R version 2.8.0 (2008-10-20) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 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(428800 + ,424800 + ,403400 + ,398400 + ,393500 + ,380500 + ,398300 + ,387300 + ,370400 + ,372800 + ,444600 + ,449900 + ,458100 + ,424800 + ,420600 + ,400100 + ,393000 + ,387100 + ,377500 + ,400400 + ,391400 + ,363600 + ,431000 + ,441700 + ,448500 + ,415600 + ,408000 + ,416600 + ,409300 + ,387600 + ,394500 + ,407600 + ,378500 + ,359600 + ,435700 + ,433800 + ,427700 + ,413300 + ,379500 + ,379300 + ,353700 + ,378200 + ,380600 + ,394000 + ,374000 + ,375000 + ,437600 + ,443900 + ,488800 + ,463900 + ,440000 + ,453800 + ,451600 + ,453400 + ,461400 + ,509100 + ,540600 + ,555100 + ,677400 + ,694600 + ,750100 + ,733900 + ,709300 + ,720500 + ,693200 + ,687200 + ,686800 + ,720900 + ,653100 + ,624700 + ,690000 + ,717800 + ,736500 + ,699900 + ,675600 + ,635600 + ,632500 + ,594900 + ,604000 + ,620800 + ,578400 + ,571200 + ,627400 + ,657700 + ,674100 + ,672800 + ,615300 + ,609100 + ,607600 + ,566900 + ,572700 + ,589200 + ,534800 + ,543100 + ,591100 + ,624800 + ,665300 + ,642600 + ,608700 + ,594500 + ,563800 + ,596100 + ,597600 + ,633100 + ,591000 + ,584200 + ,655800 + ,670700 + ,699700 + ,712900 + ,652000 + ,635100 + ,603100 + ,610100 + ,602000 + ,597600 + ,585400 + ,567100 + ,620600 + ,646200 + ,644800 + ,645200 + ,644800 + ,593000 + ,569100 + ,518800 + ,538700 + ,554600 + ,507900 + ,488400 + ,563300 + ,592400 + ,598100 + ,546300 + ,516100 + ,518500 + ,477400 + ,483400 + ,469400 + ,501300 + ,457400 + ,446700 + ,501900 + ,550400 + ,593700 + ,548900 + ,534200 + ,550500 + ,541800 + ,569300 + ,587400 + ,627700 + ,607000 + ,629500 + ,704600 + ,767700 + ,812200 + ,824600 + ,856300 + ,812200 + ,764100 + ,801700 + ,806000 + ,867200 + ,801600 + ,817500 + ,920900 + ,959700 + ,997700 + ,949100 + ,910900 + ,920400 + ,914200 + ,926300 + ,906400 + ,926100 + ,902500 + ,895300 + ,979900 + ,1009700 + ,1043800 + ,979800 + ,921600 + ,923500 + ,914500 + ,891700 + ,916000 + ,931700 + ,902400 + ,893700 + ,941500 + ,980100 + ,1006900 + ,949200 + ,883200 + ,849900 + ,839200 + ,803900 + ,797900 + ,830800 + ,753300 + ,764100 + ,807600 + ,853700 + ,886200 + ,815700 + ,743000 + ,753600 + ,724800 + ,709600 + ,721900) > 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] 625260.7 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 12429.97 > (armose <- arm / armse) [1] 50.30269 > (geo <- geomean(x)) [1] 599722.5 > (har <- harmean(x)) [1] 575142.9 > (qua <- quamean(x)) [1] 650689.4 > (win <- winmean(x)) [,1] [,2] [1,] 625127.0 12402.196 [2,] 625138.4 12394.453 [3,] 625104.3 12365.877 [4,] 624816.1 12314.571 [5,] 624839.8 12311.155 [6,] 624865.4 12308.010 [7,] 624281.5 12210.604 [8,] 623910.0 12156.648 [9,] 623918.5 12154.873 [10,] 623596.2 12105.764 [11,] 623095.7 12041.640 [12,] 622845.5 11998.933 [13,] 622839.3 11996.857 [14,] 623098.1 11935.096 [15,] 622977.3 11917.604 [16,] 622946.9 11909.134 [17,] 623212.8 11875.699 [18,] 622973.9 11818.508 [19,] 622883.9 11798.416 [20,] 622902.8 11790.685 [21,] 622624.2 11747.575 [22,] 622551.2 11656.489 [23,] 622137.0 11606.391 [24,] 622319.0 11587.378 [25,] 621513.3 11487.975 [26,] 621685.8 11431.870 [27,] 621967.3 11354.302 [28,] 621290.5 11267.383 [29,] 621056.9 11205.242 [30,] 619350.7 