neg.intcat {negligible}

Test for Negligible Interaction between Two Categorical Variables with a Continuous Outcome

Description

This function allows researchers to test whether the interaction effect among two categorical independent variables, with a continuous outcome variable, is negligible.

Usage

neg.intcat(
  iv1 = NULL,
  iv2 = NULL,
  dv = NULL,
  neiL,
  neiU,
  nboot = 50,
  alpha = 0.05,
  data = NULL
)

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

Arguments

iv1

Levels of the first independent variable

iv2

Levels of the second independent variable

dv

Score on the continuous dependent/outcome variable

neiL

Lower bound of the negligible effect interval

neiU

Upper bound of the negligible effect interval

nboot

Number of bootstrap samples for calculating CIs

alpha

Nominal Type I Error rate

data

Dataset containing iv1, iv2 and dv

x

object of class neg.twointcat

...

extra arguments

Details

This function allows researchers to test whether the interaction effect among two categorical independent variables, with a continuous outcome variable, is negligible. In this case, 'negligible' represents the minimum meaningful interaction effect.

This test uses an intersection union approach, where a decision regarding the omnibus interaction effect is inferred from the decision regarding all simple (2 x 2) interaction effects; in other words, if all simple interaction effects are deemed negligible, then the omnibus interaction is also deemed negligible.

The test also uses the percentile bootstrap to determine confidence intervals, an approach that has been found to be robust to violations of normality and variance homogeneity.

See Cribbie, R. A., Ragoonanan, C., & Counsell, A. (2016). Testing for negligible interaction: A coherent and robust approach. British Journal of Mathematical and Statistical Psychology, 69, 159-174.

Value

A list including the following:

• meanx Sample mean of the first population/group.

• meany Sample mean of the second population/group.

• trmeanx Sample trimmed mean of the first population/group.

• trmeany Sample trimmed mean of the second population/group.

• sdx Sample standard deviation of the first population/group.

• sdy Sample standard deviation of the second population/group.

• madx Sample median absolute deviation of the first population/group.

• mady Sample median absolute deviation of the second population/group.

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

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

• effsizeraw Simple difference in the means (or trimmed means if normality = FALSE)

• cilraw2 Lower bound of the 1-alpha CI for the raw mean difference.

• ciuraw2 Upper bound of the 1-alpha CI for the raw mean difference.

• cilraw Lower bound of the 1-2*alpha CI for the raw mean difference.

• ciuraw Upper bound of the 1-2*alpha CI for the raw mean difference.

• effsized Standardized mean (or trimmed mean if normality = FALSE) difference.

• cild Lower bound of the 1-alpha CI for the standardized mean (or trimmed mean if normality = FALSE) difference.

• ciud Upper bound of the 1-alpha CI for the standardized mean (or trimmed mean if normality = FALSE) difference.

• effsizepd Proportional distance statistic.

• cilpd Lower bound of the 1-alpha CI for the proportional distance statistic.

• ciupd Upper bound of the 1-alpha CI for the proportional distance statistic.

• t1 First t-statistic from the TOST procedure.

• t1 Second t-statistic from the TOST procedure.

• df1 Degrees of freedom for the first t-statistic from the TOST procedure.

• df2 Degrees of freedom for the second t-statistic from the TOST procedure.

• p1 p value associated with the first t-statistic from the TOST procedure.

• p2 p value associated with the second t-statistic from the TOST procedure.

• alpha Nominal Type I error rate

Author(s)

Rob Cribbie [e-mail]

Examples

outcome<-rnorm(60,mean=50,sd=10)
iv_1<-rep(c("male","female"),each=30)
iv_2<-rep(c("young","middle","old"),each=10,times=2)
d<-data.frame(iv_1,iv_2,outcome)
neg.intcat(iv1=iv_1,iv2=iv_2,dv=outcome,neiL=-15,neiU=15,nboot=10)
neg.intcat(iv1=iv_1,iv2=iv_2,dv=outcome,neiL=-15,neiU=15,nboot=10,data=d)