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Type 'q()' to quit R. > x <- c(27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.76 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.76 + ,27.02 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.02 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.76 + ,27.02 + ,27.76 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,27.59 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,27.59 + ,28.33 + ,28.33 + ,27.59 + ,28.33 + ,28.33 + ,28.33 + ,28.33 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59 + ,27.59) > 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] 27.76498 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.03099937 > (armose <- arm / armse) [1] 895.6626 > (geo <- geomean(x)) [1] 27.76151 > (har <- harmean(x)) [1] 27.75803 > (qua <- quamean(x)) [1] 27.76844 > (win <- winmean(x)) [,1] [,2] [1,] 27.76498 0.030999368 [2,] 27.76498 0.030999368 [3,] 27.76498 0.030999368 [4,] 27.76498 0.030999368 [5,] 27.76498 0.030999368 [6,] 27.76498 0.030999368 [7,] 27.76498 0.030999368 [8,] 27.76498 0.030999368 [9,] 27.76498 0.030999368 [10,] 27.76498 0.030999368 [11,] 27.76498 0.030999368 [12,] 27.76498 0.030999368 [13,] 27.76498 0.030999368 [14,] 27.76498 0.030999368 [15,] 27.76498 0.030999368 [16,] 27.76498 0.030999368 [17,] 27.76498 0.030999368 [18,] 27.76498 0.030999368 [19,] 27.76498 0.030999368 [20,] 27.76498 0.030999368 [21,] 27.76498 0.030999368 [22,] 27.76498 0.030999368 [23,] 27.76498 0.030999368 [24,] 27.76498 0.030999368 [25,] 27.76498 0.030999368 [26,] 27.76498 0.030999368 [27,] 27.76498 0.030999368 [28,] 27.76498 0.030999368 [29,] 27.76498 0.030999368 [30,] 27.76498 0.030999368 [31,] 27.76498 0.030999368 [32,] 27.85572 0.022413749 [33,] 27.85572 0.022413749 [34,] 27.85572 0.022413749 [35,] 27.85572 0.022413749 [36,] 27.85572 0.022413749 [37,] 27.85572 0.022413749 [38,] 27.85572 0.022413749 [39,] 27.85572 0.022413749 [40,] 27.85572 0.022413749 [41,] 27.85572 0.022413749 [42,] 27.85572 0.022413749 [43,] 27.85572 0.022413749 [44,] 27.85572 0.022413749 [45,] 27.85572 0.022413749 [46,] 27.85572 0.022413749 [47,] 27.85572 0.022413749 [48,] 27.85572 0.022413749 [49,] 27.85572 0.022413749 [50,] 27.85572 0.022413749 [51,] 27.85572 0.022413749 [52,] 27.85572 0.022413749 [53,] 27.85572 0.022413749 [54,] 27.85572 0.022413749 [55,] 27.85572 0.022413749 [56,] 27.85572 0.022413749 [57,] 27.85572 0.022413749 [58,] 27.85572 0.022413749 [59,] 27.85572 0.022413749 [60,] 27.68557 0.005963736 [61,] 27.68557 0.005963736 [62,] 27.68557 0.005963736 [63,] 27.68557 0.005963736 [64,] 27.68557 0.005963736 [65,] 27.68557 0.005963736 [66,] 27.68557 0.005963736 [67,] 27.68557 0.005963736 > (tri <- trimean(x)) [,1] [,2] [1,] 27.76588 0.030955308 [2,] 27.76680 0.030906018 [3,] 27.76774 0.030851176 [4,] 27.76870 0.030790436 [5,] 27.76969 0.030723427 [6,] 27.77069 0.030649748 [7,] 27.77171 0.030568969 [8,] 27.77276 0.030480626 [9,] 27.77383 0.030384218 [10,] 27.77492 0.030279202 [11,] 27.77603 0.030164991 [12,] 27.77718 0.030040947 [13,] 27.77834 0.029906378 [14,] 27.77954 0.029760528 [15,] 27.77954 0.029602574 [16,] 27.78201 0.029431614 [17,] 27.78329 0.029246661 [18,] 27.78461 0.029046627 [19,] 27.78595 0.028830316 [20,] 27.78733 0.028596404 [21,] 27.78874 0.028343422 [22,] 27.79019 0.028069736 [23,] 27.79168 0.027773520 [24,] 27.79320 0.027452723 [25,] 27.79477 0.027105034 [26,] 27.79638 0.026727833 [27,] 27.79803 0.026318133 [28,] 27.79972 0.025872504 [29,] 27.80147 0.025386980 [30,] 27.80147 0.024856935 [31,] 27.80511 0.024276920 [32,] 27.80701 0.023640440 [33,] 27.80474 0.023618918 [34,] 27.80241 0.023588944 [35,] 27.80000 0.023549650 [36,] 27.79752 0.023500070 [37,] 27.79496 0.023439118 [38,] 27.79232 0.023365576 [39,] 27.78959 0.023278070 [40,] 27.78678 0.023175048 [41,] 27.78387 0.023054745 [42,] 27.78085 0.022915153 [43,] 27.77774 0.022753969 [44,] 27.77451 0.022568547 [45,] 27.77117 0.022355822 [46,] 27.76771 0.022112228 [47,] 27.76411 0.021833580 [48,] 27.76038 0.021514934 [49,] 27.75650 0.021150386 [50,] 27.75248 0.020732815 [51,] 27.74828 0.020253516 [52,] 27.74392 0.019701682 [53,] 27.73937 0.019063641 [54,] 27.73462 0.018321680 [55,] 27.73462 0.017452150 [56,] 27.72449 0.016422203 [57,] 27.71908 0.015183659 [58,] 27.71341 0.013660092 [59,] 27.70747 0.011714404 [60,] 27.70747 0.009039322 [61,] 27.70190 0.009129733 [62,] 27.70260 0.009221958 [63,] 27.70333 0.009315943 [64,] 27.70411 0.009411600 [65,] 27.70493 0.009508808 [66,] 27.70580 0.009607395 [67,] 27.70672 0.009707127 > (midr <- midrange(x)) [1] 27.675 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 27.90604 27.90604 27.90604 27.90604 27.90604 27.90604 27.90604 27.90604 > postscript(file="/var/www/rcomp/tmp/1ftz71290436971.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/rcomp/tmp/282yr1290436971.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/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/3a57r1290436971.tab") > > try(system("convert tmp/1ftz71290436971.ps tmp/1ftz71290436971.png",intern=TRUE)) character(0) > try(system("convert tmp/282yr1290436971.ps tmp/282yr1290436971.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.410 0.530 1.924