neg.cat {negligible}

Equivalence Testing for Categorical Variables

Description

Testing for the presence of a negligible association between two categorical variables

Usage

neg.cat(
  v1 = NULL,
  v2 = NULL,
  tab = NULL,
  eiU = 0.2,
  data = NULL,
  plot = TRUE,
  save = FALSE,
  nbootpd = 1000,
  alpha = 0.05
)

## S3 method for class 'neg.cat'
print(x, ...)

Arguments

v1

first categorical variable

v2

second categorical variable

tab

contingency table for the two predictor variables

eiU

upper limit of equivalence interval

data

optional data file containing the categorical variables

plot

logical; should a plot be printed out with the effect and the proportional distance

save

should the plot be saved to 'jpg' or 'png'

nbootpd

number of bootstrap samples for calculating the CI for the proportional distance

alpha

nominal acceptable Type I error rate level

x

Data frame from neg.cat

...

extra arguments

Details

This function evaluates whether a negligible relationship exists among two categorical variables.

The statistical test is based on the Cramer's V statistic; namely addressing the question of whether the upper limit of the confidence interval for Cramer's V falls below the upper bound of the negligible effect (equivalence) interval (eiU).

If the upper bound of the CI for Cramer's V falls below eiU, we can reject Ho: The relationship is nonnegligible (V >= eiU).

eiU is set to .2 by default, but should be set based on the context of the research. Since Cramer's V statistic is in a correlation metric, setting eiU is a matter of determining what correlation is the minimally meaningful effect size (MMES) given the context of the research.

Users can input either the names of the categorical variables (v1, v2) or a frequency (contingency) table (tab).

The proportional distance (V/eiU) estimates the proportional distance of the effect from 0 to eiU, and acts as an alternative effect size measure.

Value

A list containing the following:

• cramv Cramer's V statistic

• propvar Proportion of variance explained (V^2)

• cil Lower bound of the confidence interval for Cramer's V

• ciu Upper bound of the confidence interval for Cramer's V

• eiU Upper bound of the negligible effect (equivalence) interval

• decis NHST decision

• PD Proportional distance

• CI95L Lower bound of the 1-alpha CI for the PD

• CI95U Upper bound of the 1-alpha CI for the PD

• alpha Nominal Type I error rate

Author(s)

Rob Cribbie [e-mail]

The confidence interval for the proportional distance is computed via bootstrapping (percentile bootstrap).

Examples

sex<-rep(c("m","f"),c(12,22))
haircol<-rep(c("bld","brn","bld","brn"),c(9,7,11,7))
d <- data.frame(sex,haircol)
tab<-table(sex,haircol)
neg.cat(tab=tab, alpha=.05, nbootpd=5)
neg.cat(v1=sex, v2=haircol, data=d, nbootpd=5)