Cramer's V (phi)

Calculates Cramer's V for a table of nominal variables; confidence intervals by bootstrap.

cramerV(
  x,
  y = NULL,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  digits = 4,
  bias.correct = FALSE,
  reportIncomplete = FALSE,
  verbose = FALSE,
  tolerance = 1e-16,
  ...
)

Arguments

x: Either a two-way table or a two-way matrix. Can also be a vector of observations for one dimension of a two-way table.
y: If x is a vector, y is the vector of observations for the second dimension of a two-way table.
ci: If TRUE, returns confidence intervals by bootstrap. May be slow.
conf: The level for the confidence interval.
type: The type of confidence interval to use. Can be any of "norm", "basic", "perc", or "bca". Passed to boot.ci.
R: The number of replications to use for bootstrap.
histogram: If TRUE, produces a histogram of bootstrapped values.
digits: The number of significant digits in the output.
bias.correct: If TRUE, a bias correction is applied.
reportIncomplete: If FALSE (the default), NA will be reported in cases where there are instances of the calculation of the statistic failing during the bootstrap procedure.
verbose: If TRUE, prints additional statistics.
tolerance: If the variance of the bootstrapped values are less than tolerance, NA is returned for the confidence interval values.
...: Additional arguments passed to chisq.test.

Value

A single statistic, Cramer's V. Or a small data frame consisting of Cramer's V, and the lower and upper confidence limits.

Details

Cramer's V is used as a measure of association between two nominal variables, or as an effect size for a chi-square test of association. For a 2 x 2 table, the absolute value of the phi statistic is the same as Cramer's V.

Because V is always positive, if type="perc", the confidence interval will never cross zero. In this case, the confidence interval range should not be used for statistical inference. However, if type="norm", the confidence interval may cross zero.

When V is close to 0 or very large, or with small counts, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

References

https://rcompanion.org/handbook/H_10.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

### Example with table
data(Anderson)
fisher.test(Anderson)
#> 
#> 	Fisher's Exact Test for Count Data
#> 
#> data:  Anderson
#> p-value = 0.000668
#> alternative hypothesis: two.sided
#> 
cramerV(Anderson)
#> Cramer V 
#>   0.4387 

### Example with two vectors
Species = c(rep("Species1", 16), rep("Species2", 16))
Color   = c(rep(c("blue", "blue", "blue", "green"),4),
            rep(c("green", "green", "green", "blue"),4))
fisher.test(Species, Color)
#> 
#> 	Fisher's Exact Test for Count Data
#> 
#> data:  Species and Color
#> p-value = 0.01211
#> alternative hypothesis: true odds ratio is not equal to 1
#> 95 percent confidence interval:
#>   1.463598 60.596055
#> sample estimates:
#> odds ratio 
#>   8.279362 
#> 
cramerV(Species, Color)
#> Cramer V 
#>      0.5