meta.sub.pbcor {vcmeta}

Confidence interval for a difference in average point-biserial correlations for two sets of studies

Description

Computes the estimate, standard error, and confidence interval for a difference in average point-biserial correlations for two mutually exclusive sets of studies. Each set can have one or more studies. Two types of point-biserial correlations can be analyzed. One type uses an unweighted variance and is recommended for 2-group experimental designs. The other type uses a weighted variance and is recommended for 2-group nonexperimental designs with simple random sampling (but not stratified random sampling) within each study. Equality of variances within or across studies is not assumed.

Usage

meta.sub.pbcor(alpha, m1, m2, sd1, sd2, n1, n2, type, group)

Arguments

alpha

alpha level for 1-alpha confidence

m1

vector of estimated means for group 1

m2

vector of estimated means for group 2

sd1

vector of estimated SDs for group 1

sd2

vector of estimated SDs for group 2

n1

vector of group 1 sample sizes

n2

vector of group 2 sample sizes

type

• set to 1 for weighted variance

• set to 2 for unweighted variance

group

vector of group indicators:

• 1 for set A

• 2 for set B

• 0 to ignore

Value

Returns a matrix with three rows:

• Row 1 - estimate for Set A

• Row 2 - estimate for Set B

• Row 3 - estimate for difference, Set A - Set B

The columns are:

• Estimate - estimated average correlation or difference

• 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.

Examples

m1 <- c(45.1, 39.2, 36.3, 34.5)
m2 <- c(30.0, 35.1, 35.3, 36.2)
sd1 <- c(10.7, 10.5, 9.4, 11.5)
sd2 <- c(12.3, 12.0, 10.4, 9.6)
n1 <- c(40, 20, 50, 25)
n2 <- c(40, 20, 48, 26)
group <- c(1, 1, 2, 2)
meta.sub.pbcor(.05,  m1, m2, sd1, sd2, n1, n2, 2, group)

# Should return:
#                   Estimate         SE         LL        UL
# Set A:          0.36338772 0.08552728  0.1854777 0.5182304
# Set B:         -0.01480511 0.08741322 -0.1840491 0.1552914
# Set A - Set B:  0.37819284 0.12229467  0.1320530 0.6075828