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Provides the Critical Value(s) for a Chi Square Distribution

Source: R/cv_chisq.R
cv_chisq.Rd

Provides the Critical Value(s) for a Chi Square Distribution

Usage

cv_chisq(
  alpha_level,
  df,
  alternative = "greater",
  alpha_lower,
  alpha_upper,
  ncp = 0,
  verbose = TRUE
)

Arguments

alpha_level

Type I error rate (i.e., the false positive rate).

df

The number of degrees of freedom (a positive number).

alternative

The type of alternative hypothesis of interest. The default, "greater", puts the whole of alpha_level in the upper tail, which is how the chi square distribution is used to test a model or an association (see Details).

alpha_lower

The error rate in the lower tail of the distribution.

alpha_upper

The error rate in the upper tail of the distribution.

ncp

The noncentral parameter (if zero, the default, it is the central chi square distribution).

verbose

Provides extra information about areas under the curve.

Value

Returns the critical value(s), based on the input specifications, in a output style (a data.frame with a row for the lower and the upper critical value, following the format used by cv_t).

Details

Like the F distribution and unlike t and z, the chi square distribution is not symmetric and takes only non-negative values. Its common uses are one-sided in the upper tail: a test of association in a contingency table, a likelihood ratio test, and a test of model fit all reject for large values, because a poorly fitting model produces a large discrepancy, never a small one. That is why alternative defaults to "greater" here whereas it defaults to "not_equal" in cv_t. Maxwell, Delaney, and Kelley (2027) tabulate these upper-tail values in their Appendix Table A.9.

Both tails remain available for the situations that need them, most commonly an interval for a variance, which uses an upper and a lower chi square quantile. Set alternative = "not_equal", or give alpha_lower and alpha_upper directly. When a tail is given zero area its critical value is the boundary of the support, so lower_cv is 0 under the default.

A noncentral parameter can be supplied, which is what a power analysis for a test of model fit needs, though it would not be used for a standard null hypothesis significance test. See conf_limits_nc_chisq for confidence limits on the noncentral parameter itself.

References

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (Appendix Table A.9 reports these critical values.)

See also

cv_t, cv_f, conf_limits_nc_chisq

Other critical values: cv_bonferroni_f(), cv_bryant_paulson(), cv_dunnett(), cv_f(), cv_scheffe(), cv_smm(), cv_t(), cv_tukey_hsd(), cv_z()

Author

Ken Kelley kkelley@nd.edu

Examples

# The critical value for a test on 3 degrees of freedom at the .05 level.
cv_chisq(alpha_level = .05, df = 3)
#>  term     value area_less area_greater
#>  lower_cv 0     0         1           
#>  upper_cv 7.81  0.95      0.05        

# Simple output.
cv_chisq(alpha_level = .05, df = 3, verbose = FALSE)
#>  term     value
#>  lower_cv 0    
#>  upper_cv 7.81 

# Both tails, as an interval for a variance would need.
cv_chisq(alpha_level = .05, df = 10, alternative = "not_equal")
#>  term     value area_less area_greater
#>  lower_cv 3.25  0.025     0.975       
#>  upper_cv 20.5  0.975     0.025