R version 2.6.0 (2007-10-03)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(0.000249254412317267
+ ,0.000299603588409276
+ ,0.000322518965091164
+ ,-0.000329538636649367
+ ,-6.43325994869136e-05
+ ,0.000218734547908577
+ ,-0.000186123790106601
+ ,0.000320044464404368
+ ,0.000105079817925291
+ ,-3.21375723064676e-05
+ ,-9.31379372201002e-05
+ ,0.000863880329915967
+ ,-0.000955068293604838
+ ,0.000191654585176615
+ ,-0.000687217159304088
+ ,-0.00133295077536133
+ ,-8.40818637339591e-05
+ ,0.000480643586810492
+ ,-0.00133724173345948
+ ,-0.00078463864413933
+ ,-9.63012198662017e-05
+ ,-0.000267289029594886
+ ,-0.000415973064666258
+ ,-0.00145962546732839
+ ,0.00114159591731011
+ ,-0.00146064163655782
+ ,-0.00105351430012057
+ ,0.000585759739068242
+ ,-0.00113140931418457
+ ,-0.00138720915811827
+ ,0.000330704048772557
+ ,0.00089730707501226
+ ,-0.00282718491905784
+ ,0.00130177229774819
+ ,0.000106725469179531
+ ,0.00194958872561832
+ ,0.000635002216373137
+ ,-0.000802593879913022
+ ,0.000669740048378942
+ ,-0.00184856803744929
+ ,-0.00115402862422859
+ ,0.000720565693177494
+ ,0.00127635646932789
+ ,0.000280808847524822
+ ,-0.00124166740902709
+ ,0.00220850912079990
+ ,0.00014951799778537
+ ,0.000246824748826507
+ ,-0.000329567131906322
+ ,-0.000100055638308394
+ ,-0.000843374093922739
+ ,-0.00182816513524967
+ ,0.000762276721414934
+ ,0.000547214397100731
+ ,-0.000261835368196878
+ ,-0.000145977686326793
+ ,-0.000418138010040314
+ ,-0.000275994456749945
+ ,0.00096506287877901
+ ,-0.000122679144738069
+ ,-0.00077104475183501
+ ,-0.000772836964526374
+ ,-9.74711304966847e-05
+ ,0.00132936498148101
+ ,0.000993746723184863
+ ,-0.000451847013386047
+ ,-0.000138456169144319
+ ,-0.00109488862631829
+ ,-0.000236567991803771
+ ,0.000228265967558205
+ ,-0.000141243730919727
+ ,7.13248149721013e-05
+ ,0.000100146168015486
+ ,-0.000101542587067266
+ ,-0.00103071143157252
+ ,-0.000910687763439777
+ ,-0.00169775499641645
+ ,0.000648520060953617
+ ,-0.00081739205188841
+ ,-0.000440416182630077
+ ,-0.000143836644462325
+ ,-0.00086105174113707
+ ,0.00118491489582653
+ ,0.00092521493356959
+ ,0.000685499195885314
+ ,-0.00170870319900812
+ ,-0.000681671133016343
+ ,-0.00207056008076914
+ ,0.000710534206097013
+ ,-0.00163014844752510
+ ,-0.00123315260753790
+ ,-0.000307767159812872
+ ,-0.000896177657593727
+ ,0.000651475976366861
+ ,0.00196454841594412
+ ,0.000447156493560086)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa, P., (2007), Central Tendency (v1.0.2) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.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] -0.0001648618
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 9.572845e-05
> (armose <- arm / armse)
[1] -1.722182
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] -0.001006701
> (qua <- quamean(x))
[1] 0.0009474985
> (win <- winmean(x))
               [,1]         [,2]
 [1,] -0.0001595215 9.308173e-05
