phi

Calculates phi for a 2 x 2 table of nominal variables; confidence intervals by bootstrap.

Usage

phi(
  x,
  y = NULL,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  verbose = FALSE,
  digits = 3,
  reportIncomplete = FALSE,
  ...
)

Arguments

x: Either a 2 x 2 table or a 2 x 2 matrix. Can also be a vector of observations for one dimension of a 2 x 2 table.
y: If x is a vector, y is the vector of observations for the second dimension of a 2 x2 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.
verbose: If TRUE, prints the table of counts.
digits: The number of significant digits in the output.
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.
...: Additional arguments. (Ignored.)

Value

A single statistic, phi. Or a small data frame consisting of phi, and the lower and upper confidence limits.

Details

phi is used as a measure of association between two binomial 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 for a 2 x 2 table.

Unlike Cramer's V, phi can be positive or negative (or zero), and ranges from -1 to 1.

When phi is close to its extremes, 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
Matrix = matrix(c(13, 26, 26, 13), ncol=2)
phi(Matrix)
#>    phi 
#> -0.333 

### 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))
phi(Species, Color)
#> phi 
#> 0.5