ci_chisq_ncp: CI for the NCP of the Chi-Squared Distribution

Description

This function calculates CIs for the non-centrality parameter (NCP) of the \(\chi^2\)-distribution. A positive lower \((1 - \alpha) \cdot 100\%\)-confidence limit for the NCP goes hand-in-hand with a significant association test at level \(\alpha\).

Usage

ci_chisq_ncp(
  x,
  probs = c(0.025, 0.975),
  correct = TRUE,
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Value

An object of class "cint", see ci_mean() for details.

Arguments

x: The result of stats::chisq.test(), a matrix/table of counts, or a data.frame with exactly two columns representing the two variables.
probs: Lower and upper probabilities, by default c(0.025, 0.975).
correct: Should Yates continuity correction be applied to the 2x2 case? The default is TRUE (also used in the bootstrap), which differs from ci_cramersv().
type: Type of CI. One of "chi-squared" (default) or "bootstrap".
boot_type: Type of bootstrap CI. Only used for type = "bootstrap".
R: The number of bootstrap resamples. Only used for type = "bootstrap".
seed: An integer random seed. Only used for type = "bootstrap".
...: Further arguments passed to boot::boot().

Details

By default, CIs are computed by Chi-squared test inversion. This can be unreliable for very large test statistics. The default bootstrap type is "bca".

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

Examples

Run this code

ci_chisq_ncp(mtcars[c("am", "vs")])
ci_chisq_ncp(mtcars[c("am", "vs")], type = "bootstrap", R = 999)  # Use larger R

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