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Confidence intervals for generalized Yule coefficients

Source: R/statpsych3.R
ci.yule.Rd

Computes confidence intervals for four generalized Yule measures of association (Yule Q, Yule Y, Digby H, and Bonett-Price Y*) using a transformation of a confidence interval for an odds ratio with .5 added to each cell frequency. This function requires the frequency counts from a 2 x 2 contingency table for two dichotomous variables. Digby H is sometimes used as a crude approximation to the tetrachoric correlation. Yule Y is equal to the phi coefficient only when all marginal frequencies are equal. Bonett-Price Y* is a better approximation to the phi coefficient when the marginal frequencies are not equal.

For more details, see Section 3.4 of Bonett (2021, Volume 3)

Usage

ci.yule(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 generalized Yule coefficient

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/. Bonett DG, Price RM (2007). “Statistical inference for generalized Yule coefficients in 2x2 contingency tables.” Sociological Methods & Research, 35(3), 429–446. ISSN 0049-1241, doi:10.1177/0049124106292358 .

Examples

ci.yule(.05, 229, 28, 96, 24)
#>     Estimate     SE    LL    UL
#> Q:     0.343 0.1328 0.062 0.573
#> Y:     0.177 0.0729 0.031 0.315
#> H:     0.262 0.1051 0.047 0.454
#> Y*:    0.131 0.0546 0.023 0.236

# Should return:
#    Estimate     SE    LL    UL
# Q:    0.343 0.1328 0.062 0.573
# Y:    0.177 0.0729 0.031 0.315
# H:    0.262 0.1051 0.047 0.454
# Y*:   0.131 0.0546 0.023 0.236