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Type 'q()' to quit R. > x <- c(3.4,3.4,4,3.4,3.1,3.3,3.5,3.5,3.7,3.4,3,3.1,2.9,2.4,2.4,2.7,2.5,2.1,1.9,0.8,0.8,0.3,0,-0.9,-1,-0.7,-1.7,-1,-0.2,0.7,0.6,1.9,2.1,2.7,3.2,4.8,5.5,5.4,5.9,5.8,5.1,4.1,4.4,3.6,3.5,3.1,2.9,2.2,1.4,1.2,1.3,1.3,1.3,1.8,1.8,1.8,1.7,2.1,2,1.7,1.9,2.3,2.4,2.5,2.8,2.6,2.2,2.8,2.8,2.8,2.3,2.2,3,2.9,2.7,2.7,2.3,2.4,2.8,2.3,2,1.9,2.3,2.7,1.8,2,2.1,2,2.4,1.7,1,1.2,1.4,1.7,1.8,1.4,1.7,1.6,1.4,1.5,0.9,1.5,1.7,1.6,1.2,1.3,1.1,1.3,1.2,1.3,1.1,0.8,1.4,1.6,2.5,2.5,2.6,2,1.8,1.9,1.9,2.5,2.8,3,3.1,2.9,2.2,2.5,2.7,3,3.7,3.7,4,3.5,1.7,3,2.4,2.3,2.5,2.1,0.3,2.1,1.6,1.4,1.3,0.9,0.7,0.7,0.8,1.1,1.3,1,1,0.7,0.6,0.7,0.8,1,1.2,1.2,1.3,1.3,1,0.8,0.5,0.9,1.3,1.2,1.6,1.7,1.9,1.6,1.4,1.1,1.3,1.9,2.1,2.1,2.1,2.2,1.5,1.2,1.5,1.9,2.1,2,1.6,1.4,1.4,1.3,1.1,1,1,0.9,0.8,1.1,1.4,1.6,1.7,1.7,1.9,1.9,2.1,2.2,2.5,2.5,2.8,2.8,2.6,2.4,2.2,2.4,2.3,2.5,2.3,2.5,2.5,2.9,2.3,2,2.3,2.6,2.7,2.5,2.5,2.2,2,1.9,2.2,1.9,2.4,2.5,2.7,2.6,2.6,2.1,2.1) > 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] 2.022785 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.06997575 > (armose <- arm / armse) [1] 28.90694 > (geo <- geomean(x)) [1] NaN Warning message: In log(x) : NaNs produced > (har <- harmean(x)) [1] 0 > (qua <- quamean(x)) [1] 2.290689 > (win <- winmean(x)) [,1] [,2] [1,] 2.025316 0.06927100 [2,] 2.022785 0.06870719 [3,] 2.022785 0.06820574 [4,] 2.021097 0.06657916 [5,] 2.025316 0.06367661 [6,] 2.020253 0.06117558 [7,] 2.020253 0.05860527 [8,] 2.016878 0.05810737 [9,] 2.024473 0.05720274 [10,] 2.016034 0.05498452 [11,] 2.016034 0.05498452 [12,] 2.021097 0.05444790 [13,] 2.015612 0.05374687 [14,] 2.009705 0.05302609 [15,] 2.009705 0.05302609 [16,] 2.009705 0.05302609 [17,] 2.016878 0.05229697 [18,] 2.009283 0.05140513 [19,] 2.009283 0.05140513 [20,] 2.009283 0.05140513 [21,] 2.009283 0.05140513 [22,] 2.000000 0.05036518 [23,] 1.990295 0.04933000 [24,] 1.990295 0.04728707 [25,] 1.990295 0.04728707 [26,] 1.990295 0.04728707 [27,] 1.990295 0.04728707 [28,] 1.990295 0.04500901 [29,] 1.990295 0.04500901 [30,] 1.990295 0.04500901 [31,] 1.990295 0.04500901 [32,] 1.990295 0.04500901 [33,] 1.976371 0.04372350 [34,] 1.976371 0.04372350 [35,] 1.991139 0.04236606 [36,] 1.991139 0.04236606 [37,] 1.991139 0.04236606 [38,] 1.975105 0.04095232 [39,] 1.975105 0.04095232 [40,] 1.975105 0.04095232 [41,] 1.992405 0.03943169 [42,] 1.992405 0.03943169 [43,] 1.992405 0.03943169 [44,] 1.992405 0.03943169 [45,] 1.992405 0.03943169 [46,] 1.972996 0.03779747 [47,] 1.972996 0.03779747 [48,] 1.972996 0.03779747 [49,] 1.993671 0.03605772 [50,] 1.993671 0.03605772 [51,] 1.993671 0.03605772 [52,] 1.993671 0.03605772 [53,] 1.993671 0.03605772 [54,] 1.970886 0.03422321 [55,] 1.970886 0.03422321 [56,] 1.970886 0.03422321 [57,] 1.970886 0.03422321 [58,] 1.970886 0.03422321 [59,] 1.970886 0.03422321 [60,] 1.945570 0.03231509 [61,] 1.945570 0.03231509 [62,] 1.971730 0.03015508 [63,] 1.971730 0.03015508 [64,] 1.971730 0.03015508 [65,] 1.971730 0.03015508 [66,] 1.971730 