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Type 'q()' to quit R. > x <- c(580,579,572,560,551,537,541,588,607,599,578,563,566,561,554,540,526,512,505,554,584,569,540,522,526,527,516,503,489,479,475,524,552,532,511,492,492,493,481,462,457,442,439,488,521,501,485,464,460,467,460,448,443,436,431,484,510,513,503,471,471,476,475,470,461,455,456,517,525,523,519,509,512,519,517,510,509,501,507,569,580,578,565,547,555,562,561,555,544,537,543,594,611,613,611,594,595,591,589,584,573,567,569,621,629,628,612,595,597,593,590,580,574,573,573,620,626,620,588,566,557,561,549,532,526,511,499,555,565,542,527,510,514,517,508,493,490,469,478,528,534,518,506,502,516) > 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] 532.9379 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 4.011564 > (armose <- arm / armse) [1] 132.8504 > (geo <- geomean(x)) [1] 530.7458 > (har <- harmean(x)) [1] 528.5382 > (qua <- quamean(x)) [1] 535.1076 > (win <- winmean(x)) [,1] [,2] [1,] 532.9655 4.004480 [2,] 532.9793 3.993115 [3,] 532.9379 3.966759 [4,] 532.9379 3.958153 [5,] 533.1103 3.931588 [6,] 533.1103 3.846244 [7,] 533.1103 3.832535 [8,] 533.1103 3.817008 [9,] 533.2966 3.791616 [10,] 533.0207 3.753102 [11,] 532.4897 3.662996 [12,] 532.4069 3.631156 [13,] 532.4069 3.585257 [14,] 532.6966 3.547439 [15,] 532.8000 3.508495 [16,] 532.9103 3.494631 [17,] 532.9103 3.465856 [18,] 532.6621 3.436273 [19,] 533.0552 3.356682 [20,] 532.9172 3.340517 [21,] 532.9172 3.306320 [22,] 533.2207 3.270389 [23,] 532.7448 3.179342 [24,] 533.0759 3.140852 [25,] 532.9034 3.005460 [26,] 533.0828 2.985301 [27,] 533.6414 2.923771 [28,] 533.6414 2.881731 [29,] 533.6414 2.838512 [30,] 534.0552 2.794798 [31,] 533.2000 2.703262 [32,] 533.2000 2.656943 [33,] 533.2000 2.656943 [34,] 534.6069 2.513704 [35,] 534.8483 2.441153 [36,] 534.1034 2.363591 [37,] 534.3586 2.338923 [38,] 534.6207 2.313898 [39,] 534.0828 2.258922 [40,] 534.3586 2.178871 [41,] 534.6414 2.152577 [42,] 534.6414 2.096720 [43,] 534.9379 2.069742 [44,] 534.6345 1.981616 [45,] 534.3241 1.950903 [46,] 534.3241 1.891271 [47,] 534.3241 1.891271 [48,] 534.3241 1.891271 > (tri <- trimean(x)) [,1] [,2] [1,] 532.9790 3.947322 [2,] 532.9929 3.885135 [3,] 533.0000 3.823851 [4,] 533.0219 3.767409 [5,] 533.0444 3.708429 [6,] 533.0301 3.650765 [7,] 533.0153 3.606479 [8,] 533.0000 3.560574 [9,] 532.9843 3.512916 [10,] 532.9440 3.464666 [11,] 532.9350 3.417459 [12,] 532.9835 3.378305 [13,] 533.0420 3.339273 [14,] 533.1026 3.301938 [15,] 533.1391 3.265190 [16,] 533.1681 3.228960 [17,] 533.1892 3.190165 [18,] 533.2110 3.150141 [19,] 533.2523 3.108685 [20,] 533.2667 3.071113 [21,] 533.2913 3.030608 [22,] 533.3168 2.988722 [23,] 533.3232 2.945384 [24,] 533.3608 2.906186 [25,] 533.3789 2.865838 [26,] 533.4086 2.834257 [27,] 533.4286 2.800146 [28,] 533.4157 2.767451 [29,] 533.4023 2.734166 [30,] 533.3882 2.700249 [31,] 533.3494 2.665527 [32,] 533.3580 2.635074 [33,] 533.3671 2.604342 [34,] 533.3766 2.568078 [35,] 533.3067 2.541261 [36,] 533.2192 2.517084 [37,] 533.1690 2.496757 [38,] 533.1014 2.474348 [39,] 533.0149 2.449443 [40,] 532.9538 2.425568 [41,] 532.8730 2.405457 [42,] 532.7705 2.382816 [43,] 532.6610 2.361117 [44,] 532.5263 2.336255 [45,] 532.4000 2.316621 [46,] 532.2830 2.294908 [47,] 532.1569 2.274561 [48,] 532.0204 2.246405 > (midr <- midrange(x)) [1] 530 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 532.7838 532.7838 532.7838 532.7838 532.7838 532.7838 532.7838 532.7838 > postscript(file="/var/www/html/rcomp/tmp/1tppx1237424222.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/rcomp/tmp/2jb4y1237424222.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/www/html/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/rcomp/tmp/3k0g71237424222.tab") > > system("convert tmp/1tppx1237424222.ps tmp/1tppx1237424222.png") > system("convert tmp/2jb4y1237424222.ps tmp/2jb4y1237424222.png") > > > proc.time() user system elapsed 0.799 0.301 0.997