Computes a confidence interval for a population biserial correlation. A biserial correlation can be used when one variable is quantitative and the other variable has been artificially dichotomized to create two groups. The biserial correlation estimates the correlation between the observed quantitative variable and the unobserved quantitative variable that has been measured on a dichotomous scale.
ci.bscor(alpha, m1, m2, sd1, sd2, n1, n2)alpha level for 1-alpha confidence
estimated mean for group 1
estimated mean for group 2
estimated standard deviation for group 1
estimated standard deviation for group 2
sample size for group 1
sample size for group 2
Returns a 1-row matrix. The columns are:
Estimate - estimated biserial correlation
SE - standard error
LL - lower limit of the confidence interval
UL - upper limit of the confidence interval
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 .
ci.bscor(.05, 28.32, 21.48, 3.81, 3.09, 40, 40)
#> Estimate SE LL UL
#> 0.8855666 0.06129908 0.7376327 0.984412
# Should return:
# Estimate SE LL UL
# 0.8855666 0.06129908 0.7376327 0.984412