R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(3.03292826890205
+ ,12.0260515677640
+ ,59.7475455407064
+ ,-114.465065205481
+ ,-2.22693508199627
+ ,4.35951995596352
+ ,-147.147615338686
+ ,65.153572198053
+ ,-58.9442153086111
+ ,94.5064127441215
+ ,54.0497539166126
+ ,-31.9582830652207
+ ,-291.427228013426
+ ,103.210014980995
+ ,13.4184752845463
+ ,25.848767749962
+ ,81.7651411018169
+ ,0.0342656138418533
+ ,-13.8542282976155
+ ,63.9062793697858
+ ,-37.9084354029856
+ ,-239.488697273233
+ ,-197.314334937415
+ ,-18.3811532105201
+ ,-78.8708128245712
+ ,-37.8295732489139
+ ,153.835701431603
+ ,-46.2523335694268
+ ,-13.131794384233
+ ,-185.299119376881
+ ,-72.9117819276823
+ ,243.825225144514
+ ,56.6148178109725
+ ,51.4504706290238
+ ,-39.3475780548667
+ ,74.1339479106434
+ ,-2.27501727330446
+ ,16.1353440571070
+ ,29.3431180387506
+ ,1.19479122514349
+ ,142.274824521032
+ ,37.8895641544145
+ ,-61.2157143422046
+ ,44.3522168977665
+ ,-99.399814019555
+ ,69.8361993067019
+ ,-30.5517825502993
+ ,62.8935794195445
+ ,125.965949022935
+ ,71.5094060664719
+ ,52.3393013125101
+ ,19.3218862161034
+ ,19.4930838292207
+ ,64.6403579028697
+ ,-15.0861494969154
+ ,-5.69174869726749
+ ,-79.8892245215648
+ ,46.8017120289928
+ ,52.3915521634676
+ ,88.1573151431521
+ ,-12.8910808605979
+ ,0.555556031137257
+ ,46.017345842899
+ ,107.370226415589
+ ,133.534342762899
+ ,85.592463340406
+ ,40.2118083758105
+ ,-83.726149814921
+ ,-116.032498074396
+ ,-224.597367333123
+ ,198.730124441566
+ ,143.260275801969
+ ,105.426085784684
+ ,115.125784565585
+ ,-14.9411382270919
+ ,53.3217795102973
+ ,96.8611024849115
+ ,4.70669897899825
+ ,-179.314662214792
+ ,245.649258923567
+ ,31.3333205409763
+ ,-79.5796685631494
+ ,-80.4379200791709
+ ,-363.924056075888
+ ,205.939379895812
+ ,126.011618846088
+ ,-302.947102260051
+ ,85.1467909607727
+ ,-298.923496535926
+ ,10.0005383240823
+ ,-12.1778514262342
+ ,245.932788294570
+ ,-82.9134977046492
+ ,-273.362164089219
+ ,-423.468312216033
+ ,154.459638009162
+ ,-32.0064376545452
+ ,-654.887885136994
+ ,24.9943895258984
+ ,-81.9085187968208
+ ,223.842710037987
+ ,-69.0844660783794
+ ,-87.1663497407853
+ ,226.244015203884
+ ,152.276241081288
+ ,-48.8432924693116
+ ,11.6091732540151
+ ,176.746655051392
+ ,92.2077545126504
+ ,20.3296664845438
+ ,-106.660701819339)
> 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: 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] -2.538438
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 13.34063
> (armose <- arm / armse)
[1] -0.1902788
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] 3.487127
> (qua <- quamean(x))
[1] 139.9407
> (win <- winmean(x))
            [,1]      [,2]
 [1,] -0.4561314 12.553055
 [2,]  0.5838726 12.237321
 [3,]  1.7567306 11.734794
 [4,]  1.8151918 11.685721
 [5,]  1.3464053 11.471985
 [6,]  1.9332057 11.186671
 [7,]  2.6830254 10.508023
 [8,]  2.1500029 10.053733
 [9,]  4.3115512  9.608538
[10,]  5.2535112  9.385416
[11,]  4.9530914  9.151373
[12,]  8.3240747  8.528979
[13,] 10.9445275  7.810191
[14,] 10.1934098  7.647904
[15,] 11.2418819  7.493457
[16,] 10.7259501  7.132295
[17,] 11.4117555  6.719477
[18,] 11.6543597  6.604841
[19,] 11.4141349  6.537898
[20,] 10.4512640  6.370521
[21,] 10.2840035  6.279286
[22,]  9.9371641  6.209780
[23,]  9.1620261  6.101378
[24,]  8.7607296  6.016267
[25,] 10.0024771  5.828888
[26,] 10.1068673  5.621182
[27,] 10.1646518  5.166141
[28,] 10.0755959  5.020250
[29,] 12.2774317  4.648426
[30,] 11.7121159  4.424103
[31,] 13.4971410  4.182568
[32,] 13.7004027  4.111560
[33,] 13.4227752  4.075559
[34,] 14.2427884  3.767911
[35,] 13.2701752  3.658778
[36,] 12.8944250  3.518504
[37,] 16.7086433  3.051533
> (tri <- trimean(x))
           [,1]      [,2]
 [1,]  1.166867 11.961285
 [2,]  2.850538 11.282812
 [3,]  4.048632 10.703781
 [4,]  4.871936 10.266891
 [5,]  5.711784  9.785402
 [6,]  6.690688  9.297300
 [7,]  6.690688  8.812981
 [8,]  8.418444  8.422781
 [9,]  9.353655  8.074407
[10,] 10.037017  7.767911
[11,] 10.633611  7.459187
[12,] 11.292480  7.145904
[13,] 11.615513  6.898544
[14,] 11.615513  6.734036
[15,] 11.830496  6.569279
[16,] 11.885632  6.402337
[17,] 11.990116  6.262868
[18,] 12.040468  6.160123
[19,] 12.073084  6.055211
[20,] 12.127305  5.940444
[21,] 12.262117  5.827915
[22,] 12.418172  5.706583
[23,] 12.610754  5.571074
[24,] 12.874942  5.423740
[25,] 13.186881  5.258134
[26,] 13.426521  5.088262
[27,] 13.675159  4.915171
[28,] 13.675159  4.779569
[29,] 14.226427  4.635355
[30,] 14.372700  4.522081
[31,] 14.372700  4.417105
[32,] 14.655610  4.326785
[33,] 14.729241  4.221523
[34,] 14.831438  4.089490
[35,] 14.878311  3.981059
[36,] 15.009082  3.857779
[37,] 15.185303  3.722214
> (midr <- midrange(x))
[1] -204.4775
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 12.59554 13.67516 13.67516 13.67516 13.93756 12.59554 13.67516 13.67516
> postscript(file="/var/www/html/rcomp/tmp/1t5oi1262181799.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/2qbke1262181799.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 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> 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/3qcqq1262181800.tab") 
> 
> try(system("convert tmp/1t5oi1262181799.ps tmp/1t5oi1262181799.png",intern=TRUE))
character(0)
> try(system("convert tmp/2qbke1262181799.ps tmp/2qbke1262181799.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.771   0.339   1.381