Confidence interval for a tetrachoric correlation

Source: R/statpsych3.R

Computes a confidence interval for an approximation to the tetrachoric correlation. This function requires the frequency counts from a 2 x 2 contingency table for two dichotomous variables. This measure of association assumes both of the dichotomous variables are artificially dichotomous. An approximate standard error is recovered from the confidence interval.

ci.tetra(alpha, f00, f01, f10, f11)

Arguments

alpha

alpha level for 1-alpha confidence

f00

number of participants with y = 0 and x = 0

f01

number of participants with y = 0 and x = 1

f10

number of participants with y = 1 and x = 0

f11

number of participants with y = 1 and x = 1

Value

Returns a 1-row matrix. The columns are:

  • Estimate - estimate of tetrachoric approximation

  • SE - recovered standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2005). “Inferential methods for the tetrachoric correlation coefficient.” Journal of Educational and Behavioral Statistics, 30(2), 213--225. ISSN 1076-9986, doi:10.3102/10769986030002213 .

Examples

ci.tetra(.05, 46, 15, 54, 85)
#>   Estimate         SE        LL        UL
#>  0.5135167 0.09301703 0.3102345 0.6748546

# Should return:
#  Estimate         SE        LL        UL
# 0.5135167 0.09301703 0.3102345 0.6748546