# Negligible Effect Test on the Difference between the Means of Dependent Populations 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) ```r 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` ## Returns 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 ## 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. ## Examples ```r #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) ``` ## Author(s) Rob Cribbie cribbie@yorku.ca Naomi Martinez Gutierrez naomimg@yorku.ca

neg.paired function