10904.188 [31,] 618087.2 10702.210 [32,] 617844.5 10646.858 [33,] 617875.8 10528.260 [34,] 616828.4 10288.775 [35,] 615435.1 10146.649 [36,] 614872.0 9996.150 [37,] 613819.9 9855.465 [38,] 613891.9 9788.264 [39,] 613762.6 9678.992 [40,] 614122.7 9647.185 [41,] 613598.1 9527.657 [42,] 613757.3 9454.884 [43,] 613675.8 9383.231 [44,] 613675.8 9299.038 [45,] 613803.8 9284.016 [46,] 613455.0 9166.827 [47,] 607128.9 8506.317 [48,] 606628.4 8404.692 [49,] 607023.2 8369.709 [50,] 604961.6 8112.107 [51,] 604985.8 8097.182 [52,] 605084.4 7949.852 [53,] 603476.8 7780.639 [54,] 602657.8 7564.399 [55,] 602631.8 7449.544 [56,] 601676.3 7119.425 [57,] 603054.0 6865.067 [58,] 604428.4 6699.533 [59,] 605714.7 6570.675 [60,] 605060.7 6497.339 [61,] 607257.8 6076.041 [62,] 606464.5 5981.431 [63,] 608166.4 5826.063 [64,] 607104.7 5678.993 [65,] 607813.3 5384.769 [66,] 608501.4 5318.979 [67,] 606977.3 5179.934 [68,] 611489.1 4749.459 [69,] 610638.9 4648.834 [70,] 611003.8 4473.347 > (tri <- trimean(x)) [,1] [,2] [1,] 624557.4 12318.848 [2,] 623976.8 12230.341 [3,] 623379.0 12140.521 [4,] 622781.3 12055.648 [5,] 622247.3 11980.012 [6,] 621697.5 11900.226 [7,] 621132.0 11815.830 [8,] 620645.1 11743.062 [9,] 620199.0 11673.880 [10,] 619742.4 11600.185 [11,] 619312.2 11527.933 [12,] 618924.1 11458.573 [13,] 618551.4 11389.234 [14,] 618171.0 11315.148 [15,] 617760.8 11242.081 [16,] 617350.8 11165.441 [17,] 616933.9 11084.005 [18,] 616488.6 10999.615 [19,] 616049.1 10914.165 [20,] 615605.3 10824.093 [21,] 615149.7 10727.889 [22,] 614700.0 10628.097 [23,] 614243.6 10528.227 [24,] 613799.4 10424.807 [25,] 613334.2 10314.770 [26,] 612900.0 10204.200 [27,] 612900.0 10089.172 [28,] 611965.8 9970.829 [29,] 611506.5 9849.782 [30,] 611046.4 9723.594 [31,] 611046.4 9610.540 [32,] 610310.2 9503.498 [33,] 609967.6 9391.427 [34,] 609614.0 9278.480 [35,] 609296.5 9173.735 [36,] 609030.2 9070.429 [37,] 608780.3 8968.946 [38,] 608567.4 8868.651 [39,] 608345.1 8763.856 [40,] 608121.4 8657.243 [41,] 607876.0 8542.590 [42,] 607644.1 8425.945 [43,] 607398.4 8303.243 [44,] 607148.0 8173.747 [45,] 606889.3 8037.637 [46,] 606616.8 7888.382 [47,] 606348.7 7733.088 [48,] 606318.3 7617.195 [49,] 606306.2 7496.850 [50,] 606278.4 7365.886 [51,] 606329.4 7241.956 [52,] 606381.3 7104.825 [53,] 606431.4 6964.568 [54,] 606431.4 6822.533 [55,] 606696.0 6682.804 [56,] 606853.5 6536.221 [57,] 607054.6 6402.201 [58,] 607210.5 6275.495 [59,] 607319.4 6148.242 [60,] 607382.4 6016.586 [61,] 607474.2 5873.819 [62,] 607474.2 5755.303 [63,] 607482.8 5629.235 [64,] 607497.6 5501.195 [65,] 607513.6 5369.956 [66,] 607501.3 5251.981 [67,] 607459.7 5122.330 [68,] 607480.0 4988.136 [69,] 607309.6 4883.972 [70,] 607166.2 4774.082 > (midr <- midrange(x)) [1] 698750 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 605025.5 606381.3 606381.3 606381.3 606431.4 605025.5 606381.3 606381.3 > postscript(file="/var/www/html/freestat/rcomp/tmp/1tr7k1240404716.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/freestat/rcomp/tmp/25vw51240404716.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3tu6g1240404716.tab") > > system("convert tmp/1tr7k1240404716.ps tmp/1tr7k1240404716.png") > system("convert tmp/25vw51240404716.ps tmp/25vw51240404716.png") > > > proc.time() user system elapsed 1.466 0.559 1.579