R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(8.7,10.6,9.0,9.2,8.3,7.6,9.0,8.2,9.0,8.7,9.1,8.0,7.7,9.9,8.4,9.0,8.8,8.3,8.8,9.8,8.1,8.9,7.4,8.9,9.8,8.5,9.7,7.7,8.8,9.6,9.6,7.8,9.4,9.4,8.8,10.1,9.0,8.0,7.8,10.0,8.9,8.9,8.6,9.0,9.3,8.9,7.0,9.3,8.4,9.0,8.9,9.4,8.3,8.8,7.5,7.5,8.2,8.1,8.2,8.4,9.3,9.2,8.3,8.6,9.2,9.5,9.2,9.4,8.8,8.4,9.3,9.1,8.9,9.3,8.9,8.8,8.6,9.7,10.4,9.7,10.0,9.8,9.3,9.5,8.4,9.8,8.6,9.7,10.5,8.6,9.3,9.1,9.1,9.9,9.3,9.7,8.9,10.0,9.1,9.7,9.1,10.3,9.7,9.6,9.8,9.8,9.8,8.7,9.1,8.9,10.1,9.5,10.3,9.3,10.2,10.1,10.3,9.8,9.8,9.3,9.9,9.3,9.2,8.4,10.1,9.6,10.6,10.0,10.4,8.6,8.4,9.6,9.1,10.0,10.0,9.3,9.6,9.6,9.9,9.3,9.7,10.0,9.9,10.4,9.8,9.4,9.0,9.4,9.7,10.5,10.5,9.9,8.9,9.4,9.2,10.6,11.3,11.2,10.0,10.6,10.1,11.1,10.9,9.1,10.8,10.6,11.1,11.2,10.7,11.2,11.1,10.7,11.0,11.4,11.5,10.9)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency Temp.'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> geomean <- function(x) {
+ return(exp(mean(log(x))))
+ }
> harmean <- function(x) {
+ return(1/mean(1/x))
+ }
> quamean <- function(x) {
+ return(sqrt(mean(x*x)))
+ }
> winmean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ win <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
+ win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
+ }
+ return(win)
+ }
> trimean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ tri <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ tri[j,1] <- mean(x,trim=j/n)
+ tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
+ }
+ return(tri)
+ }
> midrange <- function(x) {
+ return((max(x)+min(x))/2)
+ }
> q1 <- function(data,n,p,i,f) {
+ np <- n*p;
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q2 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q3 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q4 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q5 <- function(data,n,p,i,f) {
+ np <- (n-1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i+1]
+ } else {
+ qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
+ }
+ }
> q6 <- function(data,n,p,i,f) {
+ np <- n*p+0.5
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- data[i]
+ }
> q7 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- f*data[i] + (1-f)*data[i+1]
+ }
+ }
> q8 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ if (f == 0.5) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ if (f < 0.5) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
+ }
+ }
> midmean <- function(x,def) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ if (def==1) {
+ qvalue1 <- q1(x,n,0.25,i,f)
+ qvalue3 <- q1(x,n,0.75,i,f)
+ }
+ if (def==2) {
+ qvalue1 <- q2(x,n,0.25,i,f)
+ qvalue3 <- q2(x,n,0.75,i,f)
+ }
+ if (def==3) {
+ qvalue1 <- q3(x,n,0.25,i,f)
+ qvalue3 <- q3(x,n,0.75,i,f)
+ }
+ if (def==4) {
+ qvalue1 <- q4(x,n,0.25,i,f)
+ qvalue3 <- q4(x,n,0.75,i,f)
+ }
+ if (def==5) {
+ qvalue1 <- q5(x,n,0.25,i,f)
+ qvalue3 <- q5(x,n,0.75,i,f)
+ }
+ if (def==6) {
+ qvalue1 <- q6(x,n,0.25,i,f)
+ qvalue3 <- q6(x,n,0.75,i,f)
+ }
+ if (def==7) {
+ qvalue1 <- q7(x,n,0.25,i,f)
+ qvalue3 <- q7(x,n,0.75,i,f)
+ }
+ if (def==8) {
+ qvalue1 <- q8(x,n,0.25,i,f)
+ qvalue3 <- q8(x,n,0.75,i,f)
+ }
+ midm <- 0
+ myn <- 0
+ roundno4 <- round(n/4)
+ round3no4 <- round(3*n/4)
+ for (i in 1:n) {
+ if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
+ midm = midm + x[i]
+ myn = myn + 1
+ }
+ }
+ midm = midm / myn
+ return(midm)
+ }
> (arm <- mean(x))
[1] 9.386932
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.06685416
> (armose <- arm / armse)
[1] 140.4091
> (geo <- geomean(x))
[1] 9.344992
> (har <- harmean(x))
[1] 9.302686
> (qua <- quamean(x))
[1] 9.428502
> (win <- winmean(x))
          [,1]       [,2]
 [1,] 9.388636 0.06632693
 [2,] 9.388636 0.06594401
 [3,] 9.386932 0.06566838
 [4,] 9.389205 0.06530386
 [5,] 9.392045 0.06486972
 [6,] 9.388636 0.06433912
 [7,] 9.392614 0.06375694
 [8,] 9.392614 0.06375694
 [9,] 9.397727 0.06159121
[10,] 9.392045 0.06076591
[11,] 9.398295 0.05997009
[12,] 9.391477 0.05901717
[13,] 9.391477 0.05712745
[14,] 9.391477 0.05712745
[15,] 9.382955 0.05604059
[16,] 9.392045 0.05497605
[17,] 9.392045 0.05497605
[18,] 9.392045 0.05497605
[19,] 9.392045 0.05497605
[20,] 9.392045 0.05231301
[21,] 9.392045 0.05231301
[22,] 9.392045 0.05231301
[23,] 9.378977 0.05077075
[24,] 9.378977 0.05077075
[25,] 9.378977 0.05077075
[26,] 9.364205 0.04911704
[27,] 9.379545 0.04744319
[28,] 9.395455 0.04581030
[29,] 9.378977 0.04400126
[30,] 9.361932 0.04224040
[31,] 9.361932 0.04224040
[32,] 9.361932 0.04224040
[33,] 9.361932 0.04224040
[34,] 9.381250 0.04031053
[35,] 9.361364 0.03834959
[36,] 9.361364 0.03834959
[37,] 9.382386 0.03634940
[38,] 9.382386 0.03634940
[39,] 9.382386 0.03634940
[40,] 9.382386 0.03634940
[41,] 9.382386 0.03634940
[42,] 9.382386 0.03634940
[43,] 9.357955 0.03404965
