals from an original study and a follow-up study where the effect size is a paired-samples standardized mean difference. Confidence intervals for the difference and average effect size are also computed. Equality of variances within or across studies is not assumed. The confidence level for the difference is 1 – 2*alpha, which is recommended for equivalence testing. Square root unweighted variances and single-condition standard deviation are options for the standardizer.

replicate.stdmean.ps(
  alpha,
  m11,
  m12,
  sd11,
  sd12,
  cor1,
  n1,
  m21,
  m22,
  sd21,
  sd22,
  cor2,
  n2,
  stdzr
)

Arguments

alpha

alpha level for 1-alpha confidence

m11

estimated mean for group 1 in original study

m12

estimated mean for group 2 in original study

sd11

estimated SD for group 1 in original study

sd12

estimated SD for group 2 in original study

cor1

estimated correlation of paired observations in orginal study

n1

sample size in original study

m21

estimated mean for group 1 in follow-up study

m22

estimated mean for group 2 in follow-up study

sd21

estimated SD for group 1 in follow-up study

sd22

estimated SD for group 2 in follow-up study

cor2

estimated correlation of paired observations in follow-up study

n2

sample size in follow-up study

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

Value

A 4-row matrix. The rows are:

  • Row 1 summarizes the original study

  • Row 2 summarizes the follow-up study

  • Row 3 estimates the difference in standardized mean differences

  • Row 4 estimates the average standardized mean difference

The columns are:

  • Estimate - standardized mean difference estimate (single study, difference, average)

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2021). “Design and analysis of replication studies.” Organizational Research Methods, 24(3), 513--529. ISSN 1094-4281, doi:10.1177/1094428120911088 .

Examples

replicate.stdmean.ps(alpha = .05, 86.22, 70.93, 14.89, 12.32, .765, 20, 
                                  84.81, 77.24, 15.68, 16.95, .702, 75, 0)
#>                        Estimate         SE        LL        UL
#> Orginal:              1.0890300 0.22915553 0.6697353 1.5680085
#> Follow-up:            0.4604958 0.09590506 0.2756687 0.6516096
#> Original - Follow-up: 0.6552328 0.24841505 0.2466264 1.0638392
#> Average:              0.7747629 0.12420752 0.5313206 1.0182052

# Should return:
#                         Estimate         SE        LL        UL
#  Orginal:              1.0890300 0.22915553 0.6697353 1.5680085
#  Follow-up:            0.4604958 0.09590506 0.2756687 0.6516096
#  Original - Follow-up: 0.6552328 0.24841505 0.2466264 1.0638392
#  Average:              0.7747629 0.12420752 0.5313206 1.0182052