R script to accompany blogpost http://deevybee.blogspot.co.uk/2013/06/interpreting-unexpected-significant.html Generates random normal numbers to simulate ERP data. Used to demonstrate how false positive rate depends on N factors in ANOVA.

1. #-------------------------------------------------------------------------------------
# ERPsimulate
# by D V M Bishop, 18th
June 2013
# Script to accompany blogpost:
# http://deevybee.blogspot.co.uk/2013/06/interpreting-unexpected-significant.html
#-------------------------------------------------------------------------------------
# Create datasets of simulated ERP averages by random number generation
# Assign means to fictitious subjects/conditions/electrodes and use ezANOVA
# to analyse
# ForezANOVA, data are organised in a format where repeated
# measures are stacked below one another
#For each dataset, do ANOVA for 4 way, 3 way (elec as factor) and 2 way (difference score as factor)
require(MASS) #used for multivariate random normal data generation, mvrnorm command
require(ez) #for ezanova
ptm<- proc.time() #500 runs took about 5 mins
nsims=8# n values to simulate for each subject; 2 locs x 2 sides x 2 conditions
mycorrel=0 #intercorrelation between dvs, will be in mysigma matrix
mysigma=matrix(c(rep(mycorrel,nsims*nsims)),nsims,nsims)
for (i in 1:nsims){mysigma[i,i]=1} #ones on diagonal
mymu=rep(0,nsims) #mean is zero
nsub=40 # here 2 groups of 20
mydata=matrix(rep(0,nsub*nsims*8),nsub*nsims,8)#initialise data matrix; 8 cols to include all
possible factors
nrun=20 #N runs through the simulation; ANOVA done for each one; once working, try around 1000
runs
mypvalues=array(0,dim=c(25,nrun)) #initialise array for 4way, 3way and 2way stacked: used to save
ANOVA pvalue outputs - 15 terms altogether
myeffect=0 #this effect will be added to cols 4-8 (one level of 'task' factor); .2 will give a modest
effect
for (myrun in 1:nrun){ # do repeated runs of the simulation
myavg=mvrnorm(n = nsub, mymu, mysigma, empirical = FALSE) #make matrix of random values
#for all subjects with intercorrelation
#determined by mysigma
myavg[,4:8]=myavg[,4:8]+myeffect #constant effect added to cols corresponding to one level of
'task'
for (mysub in 1:nsub){
mygrp=1

2. if (mysub>20){mygrp=2}#2 groups each of 20 #can change this if desired
startrow=(mysub-1)*(nsims)+1
endrow=mysub*nsims
mydata[startrow:endrow,1]=mysub;#ID in col 1
mydata[startrow:endrow,2]=t(myavg[mysub,]) #simulated avgs stacked in col 2
mydata[startrow:endrow,3]=mygrp;#group in col 3
mydata[startrow:endrow,4]=c(1,1,1,1,2,2,2,2);#task in col 4
mydata[startrow:endrow,5]=c(1,1,2,2,1,1,2,2) #side in col 5
mydata[startrow:endrow,6]=c(1,2,1,2,1,2,1,2) #loc in col 6
mydata[startrow:endrow,7]=c(1,2,3,4,1,2,3,4) #electrode in col 7 (equiv to side x loc)
mydata[startrow:endrow,8]=c(myavg[mysub,1]-myavg[mysub,5],myavg[mysub,2]-
myavg[mysub,6],myavg[mysub,3]-myavg[mysub,7],myavg[mysub,4]-myavg[mysub,8])
#difference between the two levels of task
} #end of mysub loop
mydf=data.frame(mydata)
names(mydf)=c("id","amp","group" ,"task", "side", "loc","elec","diff")
mydf$id<- as.factor(mydf$id)
mydf$group<- as.factor(mydf$group)
mydf$task<- as.factor(mydf$task)
mydf$side<- as.factor(mydf$side)
mydf$loc<- as.factor(mydf$loc)
mydf$elec<- as.factor(mydf$elec)
mydf$diff=as.numeric(mydf$diff)
mydf2 <- mydf[which(mydf$task==1 ), ] #for 2 way Anova, just take rows where task=1 so there's
just one difference value
attach(mydf)
attach(mydf2)
myresult4=ezANOVA(data=mydf, dv=.(amp), wid=.(id), between=.(group),within=.(task, side,loc),
type=3)
myresult3=ezANOVA(data=mydf,dv=.(amp),wid=.(id),between=.(group),within=.(task,elec),type=3)
myresult2=ezANOVA(data=mydf2,dv=.(diff),wid=.(id),between=.(group),within=.(elec),type=3)
detach(mydf)
detach(mydf2)
mypvalues[,myrun]=c(myresult4$ANOVA[,5],myresult3$ANOVA[,5],myresult2$ANOVA[,5]) #5th col
of ANOVA output has pvalues
rownames(mypvalues)=
c(myresult4$ANOVA$Effect,myresult3$ANOVA$Effect,myresult2$ANOVA$Effect)
}
myfilename="mypvalues_all.TXT"
#write.table(mydata, "mydata.txt", sep="t") #write data from last run only to a tab-sep text file; will
be saved in default directory

3. write.table(t(mypvalues), myfilename, sep="t") #write transposed pvalues to a tab-sep text file; will
be saved in default directory
#First 15 cols will give output for 4-way, next 7 give output for 3-way, and last 3 for 2-way
#NB for 2-way, the 'group' term is equivalent to group x task in other ANOVAs, because dv is task
difference
proc.time()-ptm #check how long it takes to run