se.pbcor {vcmeta}

Computes the standard error for a point-biserial correlation

Description

This function computes a point-biserial correlation and its standard error for two types of point-biserial correlations in 2-group designs using the estimated means, estimated standard deviations, and samples sizes. Equality of variances is not assumed. One type of point-biserial correlation uses an unweighted average of variances and is recommended for 2-group experimental designs. The other type of point-biserial correlation uses a weighted average of variances and is recommended for 2-group nonexperimental designs with simple random sampling (but not stratified random sampling). This function is useful in a meta-analysis of compatible point-biserial correlations where some studies used a 2-group experimental design and other studies used a 2-group nonexperimental design. The effect size estimate and standard error output from this function can be used as input in the meta.ave.cor.gen function.

Usage

se.pbcor(m1, m2, sd1, sd2, n1, n2, type)

Arguments

m1

estimated mean for group 1

m2

estimated mean for group 2

sd1

estimated standard deviation for group 1

sd2

estimated standard deviation for group 2

n1

sample size for group 1

n2

sample size for group 2

type

• set to 1 for weighted variance average

• set to 2 for unweighted variance average

Value

Returns a one-row matrix:

• Estimate - estimated point-biserial correlation

• SE - standard error

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

se.pbcor(21.9, 16.1, 3.82, 3.21, 40, 40, 1)

#  Should return: 
#                                Estimate         SE
#  Point-biserial correlation:  0.6349786 0.05981325