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Type 'q()' to quit R. > x <- c(-22.15310543 + ,-11.34582801 + ,19.86592987 + ,-6.178464327 + ,4.671969315 + ,-33.66882275 + ,20.4798674 + ,-11.14034927 + ,-15.76237779 + ,8.79438553 + ,-17.11562914 + ,1.031858244 + ,-6.694144837 + ,-7.700494719 + ,13.77530443 + ,19.27755878 + ,0.707840155 + ,16.81803545 + ,-0.383958241 + ,15.03829212 + ,-3.633965572 + ,0.352663015 + ,3.823710504 + ,2.061792009 + ,17.33363689 + ,0.702042858 + ,14.077444 + ,13.56037095 + ,-5.620883909 + ,20.84821529 + ,6.902993681 + ,-22.78225226 + ,-0.593441957 + ,-0.165276233 + ,-16.65252635 + ,20.01159167 + ,-5.956661493 + ,-1.60712791 + ,3.879213367 + ,9.010771202 + ,20.68954083 + ,-2.591800312 + ,-2.026765441 + ,-4.277675602 + ,-0.062944884 + ,13.90119728 + ,-12.93524427 + ,-3.634175509 + ,0.178098598 + ,0.891786939 + ,2.228268917 + ,-1.240621545 + ,-30.85789164 + ,-4.758951524 + ,-0.411889596 + ,-3.525704565 + ,3.137692332 + ,-38.24832905 + ,3.582851768 + ,10.52389038 + ,13.10096753 + ,2.286566037 + ,9.782110873 + ,-13.29380674 + ,-27.59731736 + ,9.441188725 + ,-4.812077023 + ,0.763109781 + ,8.695863983 + ,43.52793087 + ,6.431263866 + ,-5.630548143 + ,-7.71240619 + ,-5.762433964 + ,18.73654126 + ,22.20538354 + ,-2.492882178 + ,13.36226101 + ,8.587502622 + ,-6.567394793 + ,5.407913754 + ,34.02045404 + ,-15.05012735 + ,9.732717104 + ,8.465598559 + ,-11.77772961 + ,-23.41816892 + ,-15.72865745 + ,0.982950688 + ,14.15774538 + ,0.122507857 + ,5.836351819 + ,-16.07934282 + ,12.30885991 + ,-20.61584062 + ,-2.957192053 + ,-19.31468409 + ,15.83171713 + ,6.215914695 + ,-12.65770784 + ,15.06701843 + ,6.198700633 + ,-1.436107103 + ,-28.66688714 + ,28.84285843 + ,-16.51125725 + ,13.10781729 + ,24.20148285 + ,-19.6559911 + ,20.25141569 + ,-15.61012099 + ,13.91308938 + ,4.175723865 + ,19.24896729 + ,0.361524856 + ,1.589949761 + ,-8.4033056 + ,-0.84497277 + ,12.1658228 + ,-6.692024562 + ,14.36315559 + ,-17.79291989 + ,-10.19815936 + ,-21.90214109 + ,-1.645381825 + ,-9.24701461 + ,-18.64898269 + ,-60.34254786 + ,16.22309476 + ,29.83278992 + ,-12.52585078 + ,-7.51057201 + ,-7.928640081 + ,-16.85163894 + ,-12.9463718 + ,-14.67483167 + ,-1.905288429 + ,-6.647137203 + ,6.112436002 + ,-12.64294097 + ,-24.16692762 + ,-3.400546418 + ,-11.71018644 + ,8.740586961 + ,24.57839934 + ,44.69833165 + ,-1.503545458 + ,6.067531989 + ,8.501836832 + ,-1.594430251 + ,-2.42402738 + ,-2.456942799 + ,-1.180784317 + ,-2.39111196 + ,-13.83978478 + ,18.15036707 + ,-2.39111196 + ,-2.522773638 + ,1.53961328 + ,-1.477582526 + ,-5.877182394 + ,15.81424119 + ,-2.456942799 + ,3.911597144) > 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] 4.085365e-10 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 1.165348 > (armose <- arm / armse) [1] 3.505704e-10 > (geo <- geomean(x)) [1] NaN Warning message: In log(x) : NaNs produced > (har <- harmean(x)) [1] -15.36128 > (qua <- quamean(x)) [1] 14.87817 > (win <- winmean(x)) [,1] [,2] [1,] 0.127584257 1.1280901 [2,] 0.067487055 1.0921800 [3,] 0.042302915 1.0688827 [4,] 0.071597378 1.0555961 [5,] -0.025807784 1.0297787 [6,] 0.085904652 1.0081767 [7,] 0.032664504 0.9913992 [8,] -0.002518500 0.9780594 [9,] 0.023300106 0.9720389 [10,] 0.025817844 0.9682427 [11,] 0.096771115 0.9545191 [12,] 0.149455907 0.9430484 [13,] 0.164964369 0.9380923 [14,] 