R version 2.13.0 (2011-04-13)
Copyright (C) 2011 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.

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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(186.59
+ ,244.665
+ ,248.18
+ ,253.568
+ ,171.242
+ ,413.971
+ ,216.89
+ ,227.901
+ ,259.823
+ ,148.438
+ ,241.013
+ ,206.248
+ ,108.908
+ ,267.952
+ ,314.219
+ ,235.115
+ ,203.027
+ ,365.415
+ ,350.933
+ ,263.304
+ ,738.751
+ ,959.073
+ ,483.828
+ ,213.016
+ ,177.341
+ ,352.622
+ ,352.622
+ ,217.307
+ ,236.184
+ ,215.701
+ ,228.383
+ ,485.625
+ ,252.502
+ ,342.515
+ ,196.931
+ ,365.315
+ ,316.664
+ ,313.523
+ ,188.124
+ ,184.083
+ ,362.962
+ ,170.161
+ ,167.484
+ ,211.752
+ ,276.469
+ ,182.097
+ ,266.904
+ ,235.328
+ ,329.45
+ ,258.118
+ ,952.515
+ ,247.141
+ ,498.726
+ ,313.308
+ ,420.188
+ ,231.156
+ ,227.844
+ ,204.385
+ ,216.563
+ ,207.19
+ ,232.417
+ ,203.109
+ ,221.07
+ ,254.623
+ ,108.981
+ ,229.417
+ ,476.376
+ ,221.91
+ ,158.946
+ ,295.746
+ ,187.976
+ ,283.76
+ ,705.401
+ ,178.69
+ ,232.635
+ ,245.185
+ ,186.03
+ ,181.142
+ ,228.478
+ ,491.849
+ ,506.461
+ ,182.828
+ ,263.654
+ ,253.718
+ ,480.937
+ ,209.894
+ ,655.92
+ ,223.408
+ ,103.138
+ ,255.664
+ ,184.661
+ ,372.945
+ ,758.6
+ ,256.445
+ ,204.868
+ ,197.384
+ ,245.311
+ ,301.707
+ ,501.478
+ ,278.731
+ ,205.92
+ ,177.14
+ ,139.753
+ ,366.46
+ ,435.522
+ ,239.906
+ ,178.722
+ ,340.04
+ ,236.948
+ ,221.152
+ ,263.303
+ ,222.814
+ ,317.99
+ ,149.593
+ ,221.983
+ ,201.551
+ ,266.901
+ ,185.218
+ ,347.536
+ ,395.593
+ ,238.217
+ ,254.697
+ ,157.584
+ ,807.302
+ ,252.391
+ ,189.194
+ ,267.834
+ ,173.15
+ ,267.633
+ ,283.284
+ ,209.475
+ ,135.135
+ ,285.012
+ ,178.495
+ ,256.852
+ ,301.828
+ ,158.403
+ ,355.963
+ ,364.117
+ ,233.203
+ ,257.634
+ ,208.57
+ ,212.503
+ ,251.059
+ ,276.803
+ ,198.339
+ ,301.018
+ ,369.761
+ ,162.768
+ ,199.968
+ ,406.676
+ ,364.156
+ ,202.391
+ ,319.491
+ ,185.546
+ ,243.559
+ ,220.928
+ ,193.714
+ ,372.943
+ ,163.822
+ ,217.566
+ ,232.527)
> 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] 281.0759
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 11.02478
> (armose <- arm / armse)
[1] 25.49493
> (geo <- geomean(x))
[1] 257.7475
> (har <- harmean(x))
[1] 240.7068
> (qua <- quamean(x))
[1] 313.9626
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 281.0711 11.005859
 [2,] 279.2792 10.381273
 [3,] 278.8617 10.058870
 [4,] 278.4856  9.905522
 [5,] 277.7243  9.591468
 [6,] 275.9345  9.095872
 [7,] 269.8217  7.582142
 [8,] 269.6160  7.531048
 [9,] 269.4933  7.499151
[10,] 269.3047  7.397835
[11,] 268.9537  7.313067
[12,] 269.0918  7.264706
[13,] 269.0747  7.203727
[14,] 268.7739  7.124098
[15,] 265.1678  6.454804
[16,] 264.0474  6.177000
[17,] 263.4161  6.073704
[18,] 262.7338  5.938989
[19,] 261.4568  5.744803
[20,] 258.6647  5.355798
[21,] 258.9781  5.326986
[22,] 258.6757  5.258171
