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Type 'q()' to quit R. > x <- c(6.9,7.2,7.1,6.5,6.6,6.7,6.9,7.1,7.4,7.6,7.8,8.1,8.5,8.7,8.8,8,8,8.3,8.5,8.7,8.6,8.3,7.9,7.9,8.1,8.3,8.1,7.4,7.3,7.7,8,8,7.7,6.9,6.6,6.9,7.5,7.9,7.7,6.5,6.1,6.4,6.8,7.1,7.3,7.2,7,7,7,7.3,7.5,7.2,7.7,8,7.9,8,8,7.9,7.9,8,8.1,8.1,8.2,8,8.3,8.5,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,7.9,8.1,8.2,8.5,8.6,8.5,8.3,8.2,8.7,9.3,9.3,8.8,7.4,7.2,7.5,8.3,8.8,8.9,8.6,8.4,8.4,8.4,8.4,8.3,7.6,7.6,7.9,8,8.2,8.3,8.2,8.1,8,7.8,7.6,7.5,6.8,6.9,7.1,7.3,7.4,7.6,7.6,7.5,7.5,6.8,6.4,6.2,6,6.3,6.3,6.1,6.1,6.3,6.6,6.8,7,7.1,7.3,6.8,6.3,6.4,6.7,6.8,7.2,7.5,7.7,7.8,8.1,8.4,8.7,8.5,8.3,8.5,8.7,8.9,9,9.1,9.1,9.2,9.6,9.9,9.8,9.2,8.9,9,9.2,9.3,9.4,9.5,9.4,9.4,9.6,9.8,9.7,9.1,8.7,8.7,8.8,9,9.2,9.2,9.3,9.4,9.6,9.8,9.8,9.3,9,9.2,9.5,9.7,9.9,10,9.9,10,10.1,10.2,10,9.5,9,9.1,9.3,9.5,9.7,9.8,9.8,9.9,10.1,10.2,10.2,9.6,9.3,9.4,9.5,9.6,9.7,9.7,9.6,9.5,9.5,9.4,9.2,8.5,8,7.9,7.9,8,8,8,7.8,7.6,7.6,7.6,7.5,7,6.5,6.5,6.6,6.7,6.8,6.9) > 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] 8.192827 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.06857967 > (armose <- arm / armse) [1] 119.4644 > (geo <- geomean(x)) [1] 8.123896 > (har <- harmean(x)) [1] 8.053964 > (qua <- quamean(x)) [1] 8.260288 > (win <- winmean(x)) [,1] [,2] [1,] 8.193249 0.06852378 [2,] 8.193249 0.06852378 [3,] 8.191983 0.06837040 [4,] 8.193671 0.06815638 [5,] 8.193671 0.06765614 [6,] 8.193671 0.06765614 [7,] 8.193671 0.06765614 [8,] 8.190295 0.06728345 [9,] 8.194093 0.06684144 [10,] 8.194093 0.06684144 [11,] 8.194093 0.06684144 [12,] 8.194093 0.06574105 [13,] 8.194093 0.06574105 [14,] 8.194093 0.06574105 [15,] 8.194093 0.06574105 [16,] 8.200844 0.06502023 [17,] 8.200844 0.06502023 [18,] 8.193249 0.06424700 [19,] 8.193249 0.06424700 [20,] 8.201688 0.06337988 [21,] 8.201688 0.06337988 [22,] 8.201688 0.06337988 [23,] 8.201688 0.06146954 [24,] 8.201688 0.06146954 [25,] 8.201688 0.06146954 [26,] 8.201688 0.06146954 [27,] 8.201688 0.06146954 [28,] 8.201688 0.06146954 [29,] 8.189451 0.06031628 [30,] 8.202110 0.05910743 [31,] 8.202110 0.05910743 [32,] 8.202110 0.05910743 [33,] 8.202110 0.05910743 [34,] 8.202110 0.05910743 [35,] 8.202110 0.05910743 [36,] 8.202110 0.05631934 [37,] 8.202110 0.05631934 [38,] 8.202110 0.05631934 [39,] 8.202110 0.05631934 [40,] 8.202110 0.05631934 [41,] 8.219409 0.05478771 [42,] 8.201688 0.05320308 [43,] 8.201688 0.05320308 [44,] 8.201688 0.05320308 [45,] 8.201688 0.05320308 [46,] 8.221097 0.05153624 [47,] 8.221097 0.05153624 [48,] 8.221097 0.05153624 [49,] 8.200422 0.04973828 [50,] 8.200422 0.04973828 [51,] 8.221941 0.04794383 [52,] 8.221941 0.04794383 [53,] 8.221941 0.04794383 [54,] 8.221941 0.04794383 [55,] 8.221941 0.04794383 [56,] 8.221941 0.04402469 [57,] 8.221941 0.04402469 [58,] 8.221941 0.04402469 [59,] 8.221941 0.04402469 [60,] 8.221941 0.03993619 [61,] 8.221941 0.03993619 [62,] 8.221941 0.03993619 [63,] 8.221941 0.03993619 [64,] 8.221941 0.03993619 [65,] 8.194515 0.03771595 [66,] 8.194515 0.03771595 [67,] 8.194515 0.03771595 [68,] 8.194515 0.03326251 [69,] 8.194515 0.03326251 [70,] 8.194515 0.03326251 [71,] 8.194515 0.03326251 [72,] 8.164135 0.03097533 [73,] 8.164135 0.03097533 [74,] 8.164135 0.03097533 [75,] 8.164135 0.03097533 [76,] 8.164135 0.03097533 [77,] 8.196624 0.02852086 [78,] 8.196624 0.02852086 [79,] 8.196624 0.02852086 > (tri <- trimean(x)) [,1] [,2] [1,] 8.192827 0.06799287 [2,] 8.193617 0.06743405 [3,] 8.194372 0.06684561 [4,] 8.194372 0.06628222 [5,] 8.195595 0.06574909 [6,] 8.196000 0.06530247 [7,] 8.196413 0.06483108 [8,] 8.196413 0.06433340 [9,] 8.197717 0.06386529 [10,] 8.198157 0.06343271 [11,] 8.198605 0.06297514 [12,] 8.199061 0.06249100 [13,] 8.199526 0.06210226 [14,] 8.200000 0.06169010 [15,] 8.200483 0.06125303 [16,] 8.200483 0.06078944 [17,] 8.200985 0.06036433 [18,] 8.200995 0.05991283 [19,] 8.201508 0.05949928 [20,] 8.202030 0.05905941 [21,] 8.202051 0.05866142 [22,] 8.202073 0.05823745 [23,] 8.202094 0.05778571 [24,] 8.202116 0.05744650 [25,] 8.202139 0.05708378 [26,] 8.202162 0.05669593 [27,] 8.202186 0.05628118 [28,] 8.202210 0.05583759 [29,] 8.202235 0.05536303 [30,] 8.202825 0.05493395 [31,] 8.202857 0.05455555 [32,] 8.202857 0.05414918 [33,] 8.202924 0.05371270 [34,] 8.202959 0.05324379 [35,] 8.202994 0.05273985 [36,] 8.203030 0.05219799 [37,] 8.203067 0.05179811 [38,] 8.203106 0.05136659 [39,] 8.203145 0.05090082 [40,] 8.203185 0.05039790 [41,] 8.203226 0.04985458 [42,] 8.202614 0.04936776 [43,] 8.202649 0.04894424 [44,] 8.202685 0.04848462 [45,] 8.202721 0.04798566 [46,] 8.202759 0.04744370 [47,] 8.202098 0.04696510 [48,] 8.201418 0.04644381 [49,] 8.200719 0.04587563 [50,] 8.200730 0.04538013 [51,] 8.200741 0.04483859 [52,] 8.200000 0.04436843 [53,] 8.199237 0.04385285 [54,] 8.198450 0.04328706 [55,] 8.197638 0.04266560 [56,] 8.196800 0.04198212 [57,] 8.195935 0.04151917 [58,] 8.195041 0.04100748 [59,] 8.194118 0.04044148 [60,] 8.193162 0.03981475 [61,] 8.192174 0.03943050 [62,] 8.191150 0.03900139 [63,] 8.191150 0.03852215 [64,] 8.190090 0.03798661 [65,] 8.187850 0.03738759 [66,] 8.187619 0.03690636 [67,] 8.187379 0.03636542 [68,] 8.187129 0.03575670 [69,] 8.186869 0.03545058 [70,] 8.186598 0.03510015 [71,] 8.186316 0.03469949 [72,] 8.186022 0.03424165 [73,] 8.186813 0.03392187 [74,] 8.187640 0.03355130 [75,] 8.188506 0.03312251 [76,] 8.189412 0.03262655 [77,] 8.190361 0.03205263 [78,] 8.190123 0.03165228 [79,] 8.189873 0.03118325 > (midr <- midrange(x)) [1] 8.1 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 8.166942 8.196800 8.196800 8.196800 8.196800 8.196800 8.196800 8.196800 > postscript(file="/var/wessaorg/rcomp/tmp/1888g1322592158.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/2nvzt1322592158.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/33qow1322592158.tab") > > try(system("convert tmp/1888g1322592158.ps tmp/1888g1322592158.png",intern=TRUE)) character(0) > try(system("convert tmp/2nvzt1322592158.ps tmp/2nvzt1322592158.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.345 0.150 1.503