R version 2.6.1 (2007-11-26)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(0.00200147839087365
+ ,-0.0216058444005542
+ ,-0.0222145391353238
+ ,-0.0463985224381376
+ ,-0.0353895324141767
+ ,-0.00932747082545202
+ ,0.0323671470576175
+ ,0.0524787528909093
+ ,-0.0345828840913102
+ ,0.0218191134390016
+ ,-0.0197276173643167
+ ,-0.0167535721706866
+ ,-0.0612768206067064
+ ,-0.0161420992820751
+ ,-0.0197857153606179
+ ,0.0544297619502803
+ ,-0.00217303079785906
+ ,-0.0228193177289160
+ ,0.0144316044983902
+ ,0.0274435630572674
+ ,0.0142137759982791
+ ,0.159834240154226
+ ,-0.0214959343099046
+ ,0.00675270350609719
+ ,0.0985968705390431
+ ,-0.0145013124776513
+ ,0.0170492335281872
+ ,-0.0531272284338411
+ ,-0.00444892352079798
+ ,0.0131112572585838
+ ,0.0561877511329985
+ ,-0.0239301906202676
+ ,-0.00494997317367667
+ ,0.0347398710767976
+ ,-0.00436421755315953
+ ,0.0100763865618025
+ ,0.0313879952146342
+ ,-0.00476915900880408
+ ,-0.00452389727569396
+ ,-0.0303248377253466
+ ,-0.00947344518451138
+ ,0.0124410167441955
+ ,0.0089866232118211
+ ,0.0120244946854947
+ ,0.00722018999236059
+ ,-0.0294831633822169
+ ,-0.00306040964075164
+ ,0.00649679218741509
+ ,-0.0123572816765002
+ ,0.00439863636840774
+ ,-0.00623602489273799
+ ,-0.106126447542172
+ ,-0.00238282008985389
+ ,0.00251495964172511
+ ,0.109705993487879
+ ,0.010080866523411
+ ,0.0074489176906658
+ ,-0.0244593383436526
+ ,-0.0082576514941279
+ ,-0.0049345890875587
+ ,0.000421793444245806
+ ,-0.00441571103437802
+ ,-0.00534514728290785
+ ,0.0213902267384058
+ ,0.00608139143442771
+ ,-0.0197927389349290
+ ,-0.00652549674086137
+ ,-0.000316549923858597
+ ,-0.0110717984282002
+ ,0.00830966692376999
+ ,-0.0106978412552433
+ ,-0.00205385008959703
+ ,0.0167323581047296
+ ,-0.00374319446726109
+ ,-0.0193040237051260
+ ,0.0313676465741677
+ ,0.00203221930894221
+ ,-0.0032515955901252
+ ,-0.0799819891658529
+ ,0.00784734309454633
+ ,-0.00759310363931603
+ ,-0.00680303446603329
+ ,-0.0106429612240380
+ ,-0.0284949069867679
+ ,0.0444628650674193
+ ,-0.0171287395161674
+ ,-0.0343181733968545
+ ,0.0208233058747531
+ ,-0.032083747726223
+ ,-0.0325805438051414
+ ,0.0687576767971405
+ ,0.00826018419130082
+ ,-0.0442807032733388)
> 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] -0.0001839031
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.003665507
> (armose <- arm / armse)
[1] -0.05017126
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] -0.02941348
> (qua <- quamean(x))
[1] 0.03515879
> (win <- winmean(x))
               [,1]         [,2]
 [1,] -0.0004417933 0.0033595095
 [2,] -0.0002784375 0.0031826121
 [3,] -0.0009781020 0.0028357713
 [4,] -0.0012293373 0.0026435285
 [5,] -0.0012099916 0.0026005552
 [6,] -0.0007622392 0.0024757766
 [7,] -0.0013048702 0.0023313826
 [8,] -0.0021184859 0.0021605490
 [9,] -0.0021799467 0.0020917298
[10,] -0.0022318129 0.0020645430
[11,] -0.0020261766 0.0020320154
[12,] -0.0024239068 0.0019275819
[13,] -0.0030719768 0.0017801155
[14,] -0.0025290355 0.0016798420
[15,] -0.0025351279 0.0016536891
[16,] -0.0029933128 0.0015306038
[17,] -0.0029406853 0.0015069037
[18,] -0.0032681806 0.0014288805
[19,] -0.0032902284 0.0014197715
[20,] -0.0031610506 0.0013379110
[21,] -0.0033108093 0.0013178595
[22,] -0.0033955978 0.0013032527
[23,] -0.0037715203 0.0012285116
[24,] -0.0032113128 0.0011529105
[25,] -0.0034034085 0.0011034257
[26,] -0.0034217156 0.0010580569
[27,] -0.0029597241 0.0009951266
[28,] -0.0024385057 0.0009003587
[29,] -0.0021618963 0.0008376986
[30,] -0.0021150481 0.0008146213
[31,] -0.0022525836 0.0007932010
> (tri <- trimean(x))
               [,1]         [,2]
 [1,] -0.0007781405 0.0030879684
 [2,] -0.0011296043 0.0027587070
 [3,] -0.0015845383 0.0024801833
 [4,] -0.0018057092 0.0023195449
 [5,] -0.0019671628 0.0022040134
 [6,] -0.0021410317 0.0020819566
 [7,] -0.0024115543 0.0019732582
 [8,] -0.0026025035 0.0018834033
 [9,] -0.0026775263 0.0018186968
[10,] -0.0027479599 0.0017575030
[11,] -0.0028155679 0.0016908229
[12,] -0.0029122917 0.0016179636
[13,] -0.0029122917 0.0015522735
[14,] -0.0029574267 0.0015023229
[15,] -0.0030025972 0.0014606762
[16,] -0.0030501105 0.0014149830
[17,] -0.0030557060 0.0013817252
[18,] -0.0030667452 0.0013450137
[19,] -0.0030478224 0.0013135675
[20,] -0.0030254354 0.0012758635
[21,] -0.0030130705 0.0012437688
[22,] -0.0029861611 0.0012066574
[23,] -0.0029493356 0.0011619357
[24,] -0.0028754581 0.0011194778
[25,] -0.0028451922 0.0010810076
[26,] -0.0028451922 0.0010409045
[27,] -0.0027370226 0.0009977441
[28,] -0.0027162906 0.0009554522
[29,] -0.0027426518 0.0009219110
[30,] -0.0027990889 0.0008908504
[31,] -0.0028674930 0.0008520283
> (midr <- midrange(x))
[1] 0.02685390
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] -0.003232601 -0.002949336 -0.002949336 -0.002949336 -0.002949336
[6] -0.003298883 -0.002949336 -0.002949336
> postscript(file="/var/www/html/rcomp/tmp/1dq5k1198238931.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/233ok1198238931.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/3j3ds1198238932.tab") 
> 
> system("convert tmp/1dq5k1198238931.ps tmp/1dq5k1198238931.png")
> system("convert tmp/233ok1198238931.ps tmp/233ok1198238931.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.719   0.557   1.812