0.171565737 0.9245033 [15,] 0.247249089 0.9145428 [16,] 0.263333451 0.9002980 [17,] 0.229936331 0.8894856 [18,] 0.162149034 0.8759803 [19,] 0.118781263 0.8669318 [20,] 0.098900012 0.8522669 [21,] 0.089371569 0.8417754 [22,] 0.091550696 0.8409841 [23,] 0.003381276 0.8271975 [24,] 0.081127714 0.8173275 [25,] 0.035420268 0.7994124 [26,] 0.135240717 0.7810880 [27,] 0.211906996 0.7698586 [28,] 0.243164612 0.7604126 [29,] 0.243029414 0.7599713 [30,] 0.270769093 0.7520555 [31,] 0.232932721 0.7473003 [32,] 0.217123990 0.7406678 [33,] 0.316461525 0.7193775 [34,] 0.329044306 0.7177800 [35,] 0.237756369 0.6915013 [36,] 0.251463068 0.6835174 [37,] 0.093594331 0.6230071 [38,] 0.142105790 0.5834079 [39,] 0.330997829 0.5627472 [40,] 0.375665424 0.5445427 [41,] 0.322119516 0.5285713 [42,] 0.269754172 0.5227198 [43,] 0.305445257 0.5166678 [44,] 0.512487846 0.4955145 [45,] 0.483336329 0.4924553 [46,] 0.471898476 0.4889067 [47,] 0.484366125 0.4858218 [48,] 0.140851663 0.4304855 [49,] 0.066178358 0.4110340 [50,] 0.024754555 0.4026396 [51,] 0.055085365 0.3989335 [52,] 0.069550620 0.3926171 [53,] 0.058162155 0.3909695 [54,] 0.248356317 0.3604091 > (tri <- trimean(x)) [,1] [,2] [1,] 0.096569236 1.0842570 [2,] 0.064778840 1.0360175 [3,] 0.063373311 1.0041963 [4,] 0.070756954 0.9789403 [5,] 0.070533205 0.9556543 [6,] 0.091322576 0.9370287 [7,] 0.092309843 0.9215932 [8,] 0.101751769 0.9080970 [9,] 0.116392457 0.8957662 [10,] 0.128172662 0.8833350 [11,] 0.139993923 0.8703829 [12,] 0.144596871 0.8582086 [13,] 0.144115662 0.8464573 [14,] 0.142181732 0.8342597 [15,] 0.139612981 0.8225817 [16,] 0.130697668 0.8109653 [17,] 0.120239846 0.7998476 [18,] 0.111972280 0.7888390 [19,] 0.108343979 0.7781923 [20,] 0.107617445 0.7674241 [21,] 0.108203370 0.7570642 [22,] 0.109428932 0.7466864 [23,] 0.110558374 0.7352880 [24,] 0.117146471 0.7240437 [25,] 0.119305490 0.7125565 [26,] 0.124218768 0.7015627 [27,] 0.123586740 0.6911194 [28,] 0.118619483 0.6805560 [29,] 0.111737609 0.6696642 [30,] 0.104598399 0.6575005 [31,] 0.095692519 0.6446394 [32,] 0.088432070 0.6306581 [33,] 0.081702007 0.6155811 [34,] 0.069549053 0.6007912 [35,] 0.056233276 0.5841720 [36,] 0.046988001 0.5682226 [37,] 0.036638028 0.5509150 [38,] 0.033769222 0.5380456 [39,] 0.028332503 0.5276479 [40,] 0.013180759 0.5178826 [41,] -0.004943474 0.5085715 [42,] -0.021296624 0.4995584 [43,] -0.035866932 0.4897395 [44,] -0.052995206 0.4789586 [45,] -0.081477768 0.4687337 [46,] -0.110067123 0.4570717 [47,] -0.110067123 0.4437305 [48,] -0.171731416 0.4282535 [49,] -0.187913116 0.4179608 [50,] -0.201201063 0.4083461 [51,] -0.213154844 0.3979446 [52,] -0.227531116 0.3858362 [53,] -0.243685428 0.3720398 [54,] -0.260364338 0.3553095 > (midr <- midrange(x)) [1] -7.822108 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] -0.100409699 -0.004943474 -0.100409699 -0.004943474 -0.004943474 [6] -0.100409699 -0.004943474 0.013180759 > postscript(file="/var/wessaorg/rcomp/tmp/1dpej1321535526.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/2u0x91321535526.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/317t31321535526.tab") > > try(system("convert tmp/1dpej1321535526.ps tmp/1dpej1321535526.png",intern=TRUE)) character(0) > try(system("convert tmp/2u0x91321535526.ps tmp/2u0x91321535526.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.078 0.130 1.231