Sample size for a point-biserial correlation confidence interval

Computes the sample size required to estimate a population point-biserial correlation with desired confidence interval precision in a two-group nonexperimental design with simple random sampling. A two-group nonexperimental design implies two subpopulations (e.g., all boys and all girls in a school district). This function requires a planning value for the proportion of population members who belong to one of the two subpopulations. Set the correlation planning value to the smallest absolute value within a plausible range for a conservatively large sample size.

Usage

size.ci.pbcor(alpha, cor, w, p)

Arguments

alpha: alpha level for 1-alpha confidence
cor: planning value of point-biserial correlation
w: desired confidence interval width
p: proportion of members in one of the two subpopulations

Value

Returns the required sample size

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

size.ci.pbcor(.05, .40, .25, .73)
#>  Sample size
#>          168

# Should return:
# Sample size
#         168