This function computes a biserial correlation and its standard error. A biserial correlation can be used when one variable is quantitative and the other variable has been artifically dichotmized. The biserial correlation estimates the correlation between an observable quantitative variable and an unobserved quantitative variable that is measured on a dichotomous scale. This function requires the estimated mean, estimated standard deviation, and samples size from each level of the dichotomized variable. This function is useful in a meta-analysis of Pearson correlations where some studies report a Pearson correlation and other studies report the information needed to compute a biserial correlation. The biserial correlation and standard error output from this function can be used as input in the meta.ave.cor.gen function.
se.bscor(m1, m2, sd1, sd2, n1, n2)estimated mean for level 1
estimated mean for level 2
estimated standard deviation for level 1
estimated standard deviation for level 2
sample size for level 1
sample size for level 2
Returns a one-row matrix:
Estimate - estimated biserial correlation
SE - standard error
This function computes a point-biserial correlation and its standard error as a function of a standardized mean difference with a weighted variance standardizer. Then the point-biserial estimate is transformed into a biserial correlation using the traditional adjustment. The adjustment is also applied to the point-biserial standard error to obtain the standard error for the biserial correlation.
The biserial correlation assumes that the observed quantitative variable and the unobserved quantitative variable have a bivariate normal distribution. Bivariate normality is a crucial assumption underlying the transformation of a point-biserial correlation to a biserial correlation. Bivariate normality also implies equal variances of the observed quantitative variable at each level of the dichotomized variable, and this assumption is made in the computation of the standard error.
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 .
se.bscor(21.9, 16.1, 3.82, 3.21, 40, 40)
#> Estimate SE
#> Biserial correlation: 0.8018318 0.07451665
# Should return:
# Estimate SE
# Biserial correlation: 0.8018318 0.07451665