neg.twoindmeans {negligible}

Negligible Effect Test on the Difference between the Means of Independent Populations

Description

This function allows researchers to test whether the difference between the means of two independent populations is negligible, where negligible represents the smallest meaningful effect size (MMES, which in this case the effect is the mean difference)

Usage

neg.twoindmeans(
  v1 = NULL,
  v2 = NULL,
  dv = NULL,
  iv = NULL,
  eiL,
  eiU,
  varequiv = FALSE,
  normality = FALSE,
  tr = 0.2,
  nboot = 500,
  alpha = 0.05,
  plot = TRUE,
  saveplot = FALSE,
  data = NULL
)

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

Arguments

v1

Data for Group 1 (if dv and iv are omitted)

v2

Data for Group 2 (if dv and iv are omitted)

dv

Dependent Variable (if v1 and v2 are omitted)

iv

Dichotomous Predictor/Independent Variable (if v1 and v2 are omitted)

eiL

Lower Bound of the Equivalence Interval

eiU

Upper Bound of the Equivalence Interval

varequiv

Are the population variances assumed to be equal? Population variances are assumed to be unequal if normality=FALSE.

normality

Are the population variances (and hence the residuals) assumed to be normally distributed?

tr

Proportion of trimming from each tail (relevant if normality = FALSE)

nboot

Number of bootstrap samples for calculating CIs

alpha

Nominal Type I Error rate

plot

Should a plot of the results be produced?

saveplot

Should the plot be saved?

data

Dataset containing v1/v2 or iv/dv

x

object of class neg.twoindmeans

...

extra arguments

Details

This function evaluates whether the difference in the means of 2 independent populations can be considered negligible (i.e., the population means can be considered equivalent).

The user specifies either the data associated with the first and second groups/populations (iv1, iv2, both should be continuous) or specifies the Indepedent Variable/Predictor (iv, should be a factor) and the Dependent Variable (outcome, should be continuous). A 'data' statement can be used if the variables are stored in an R dataset.

The user must also specify the lower and upper bounds of the negligible effect (equivalence) interval. These are specified in the original units of the outcome variable.

The arguments 'varequiv' and 'normality' control what test statistic is adopted. If varequiv = TRUE and normality = TRUE the ordinary Student t statistic is adopted. If varequiv = FALSE and normality = TRUE the Welch t statistic is adopted. If normality = FALSE the ordinary Student t statistic is adopted. d

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] R. Philip Chalmers [e-mail] Naomi Martinez Gutierrez [e-mail]

Examples

indvar<-rep(c("a","b"),c(10,12))
depvar<-rnorm(22)
d<-data.frame(indvar,depvar)
neg.twoindmeans(dv=depvar,iv=indvar,eiL=-1,eiU=1,plot=TRUE,data=d)
neg.twoindmeans(dv=depvar,iv=indvar,eiL=-1,eiU=1)
neg.twoindmeans(v1=depvar[indvar=="a"],v2=depvar[indvar=="b"],eiL=-1,eiU=1)
xx<-neg.twoindmeans(dv=depvar,iv=indvar,eiL=-1,eiU=1)
xx$decis