neg.paired {negligible}

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

Description

This function allows researchers to test whether the difference between the means of two dependent populations is negligible, where negligible represents the smallest meaningful effect size (MMES)

Usage

neg.paired(
  var1 = NULL,
  var2 = NULL,
  outcome = NULL,
  group = NULL,
  ID = NULL,
  neiL,
  neiU,
  normality = TRUE,
  nboot = 10000,
  alpha = 0.05,
  plot = TRUE,
  saveplot = FALSE,
  data = NULL,
  seed = NA,
  ...
)

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

Arguments

var1

Data for Group 1 (if outcome, group and ID are omitted)

var2

Data for Group 2 (if outcome, group and ID are omitted)

outcome

Dependent Variable (if var1 and var2 are omitted)

group

Dichotomous Predictor/Independent Variable (if var1 and var2 are omitted)

ID

participant ID (if var1 and var2 are omitted)

neiL

Lower Bound of the Equivalence Interval

neiU

Upper Bound of the Equivalence Interval

normality

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

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 var1/var2 or outcome/group/ID

seed

Seed number

...

Extra arguments

x

object of class neg.paired

Details

This function evaluates whether the difference in the means of 2 dependent 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 (var1, var2, both should be continuous) or specifies the Indepedent Variable/Predictor (group, 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.

Value

A list including the following:

• meanx Sample mean of the first population/group.

• meany Sample mean of the second population/group.

• medx Sample median of the first population/group.

• medy Sample median 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.

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

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

• effsizeraw Simple difference in the means (or medians 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 median if normality = FALSE) difference.

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

• ciud Upper bound of the 1-alpha CI for the standardized mean (or median 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.

• pval1 p value associated with the first t-statistic from the TOST procedure.

• pval2 p value associated with the second t-statistic from the TOST procedure.

• alpha Nominal Type I error rate

• seed Seed number

Author(s)

Rob Cribbie [e-mail] Naomi Martinez Gutierrez [e-mail]

Examples

#wide format
ID<-rep(1:20)
control<-rnorm(20)
intervention<-rnorm(20)
d<-data.frame(ID, control, intervention)
head(d)
neg.paired(var1=control,var2=intervention,neiL=-1,neiU=1,plot=TRUE,
           data=d)
neg.paired(var1=d$control,var2=d$intervention,neiL=-1,neiU=1,plot=TRUE)
neg.paired(var1=d$control,var2=d$intervention,neiL=-1,neiU=1,normality=FALSE,
           nboot=10,plot=TRUE)

## Not run: 
#long format
sample1<-sample(1:20, 20, replace=FALSE)
sample2<-sample(1:20, 20, replace=FALSE)
ID<-c(sample1, sample2)
group<-rep(c("control","intervention"),c(20,20))
outcome<-c(control,intervention)
d<-data.frame(ID,group,outcome)
neg.paired(outcome=outcome,group=group,ID=ID,neiL=-1,neiU=1,plot=TRUE,data=d)
neg.paired(outcome=d$outcome,group=d$group,ID=d$ID,neiL=-1,neiU=1,plot=TRUE)
neg.paired(outcome=d$outcome,group=d$group,ID=d$ID,neiL=-1,neiU=1,plot=TRUE, normality=FALSE)

#long format with multiple variables
sample1<-sample(1:20, 20, replace=FALSE)
sample2<-sample(1:20, 20, replace=FALSE)
ID<-c(sample1, sample2)
attendance<-sample(1:3, 20, replace=TRUE)
group<-rep(c("control","intervention"),c(20,20))
outcome<-c(control,intervention)
d<-data.frame(ID,group,outcome,attendance)
neg.paired(outcome=outcome,group=group,ID=ID,neiL=-1,neiU=1,plot=TRUE,data=d)
neg.paired(outcome=d$outcome,group=d$group,ID=d$ID,neiL=-1,neiU=1,plot=TRUE)

#open a dataset
library(negligible)
d<-perfectionism
names(d)
head(d)
neg.paired(var1=atqpre.total,var2=atqpost.total,
           neiL=-10,neiU=10,data=d)

#Dataset with missing data
x<-rnorm(10)
x[c(3,6)]<-NA
y<-rnorm(10)
y[c(7)]<-NA
neg.paired(x,y,neiL=-1,neiU=1, normality=FALSE)

## End(Not run)