ci.bscor: Confidence interval for a biserial correlation

In statpsych: Statistical Methods for Psychologists

Confidence interval for a biserial correlation

Description

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.

Usage

ci.bscor(alpha, m1, m2, sd1, sd2, n1, n2)

Arguments

alpha	alpha level for 1-alpha confidence
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

Details

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.

Value

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

References

\insertRef

Bonett2020astatpsych

Examples

ci.bscor(.05, 28.32, 21.48, 3.81, 3.09, 40, 40)

# Should return:
#   Estimate         SE        LL        UL
#  0.8855666 0.06129908  0.7376327 0.984412
 

statpsych documentation built on Sept. 11, 2024, 7:42 p.m.