[23,] 258.3108  5.187693
[24,] 258.3419  5.150950
[25,] 258.4157  5.140989
[26,] 258.3191  5.109055
[27,] 258.3672  5.103367
[28,] 258.2513  5.070309
[29,] 257.0986  4.902544
[30,] 256.7366  4.802552
[31,] 256.7649  4.800035
[32,] 256.6426  4.740006
[33,] 256.8714  4.574472
[34,] 256.4928  4.388017
[35,] 256.0559  4.314879
[36,] 253.9148  4.016951
[37,] 252.0123  3.723804
[38,] 252.0315  3.652184
[39,] 251.9145  3.599122
[40,] 251.4678  3.518527
[41,] 251.3124  3.497264
[42,] 251.5875  3.462934
[43,] 248.6686  3.121727
[44,] 248.9214  3.093462
[45,] 248.8211  3.065335
[46,] 247.5916  2.885369
[47,] 244.8778  2.535124
[48,] 244.7750  2.474932
[49,] 244.7578  2.449641
[50,] 243.9260  2.263164
[51,] 243.5554  2.184607
[52,] 243.6129  2.159962
[53,] 241.7049  1.825848
[54,] 241.9529  1.797015
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 277.9506 10.258548
 [2,] 274.7511  9.400347
 [3,] 272.3999  8.817765
 [4,] 270.1341  8.302194
 [5,] 267.9089  7.772837
 [6,] 265.7887  7.267173
 [7,] 263.9378  6.827440
 [8,] 263.0051  6.677245
 [9,] 262.0755  6.522114
[10,] 261.1352  6.357232
[11,] 260.1898  6.192141
[12,] 259.2546  6.023327
[13,] 258.2781  5.843520
[14,] 257.2740  5.652653
[15,] 256.2659  5.451593
[16,] 255.5264  5.320967
[17,] 254.8524  5.211377
[18,] 254.2047  5.102804
[19,] 253.5857  4.998565
[20,] 253.0356  4.905756
[21,] 252.6556  4.846023
[22,] 252.2423  4.782290
[23,] 251.8339  4.718436
[24,] 251.4337  4.654477
[25,] 251.0173  4.586597
[26,] 250.5815  4.511522
[27,] 250.1351  4.430625
[28,] 249.6691  4.340233
[29,] 249.1917  4.241956
[30,] 248.7587  4.149876
[31,] 248.3279  4.056606
[32,] 247.8780  3.951011
[33,] 247.4158  3.837555
[34,] 246.9219  3.726183
[35,] 246.4263  3.620132
[36,] 245.9310  3.507212
[37,] 245.5228  3.414736
[38,] 245.1924  3.343456
[39,] 244.8453  3.268930
[40,] 244.4872  3.188623
[41,] 244.1338  3.105218
[42,] 243.7701  3.010461
[43,] 243.3734  2.902901
[44,] 243.1038  2.825545
[45,] 242.8063  2.737349
[46,] 242.4970  2.636455
[47,] 242.2331  2.543996
[48,] 242.0950  2.486399
[49,] 241.9537  2.425489
[50,] 241.8042  2.355436
[51,] 241.6896  2.299307
[52,] 241.5874  2.242815
[53,] 241.4747  2.176926
[54,] 241.4617  2.150098
> (midr <- midrange(x))
[1] 531.1055
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 243.6263 244.4872 244.4872 244.4872 244.1338 244.4872 244.4872 244.4872
> postscript(file="/var/wessaorg/rcomp/tmp/1z7l11324145161.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/wessaorg/rcomp/tmp/2bhrc1324145161.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/35uzm1324145161.tab") 
> 
> try(system("convert tmp/1z7l11324145161.ps tmp/1z7l11324145161.png",intern=TRUE))
character(0)
> try(system("convert tmp/2bhrc1324145161.ps tmp/2bhrc1324145161.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.084   0.147   1.230