freemanTheta {rcompanion}

Freeman's theta

Description

Calculates Freeman's theta for a table with one ordinal variable and one nominal variable; confidence intervals by bootstrap.

Usage

freemanTheta(
  x,
  g = NULL,
  group = "row",
  verbose = FALSE,
  progress = FALSE,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  digits = 3,
  reportIncomplete = FALSE
)

Arguments

x

Either a two-way table or a two-way matrix. Can also be a vector of observations of an ordinal variable.

g

If x is a vector, g is the vector of observations for the grouping, nominal variable.

group

If x is a table or matrix, group indicates whether the "row" or the "column" variable is the nominal, grouping variable.

verbose

If TRUE, prints statistics for each comparison.

progress

If TRUE, prints a message as each comparison is conducted.

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.

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.

Details

Freeman's coefficent of differentiation (theta) is used as a measure of association for a two-way table with one ordinal and one nominal variable. See Freeman (1965).

Currently, the function makes no provisions for NA values in the data. It is recommended that NAs be removed beforehand.

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

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

Value

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

Author(s)

Salvatore Mangiafico, [e-mail]

References

Freeman, L.C. 1965. Elementary Applied Statistics for Students in Behavioral Science. Wiley.

https://rcompanion.org/handbook/H_11.html

See Also

epsilonSquared

Examples

data(Breakfast)
library(coin)
chisq_test(Breakfast, scores = list("Breakfast" = c(-2, -1, 0, 1, 2)))
freemanTheta(Breakfast)

### Example from Freeman (1965), Table 10.6
Counts = c(1, 2, 5, 2, 0, 10, 5, 5, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 3)
Matrix = matrix(Counts, byrow=TRUE, ncol=5,
                dimnames = list(Marital.status = c("Single", "Married",
                                                   "Widowed", "Divorced"),
                                Social.adjustment = c("5","4","3","2","1")))
Matrix
freemanTheta(Matrix)

### Example after Kruskal Wallis test
data(PoohPiglet)
kruskal.test(Likert ~ Speaker, data = PoohPiglet)
freemanTheta(x = PoohPiglet$Likert, g = PoohPiglet$Speaker)

### Same data, as table of counts
data(PoohPiglet)
XT = xtabs( ~ Speaker + Likert , data = PoohPiglet)
freemanTheta(XT)

### Example from Freeman (1965), Table 10.7
Counts = c(52, 28, 40, 34, 7, 9, 16, 10, 8, 4, 10, 9, 12,6, 7, 5)
Matrix = matrix(Counts, byrow=TRUE, ncol=4,
                dimnames = list(Preferred.trait = c("Companionability",
                                                    "PhysicalAppearance",
                                                    "SocialGrace",
                                                    "Intelligence"),
                                Family.income = c("4", "3", "2", "1")))
Matrix
freemanTheta(Matrix, verbose=TRUE)