neg.cor {negligible}

Test for Lack of Association between Two Continuous Normally Distributed Variables: Equivalence-based correlation tests

Description

Function performs an equivalence based test of lack of association with resampling.

Usage

neg.cor(
  v1,
  v2,
  eiU,
  eiL,
  alpha = 0.05,
  na.rm = TRUE,
  plot = TRUE,
  data = NULL,
  saveplot = FALSE,
  seed = NA,
  ...
)

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

Arguments

v1

the first variable of interest

v2

the second variable of interest

eiU

the upper bound of the equivalence interval, in terms of the magnitude of a correlation

eiL

the lower bound of the equivalence interval, in terms of the magnitude of a correlation

alpha

desired alpha level

na.rm

logical; remove missing values?

plot

whether or not to print graphics of the results (default = TRUE)

data

data frame where two variables (v1 and y) are contained - optional

saveplot

saving plots (default = FALSE)

seed

optional argument to set seed

...

additional arguments to be passed

x

object of class neg.cor

Details

From Goertzen, J. R., & Cribbie, R. A. (2010). Detecting a lack of association. British Journal of Mathematical and Statistical Psychology, 63(3), 527–537

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

The statistical test is based on a bootstrap-generated 1-2*alpha CI for the correlation; in other words, does the 1-2*alpha CI for the falls completely within the negligible effect (equivalence) interval.

The user needs to specify the lower and upper bounds of the negligible effect (equivalence) interval (eiL,eiU). Since we working in a correlation magnitude, setting these bounds requires estimating the minimally meaningful effect size (MMES); in this case, the minimally meaningful correlation (e.g., eiL = - .3, eiU = .3).

The 'plot' argument, if TRUE, will generate a plot of the observed effect (correlation) with the associated 1-2*alpha CI, along with a plot of the PD and the associated 1-alpha CI.

Value

A list including the following:

• corxy Sample correlation value

• eiL Lower bound of the negligible effect (equivalence) interval

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

• nresamples Number of resamples for the bootstrapping procedure

• q1 Lower bound of the confidence interval for the correlation

• q2 Upper bound of the confidence interval for the correlation

• PD Proportional distance

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

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

• alpha Nominal Type I error rate

Author(s)

Rob Cribbie [e-mail] Phil Chalmers [e-mail] and Nataly Beribisky [e-mail]

Examples

#Negligible correlation test between v1 and v2
#with an interval of ei=(-.2.2)
v1 <- rnorm(50)
v2 <- rnorm(50)
cor(v1, v2)
neg.cor(v1 = v1, v2 = v2, eiU = .2, eiL = -.2)