Compares and combines point-biserial correlations in original and follow-up studies

This function computes confidence intervals from an original study and a follow-up study where the effect size is a point-biserial correlation. Confidence intervals for the difference and average effect size are also computed. The confidence level for the difference is 1 – 2*alpha, which is recommended for equivalence testing. The point-biserial correlation in each study is computed from a standardized mean difference. Two types of standardized mean differences can be requested. One type uses the square root of unweighted variances as a standardizer and is recommended for 2-group experimental designs. The other type uses the square root of weighted variances as a standardizer and is recommended for 2-group non-experimental designs with simple random sampling. Equality of variances across or within studies is not assumed.

For more details, see Chapter 4 of Bonett (2021, Volume 5).

Usage

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

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

type

set to 1 for square root weighted average variance standardizer
set to 2 for square root unweighted 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 point-biserial correlations
Row 4 estimates the average point-biserial correlation

The columns are:

Estimate - point-biserial correlation (single study, difference, average)
SE - standard error
LL - lower limit of the confidence interval
UL - upper limit of the confidence interval

References

Bonett DG (2020). “Point-biserial correlation: Interval estimation, hypothesis testing, meta-analysis, and sample size determination.” British Journal of Mathematical and Statistical Psychology, 73(S1), 113–144. ISSN 0007-1102, doi:10.1111/bmsp.12189 .

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

replicate.pbcor(.05, 21.9, 16.1, 3.82, 3.21, 40, 40, 25.2, 19.1, 3.98, 3.79, 75, 75, 2)
#>                       Estimate      SE      LL     UL
#> Original:               0.6350 0.06061  0.4915 0.7336
#> Follow-up:              0.6174 0.04578  0.5148 0.6959
#> Original - Follow-up:   0.0176 0.07595 -0.1460 0.1599
#> Average:                0.6262 0.03798  0.5460 0.6950

# Should return: 
#                       Estimate      SE      LL     UL
# Original:               0.6350 0.06061  0.4915 0.7336
# Follow-up:              0.6174 0.04578  0.5148 0.6959
# Original - Follow-up:   0.0176 0.07595 -0.1460 0.1599
# Average:                0.6262 0.03798  0.5460 0.6950

replicate.pbcor(.05, 12.2, 10.4, 1.74, 1.59, 68, 94, 13.0, 10.9, 1.48, 1.29, 124, 189, 1)
#>                       Estimate      SE      LL      UL
#> Original:               0.4753 0.05847  0.3487  0.5781
#> Follow-up:              0.6016 0.03365  0.5292  0.6617
#> Original - Follow-up:  -0.1262 0.06746 -0.2664 -0.0005
#> Average:                0.5384 0.03373  0.4691  0.6012

# Should return: 
#                       Estimate      SE      LL      UL
# Original:               0.4753 0.05847  0.3487  0.5781
# Follow-up:              0.6016 0.03365  0.5292  0.6617
# Original - Follow-up:  -0.1262 0.06746 -0.2664 -0.0005
# Average:                0.5384 0.03373  0.4691  0.6012