Compares and combines 2-group 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 2-group 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, square root weighted variances, and single-group standard deviation are options for the standardizer.

replicate.stdmean2(
  alpha,
  m11,
  m12,
  sd11,
  sd12,
  n11,
  n12,
  m21,
  m22,
  sd21,
  sd22,
  n21,
  n22,
  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

n11

sample size for group 1 in original study

n12

sample size for group 2 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

n21

sample size for group 1 in follow-up study

n22

sample size for group 2 in follow-up study

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

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.stdmean2(.05, 21.9, 16.1, 3.82, 3.21, 40, 40, 
                        25.2, 19.1, 3.98, 3.79, 75, 75, 0)
#>                         Estimate        SE         LL        UL
#> Original:             1.62803662 0.2629049  1.1286100 2.1591783
#> Follow-up:            1.56170447 0.1880713  1.2010594 1.9382853
#> Original - Follow-up: 0.07422178 0.3232488 -0.4574752 0.6059188
#> Average:              1.59487055 0.1616244  1.2780925 1.9116486

# Should return: 
#                           Estimate        SE         LL        UL
#  Original:              1.62803662 0.2594668  1.1353486 2.1524396
#  Follow-up:             1.56170447 0.1870576  1.2030461 1.9362986
#  Original - Follow-up:  0.07422178 0.3198649 -0.4519092 0.6003527
#  Average:               1.59487055 0.1599325  1.2814087 1.9083324