[44,] 9.382955 0.03179115
[45,] 9.382955 0.03179115
[46,] 9.382955 0.03179115
[47,] 9.382955 0.03179115
[48,] 9.382955 0.03179115
[49,] 9.355114 0.02928554
[50,] 9.355114 0.02928554
[51,] 9.355114 0.02928554
[52,] 9.355114 0.02928554
[53,] 9.355114 0.02928554
[54,] 9.355114 0.02928554
[55,] 9.386364 0.02659660
[56,] 9.386364 0.02659660
[57,] 9.386364 0.02659660
[58,] 9.386364 0.02659660
> (tri <- trimean(x))
          [,1]       [,2]
 [1,] 9.388506 0.06508072
 [2,] 9.388372 0.06374054
 [3,] 9.388235 0.06251390
 [4,] 9.388690 0.06130080
 [5,] 9.388554 0.06010465
 [6,] 9.387805 0.05892435
 [7,] 9.387654 0.05776666
 [8,] 9.386875 0.05662912
 [9,] 9.386076 0.05539847
[10,] 9.384615 0.05441739
[11,] 9.383766 0.05347980
[12,] 9.382237 0.05257488
[13,] 9.381333 0.05172104
[14,] 9.380405 0.05102965
[15,] 9.380405 0.05027950
[16,] 9.379167 0.04958917
[17,] 9.378169 0.04895386
[18,] 9.377143 0.04826212
[19,] 9.376087 0.04750803
[20,] 9.375000 0.04668475
[21,] 9.373881 0.04605317
[22,] 9.372727 0.04536192
[23,] 9.371538 0.04460433
[24,] 9.371094 0.04392404
[25,] 9.370635 0.04317653
[26,] 9.370161 0.04235371
[27,] 9.370492 0.04160590
[28,] 9.370000 0.04093788
[29,] 9.368644 0.04034652
[30,] 9.368644 0.03985730
[31,] 9.368421 0.03946773
[32,] 9.368750 0.03903253
[33,] 9.369091 0.03854626
[34,] 9.369444 0.03800262
[35,] 9.368868 0.03756667
[36,] 9.369231 0.03724745
[37,] 9.369608 0.03688484
[38,] 9.369000 0.03664448
[39,] 9.368367 0.03636656
[40,] 9.367708 0.03604623
[41,] 9.367021 0.03567784
[42,] 9.366304 0.03525476
[43,] 9.365556 0.03476912
[44,] 9.365909 0.03443401
[45,] 9.365116 0.03425052
[46,] 9.364286 0.03402788
[47,] 9.363415 0.03376024
[48,] 9.362500 0.03344062
[49,] 9.362500 0.03306070
[50,] 9.361842 0.03287227
[51,] 9.362162 0.03263696
[52,] 9.362500 0.03234676
[53,] 9.362857 0.03199194
[54,] 9.363235 0.03156055
[55,] 9.363636 0.03103771
[56,] 9.362500 0.03073988
[57,] 9.361290 0.03036486
[58,] 9.360000 0.02989624
> (midr <- midrange(x))
[1] 9.25
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 9.330208 9.371910 9.330208 9.371910 9.371910 9.330208 9.371910 9.330208
> postscript(file="/var/www/rcomp/tmp/19a3y1292159979.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> lb <- win[,1] - 2*win[,2]
> ub <- win[,1] + 2*win[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/2k1k11292159979.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> lb <- tri[,1] - 2*tri[,2]
> ub <- tri[,1] + 2*tri[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Measure',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.element(a,'S.E.',header=TRUE)
> a<-table.element(a,'Value/S.E.',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
> a<-table.element(a,arm)
> a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
> a<-table.element(a,armose)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
> a<-table.element(a,geo)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
> a<-table.element(a,har)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
> a<-table.element(a,qua)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> for (j in 1:length(win[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Winsorized Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(win[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
+ a<-table.element(a,win[j,1])
+ a<-table.element(a,win[j,2])
+ a<-table.element(a,win[j,1]/win[j,2])
+ a<-table.row.end(a)
+ }
> for (j in 1:length(tri[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Trimmed Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(tri[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
+ a<-table.element(a,tri[j,1])
+ a<-table.element(a,tri[j,2])
+ a<-table.element(a,tri[j,1]/tri[j,2])
+ a<-table.row.end(a)
+ }
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
> a<-table.element(a,median(x))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
> a<-table.element(a,midr)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[1])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[2])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[3])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[4])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[5])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[6])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[7])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[8])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Number of observations',header=TRUE)
> a<-table.element(a,length(x))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/www/rcomp/tmp/3xeev1292159980.tab") 
> 
> try(system("convert tmp/19a3y1292159979.ps tmp/19a3y1292159979.png",intern=TRUE))
character(0)
> try(system("convert tmp/2k1k11292159979.ps tmp/2k1k11292159979.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.070   0.430   1.501