Skip to contents

Compares and combines Cronbach reliablity in original and follow-up studies

Source: R/meta_rep.R
replicate.cronbach.Rd

This function can be used to compare and combine a Cronbach reliablity coefficient from an original study and a follow-up study. The confidence level for the difference is 1 – 2*alpha, which is recommended for equivalence testing.

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

Usage

replicate.cronbach(alpha, rel1, n1, rel2, n2, r)

Arguments

alpha

alpha level for 1-alpha confidence

rel1

estimated reliability in original study

n1

sample size in original study

rel2

estimated reliability in follow-up study

n2

sample size in follow-up study

r

number of measurements (e.g., items)

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 correlations

  • Row 4 estimates the average correlation

The columns are:

  • Estimate - correlation 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 (2010). “Varying coefficient meta-analytic methods for alpha reliability.” Psychological Methods, 15(4), 368–385. ISSN 1939-1463, doi:10.1037/a0020142 .

Bonett DG, Price RM (2015). “Varying coefficient meta-analysis methods for odds ratios and risk ratios.” Psychological Methods, 20(3), 394–406. ISSN 1939-1463, doi:10.1037/met0000032 .

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

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

Examples

replicate.cronbach(.05, .883, 100, .869, 200, 6)
#>                       Estimate      SE      LL     UL
#> Original:                0.883 0.01831  0.8436 0.9152
#> Follow-up:               0.869 0.01442  0.8387 0.8952
#> Original - Follow-up:    0.014 0.02331 -0.0334 0.0582
#> Average:                 0.876 0.01172  0.8519 0.8977

# Should return:
#                       Estimate      SE      LL     UL
# Original:                0.883 0.01831  0.8436 0.9152
# Follow-up:               0.869 0.01442  0.8387 0.8952
# Original - Follow-up:    0.014 0.02331 -0.0334 0.0582
# Average:                 0.876 0.01172  0.8519 0.8977