 [2,] -0.0001552084 9.205903e-05
 [3,] -0.0001739528 8.784228e-05
 [4,] -0.0001701249 8.667740e-05
 [5,] -0.0001708784 8.633595e-05
 [6,] -0.0001723681 8.457203e-05
 [7,] -0.0001631669 8.188680e-05
 [8,] -0.0001754030 7.988929e-05
 [9,] -0.0001713031 7.834775e-05
[10,] -0.0001702490 7.687847e-05
[11,] -0.0001729551 7.632402e-05
[12,] -0.0001657230 7.392185e-05
[13,] -0.0001783288 7.178603e-05
[14,] -0.0001728727 6.919902e-05
[15,] -0.0001709059 6.846156e-05
[16,] -0.0001689916 6.700655e-05
[17,] -0.0001644556 6.557664e-05
[18,] -0.0001636045 6.451206e-05
[19,] -0.0001492185 6.235570e-05
[20,] -0.0001427888 6.073188e-05
[21,] -0.0001503865 5.887381e-05
[22,] -0.0001511701 5.665153e-05
[23,] -0.0001628841 5.405664e-05
[24,] -0.0001647604 5.215684e-05
[25,] -0.0001912328 4.803238e-05
[26,] -0.0001885867 4.712959e-05
[27,] -0.0001859635 4.660919e-05
[28,] -0.0001914027 4.586315e-05
[29,] -0.0001717573 4.189427e-05
[30,] -0.0001798850 4.055925e-05
[31,] -0.0001064555 3.125341e-05
[32,] -0.0001088315 3.007768e-05
> (tri <- trimean(x))
               [,1]         [,2]
 [1,] -0.0001617878 9.002742e-05
 [2,] -0.0001641527 8.653226e-05
 [3,] -0.0001689229 8.315030e-05
 [4,] -0.0001670939 8.112219e-05
 [5,] -0.0001662481 7.919611e-05
 [6,] -0.0001651897 7.707893e-05
 [7,] -0.0001637891 7.509176e-05
 [8,] -0.0001638957 7.341885e-05
 [9,] -0.0001621254 7.189872e-05
[10,] -0.0001608373 7.043233e-05
[11,] -0.0001596163 6.899141e-05
[12,] -0.0001579995 6.739410e-05
[13,] -0.0001571168 6.593789e-05
[14,] -0.0001548132 6.457193e-05
[15,] -0.0001529369 6.337708e-05
[16,] -0.0001511400 6.205846e-05
[17,] -0.0001494124 6.070587e-05
[18,] -0.0001479966 5.930127e-05
[19,] -0.0001465614 5.776238e-05
[20,] -0.0001463217 5.624796e-05
[21,] -0.0001466357 5.465691e-05
[22,] -0.0001463059 5.300778e-05
[23,] -0.0001458814 5.134840e-05
[24,] -0.0001444029 4.973636e-05
[25,] -0.0001426327 4.804224e-05
[26,] -0.0001383913 4.664930e-05
[27,] -0.0001339785 4.499579e-05
[28,] -0.0001293576 4.290170e-05
[29,] -0.0001237595 4.021905e-05
[30,] -0.0001193460 3.771704e-05
[31,] -0.0001136482 3.454911e-05
[32,] -0.0001143442 3.322289e-05
> (midr <- midrange(x))
[1] -0.0003093379
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] -0.0001586677 -0.0001444029 -0.0001586677 -0.0001444029 -0.0001444029
[6] -0.0001586677 -0.0001444029 -0.0001458814
> postscript(file="/var/www/html/rcomp/tmp/1kcpx1197555920.ps",horizontal=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/html/rcomp/tmp/2ksjz1197555920.ps",horizontal=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 
> load(file='/var/www/html/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/html/rcomp/tmp/3oldh1197555920.tab") 
> 
> system("convert tmp/1kcpx1197555920.ps tmp/1kcpx1197555920.png")
> system("convert tmp/2ksjz1197555920.ps tmp/2ksjz1197555920.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.000   0.318   1.270