0.03015508 [67,] 1.971730 0.03015508 [68,] 1.971730 0.03015508 [69,] 1.971730 0.03015508 [70,] 1.971730 0.03015508 [71,] 1.971730 0.03015508 [72,] 2.002110 0.02776862 [73,] 2.002110 0.02776862 [74,] 2.002110 0.02776862 [75,] 1.970464 0.02543101 [76,] 2.002532 0.02298073 [77,] 2.002532 0.02298073 [78,] 2.002532 0.02298073 [79,] 2.002532 0.02298073 > (tri <- trimean(x)) [,1] [,2] [1,] 2.022785 0.06674640 [2,] 2.022128 0.06402363 [3,] 2.016883 0.06140708 [4,] 2.016883 0.05877877 [5,] 2.013216 0.05645367 [6,] 2.010667 0.05470600 [7,] 2.008969 0.05338349 [8,] 2.008969 0.05245680 [9,] 2.005936 0.05155662 [10,] 2.003687 0.05073640 [11,] 2.002326 0.05017007 [12,] 2.000939 0.04957071 [13,] 1.999052 0.04899804 [14,] 1.997608 0.04846959 [15,] 1.996618 0.04798545 [16,] 1.996618 0.04747222 [17,] 1.994581 0.04692777 [18,] 1.993035 0.04641642 [19,] 1.991960 0.04595377 [20,] 1.990863 0.04546215 [21,] 1.989744 0.04493938 [22,] 1.988601 0.04438304 [23,] 1.987958 0.04387609 [24,] 1.987831 0.04341794 [25,] 1.987701 0.04308343 [26,] 1.987568 0.04272635 [27,] 1.987432 0.04234505 [28,] 1.987293 0.04193771 [29,] 1.987151 0.04166082 [30,] 1.987006 0.04136386 [31,] 1.986857 0.04104536 [32,] 1.986857 0.04070368 [33,] 1.986550 0.04033702 [34,] 1.986982 0.04002824 [35,] 1.987425 0.03969601 [36,] 1.987273 0.03942645 [37,] 1.987117 0.03913543 [38,] 1.986957 0.03882124 [39,] 1.987421 0.03857115 [40,] 1.987898 0.03829997 [41,] 1.988387 0.03800596 [42,] 1.988235 0.03778277 [43,] 1.988079 0.03753941 [44,] 1.987919 0.03727417 [45,] 1.987755 0.03698519 [46,] 1.987586 0.03667036 [47,] 1.988112 0.03643053 [48,] 1.988652 0.03616763 [49,] 1.989209 0.03587956 [50,] 1.989051 0.03567540 [51,] 1.988889 0.03544968 [52,] 1.988722 0.03520040 [53,] 1.988550 0.03492532 [54,] 1.988372 0.03462192 [55,] 1.988976 0.03440767 [56,] 1.989600 0.03416892 [57,] 1.990244 0.03390319 [58,] 1.990909 0.03360769 [59,] 1.991597 0.03327921 [60,] 1.992308 0.03291412 [61,] 1.993913 0.03263853 [62,] 1.995575 0.03232923 [63,] 1.995575 0.03214749 [64,] 1.996396 0.03193975 [65,] 1.998131 0.03170301 [66,] 1.999048 0.03143384 [67,] 2.000000 0.03112828 [68,] 2.000990 0.03078173 [69,] 2.002020 0.03038880 [70,] 2.003093 0.02994316 [71,] 2.004211 0.02943727 [72,] 2.005376 0.02886207 [73,] 2.005495 0.02844624 [74,] 2.005618 0.02797012 [75,] 2.005747 0.02742423 [76,] 2.007059 0.02702775 [77,] 2.007229 0.02682006 [78,] 2.007407 0.02657262 [79,] 2.007595 0.02627916 > (midr <- midrange(x)) [1] 2.1 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 1.932813 1.962687 1.962687 1.962687 1.962687 1.962687 1.962687 1.962687 > postscript(file="/var/www/rcomp/tmp/1t0v01322592784.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/2edlv1322592784.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/352iw1322592784.tab") > > try(system("convert tmp/1t0v01322592784.ps tmp/1t0v01322592784.png",intern=TRUE)) character(0) > try(system("convert tmp/2edlv1322592784.ps tmp/2edlv1322592784.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.770 0.080 1.842