phi: Measures of association for contingency tables

Description

This function calculates various measure of association for contingency tables and returns the statistic and p-value. Supported measures are Cramer's V, Phi, Spearman's rho, Kendall's tau and Pearson's r.

Usage

phi(tab)
cramer(tab)
xtab_statistics(data, x1 = NULL, x2 = NULL, statistics = c("auto",
  "cramer", "phi", "spearman", "kendall", "pearson"), ...)

Arguments

tab

A table or ftable. Tables of class xtabs and other will be coerced to ftable objects.

data

A data frame or a table object. If a table object, x1 and x2 will be ignored. For Kendall's tau, Spearman's rho or Pearson's product moment correlation coefficient, data needs to be a data frame. If x1 and x2 are not specified, the first two columns of the data frames are used as variables to compute the crosstab.

Name of first variable that should be used to compute the contingency table. If data is a table object, this argument will be irgnored.

Name of second variable that should be used to compute the contingency table. If data is a table object, this argument will be irgnored.

statistics

Name of measure of association that should be computed. May be one of "auto", "cramer", "phi", "spearman", "kendall" or "pearson". See 'Details'.

...

Other arguments, passed down to the statistic functions chisq.test, fisher.test or cor.test.

Value

For phi(), the table's Phi value. For cramer(), the table's Cramer's V. For xtab_statistics(), a list with following components:

estimate: the value of the estimated measure of association.
p.value: the p-value for the test.
statistic: the value of the test statistic.
stat.name: the name of the test statistic.
stat.html: if applicable, the name of the test statistic, in HTML-format.
df: the degrees of freedom for the contingency table.
method: character string indicating the name of the measure of association.
method.html: if applicable, the name of the measure of association, in HTML-format.
method.short: the short form of association measure, equals the statistics-aergument.
fisher: logical, if Fisher's exact test was used to calculate the p-value.

Details

The p-value for Cramer's V and the Phi coefficient are based on chisq.test(). If any expected value of a table cell is smaller than 5, or smaller than 10 and the df is 1, then fisher.test() is used to compute the p-value. The test statistic is calculated with cramer() resp. phi().

Both test statistic and p-value for Spearman's rho, Kendall's tau and Pearson's r are calculated with cor.test().

When statistics = "auto", only Cramer's V or Phi are calculated, based on the dimension of the table (i.e. if the table has more than two rows or columns, Cramer's V is calculated, else Phi).

Examples

Run this code

# NOT RUN {
# Phi coefficient for 2x2 tables
tab <- table(sample(1:2, 30, TRUE), sample(1:2, 30, TRUE))
phi(tab)

# Cramer's V for nominal variables with more than 2 categories
tab <- table(sample(1:2, 30, TRUE), sample(1:3, 30, TRUE))
cramer(tab)

data(efc)
# 2x2 table, compute Phi automatically
xtab_statistics(efc, e16sex, c161sex)

# more dimensions than 2x2, compute Cramer's V automatically
xtab_statistics(efc, c172code, c161sex)

# ordinal data, use Kendall's tau
xtab_statistics(efc, e42dep, quol_5, statistics = "kendall")

# calcilate Spearman's rho, with continuity correction
xtab_statistics(efc,
  e42dep,
  quol_5,
  statistics = "spearman",
  exact = FALSE,
  continuity = TRUE
)

# }