Confidence interval for a biserial-phi correlation

Computes a confidence interval for a population biserial-phi correlation using a transformation of a confidence interval for an odds ratio with .5 added to each cell frequency. This measure of association assumes the group variable is naturally dichotomous and the response variable is artificially dichotomous.

Usage

ci.biphi(alpha, f1, f2, n1, n2)

Arguments

alpha

alpha level for 1-alpha confidence

f1

number of participants in group 1 who have the attribute

f2

number of participants in group 2 who have the attribute

n1

sample size for group 1

n2

sample size for group 2

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of biserial-phi correlation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Ulrich R, Wirtz M (2004). “On the correlation of a naturally and an artificially dichotomized variable.” British Journal of Mathematical and Statistical Psychology, 57(2), 235–251. ISSN 00071102, doi:10.1348/0007110042307203 .

Examples

ci.biphi(.05, 46, 15, 100, 100)
#>   Estimate         SE        LL       UL
#>  0.4145733 0.07551281 0.2508866 0.546141

# Should return:
#  Estimate         SE        LL       UL
# 0.4145733 0.07551281 0.2508866 0.546141