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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
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(-0.554046479470557
+ ,-0.583025666609207
+ ,0.506250798932448
+ ,-0.573670050105768
+ ,-0.53299634233786
+ ,-0.487644826318229
+ ,-155638538359647.00
+ ,-0.566653337728184
+ ,-0.480628113940645
+ ,-0.583025666609214
+ ,143334666227182.00
+ ,14099576210132.00
+ ,-0.456326735053768
+ ,-0.517138242326169
+ ,0.465178982405618
+ ,0.547438735569693
+ ,-14118875566624.00
+ ,-0.421243173165842
+ ,13809784338746.00
+ ,0.536656552568649
+ ,-1620448132623.00
+ ,0.45297023290697
+ ,-167138979452262.00
+ ,23505726802384.00
+ ,150533846130419.00
+ ,0.505338461304186
+ ,0.434258999900078
+ ,0.491305036549017
+ ,0.517032981933495
+ ,147961051591971.00
+ ,-14726990639348.00
+ ,-151337277170271.00
+ ,153665655256865.00
+ ,-0.609665949621953
+ ,-152181605057789.00
+ ,0.366945009119433
+ ,0.603970543349293
+ ,155017574845448.00
+ ,152171079018522.00
+ ,-0.432025356166891
+ ,0.567974643833109
+ ,-146100454330549.00
+ ,0.471681465913864
+ ,-158211332898095.00
+ ,150767736543005.00
+ ,-155170757534475.00
+ ,0.459986945284555
+ ,-141097521903414.00
+ ,0.498321748926601
+ ,-255638538359647.00
+ ,-0.520389484080292
+ ,0.415547766893185
+ ,0.507677365430048
+ ,146089928291282.00
+ ,-0.57509661660337
+ ,0.521710790185217
+ ,0.478698178291448
+ ,248520066179969.00
+ ,-0.506356059325122
+ ,-0.536761812961322
+ ,-154235195884131.00
+ ,0.464150524666937
+ ,0.534317648442787
+ ,0.402940908635617
+ ,-0.597059091364383
+ ,0.460899282912816
+ ,0.43659790402594
+ ,-0.573670050105768
+ ,-0.429686452041032
+ ,0.65308752999239
+ ,0.42165214164251
+ ,0.54133436082037
+ ,138656857975459.00
+ ,246089928291282.00
+ ,-0.555473045968216
+ ,0.456735703530433
+ ,-154702976709303.00
+ ,0.413208862767323
+ ,-157743552072923.00
+ ,-0.5624897583458
+ ,0.362267200867709
+ ,147584504529625.00
+ ,-0.627464845000585
+ ,-0.468933593311338
+ ,-145866563917963.00
+ ,-0.537674150589584
+ ,-146009220567723.00
+ ,0.392672954503909
+ ,-0.491410296941691
+ ,-0.60875361199369
+ ,0.405279812761477
+ ,0.415547766893185
+ ,-0.5610631918482
+ ,0.42165214164251
+ ,0.439849145780062
+ ,-0.539100717087184
+ ,-0.513372771702707
+ ,140202857100736.00)
> 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] -1.015592e+12
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 8.78329e+12
> (armose <- arm / armse)
[1] -0.1156277
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] 5.332908
> (qua <- quamean(x))
[1] 8.651133e+13
> (win <- winmean(x))
               [,1]         [,2]
 [1,] -1.373323e+11 8.549513e+12
 [2,] -1.813755e+12 8.047590e+12
 [3,] -1.840820e+12 8.036439e+12
 [4,] -1.815905e+12 8.007207e+12
 [5,] -1.863637e+12 7.988333e+12
 [6,] -1.849317e+12 7.979852e+12
 [7,] -1.999676e+12 7.937263e+12
 [8,] -1.862774e+12 7.898252e+12
 [9,] -1.922491e+12 7.856326e+12
[10,] -1.669270e+12 7.697648e+12
[11,] -2.010559e+12 7.627742e+12
[12,] -2.182397e+12 7.588033e+12
[13,] -1.682492e+13 5.225014e+12
[14,] -1.157220e+11 8.349231e+11
[15,] -6.699906e+10 8.103989e+11
[16,] -2.810981e+11 6.230030e+10
[17,] -4.940786e-03 5.531196e-02
[18,] -8.283093e-03 5.419763e-02
[19,] -1.208766e-02 5.374550e-02
[20,] -1.094682e-02 5.334040e-02
[21,] -8.942042e-03 5.289503e-02
[22,] -9.467102e-03 5.283926e-02
[23,] -1.056495e-02 5.231951e-02
[24,] -1.136118e-02 5.216077e-02
[25,] -1.374781e-02 5.191258e-02
[26,] -1.226471e-02 5.166694e-02
[27,] -1.136896e-02 5.151424e-02
[28,] -1.296615e-02 5.126257e-02
[29,] -1.338830e-02 5.086759e-02
[30,] -1.681083e-02 5.042676e-02
[31,] -1.430266e-02 4.968537e-02
[32,] -1.596011e-02 4.942106e-02
> (tri <- trimean(x))
               [,1]         [,2]
 [1,] -1.015592e+12 8.153209e+12
 [2,] -9.625991e+11 7.694190e+12
 [3,] -1.827899e+12 7.480465e+12
 [4,] -1.827899e+12 7.241052e+12
 [5,] -1.825243e+12 6.976353e+12
 [6,] -1.816492e+12 6.676153e+12
 [7,] -1.810110e+12 6.328515e+12
 [8,] -1.810110e+12 5.929989e+12
 [9,] -1.764724e+12 5.463254e+12
[10,] -1.742700e+12 4.903345e+12
[11,] -1.752169e+12 4.240870e+12
[12,] -1.721060e+12 3.375571e+12
[13,] -1.668733e+12 2.030138e+12
[14,] -3.652791e+10 4.090760e+11
[15,] -2.837558e+10 2.935597e+11
[16,] -2.837558e+10 2.455224e+10
[17,] -1.324905e-03 6.336834e-02
[18,] -9.887030e-04 6.387836e-02
[19,] -3.268047e-04 6.452348e-02
[20,]  7.190792e-04 6.523195e-02
[21,]  1.739845e-03 6.600387e-02
[22,]  2.662971e-03 6.684965e-02
[23,]  3.702086e-03 6.772587e-02
[24,]  4.917886e-03 6.869264e-02
[25,]  6.302736e-03 6.971206e-02
[26,]  8.011392e-03 7.079863e-02
[27,]  8.011392e-03 7.195969e-02
[28,]  1.157328e-02 7.318832e-02
[29,]  1.372048e-02 7.450229e-02
[30,]  1.613125e-02 7.593249e-02
[31,]  1.912043e-02 7.749676e-02
[32,]  1.912043e-02 7.927080e-02
> (midr <- midrange(x))
[1] -3.559236e+12
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] -0.005533443  0.004917886  0.004917886  0.004917886 -0.005533443
[6]  0.004917886  0.004917886  0.004917886
> postscript(file="/var/www/rcomp/tmp/1d13m1324395245.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/2yopq1324395245.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/3bpql1324395245.tab") 
> 
> try(system("convert tmp/1d13m1324395245.ps tmp/1d13m1324395245.png",intern=TRUE))
character(0)
> try(system("convert tmp/2yopq1324395245.ps tmp/2yopq1324395245.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.390   0.080   1.468