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Type 'q()' to quit R. > x <- c(106.19,106.2,106.09,106.23,106.23,106.22,106.22,106.61,106.95,107.74,107.8,107.8,107.2,107.56,107.72,108.14,108.16,108.16,108.16,108.1,108.95,110.49,110.72,110.82,110.82,110.75,110.71,110.86,110.84,110.84,110.84,110.92,111.46,112.46,113.04,113.15,113.15,113.21,113.37,113.47,113.71,113.71,113.71,113.8,115.46,117,117.94,118.08,118.08,118.47,118.49,118.45,118.54,118.55,118.55,118.55,119.04,121.37,122,122.14,122.14,122.03,121.91,122.23,121.73,121.83,121.83,122.49,123.02,125.98,126.13,126.39) > 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] 113.9958 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.7064281 > (armose <- arm / armse) [1] 161.3693 > (geo <- geomean(x)) [1] 113.8421 > (har <- harmean(x)) [1] 113.6903 > (qua <- quamean(x)) [1] 114.1511 > (win <- winmean(x)) [,1] [,2] [1,] 113.9936 0.7053267 [2,] 113.9897 0.7042790 [3,] 113.8672 0.6775694 [4,] 113.8378 0.6720985 [5,] 113.8204 0.6687517 [6,] 113.8129 0.6674285 [7,] 113.8499 0.6616252 [8,] 113.8754 0.6537430 [9,] 113.9029 0.6484776 [10,] 113.9404 0.6391251 [11,] 113.9526 0.6335696 [12,] 113.9560 0.6331082 [13,] 113.9487 0.6284570 [14,] 113.8788 0.6163609 [15,] 113.4558 0.5295662 [16,] 113.3558 0.5124322 [17,] 113.3606 0.5117557 [18,] 113.3606 0.5117557 [19,] 113.3579 0.5113790 [20,] 113.5635 0.4787550 [21,] 114.0068 0.4207141 [22,] 114.0679 0.4119831 [23,] 113.9529 0.3940409 [24,] 113.9629 0.3928872 > (tri <- trimean(x)) [,1] [,2] [1,] 113.9317 0.6952502 [2,] 113.8662 0.6830550 [3,] 113.7988 0.6689678 [4,] 113.7731 0.6639343 [5,] 113.7544 0.6593679 [6,] 113.7385 0.6543677 [7,] 113.7231 0.6481490 [8,] 113.6998 0.6414701 [9,] 113.6706 0.6345438 [10,] 113.6348 0.6265428 [11,] 113.5908 0.6179555 [12,] 113.5415 0.6076899 [13,] 113.4874 0.5941016 [14,] 113.4293 0.5771297 [15,] 113.3743 0.5575550 [16,] 113.3645 0.5520311 [17,] 113.3655 0.5473374 [18,] 113.3661 0.5398638 [19,] 113.3668 0.5283870 [20,] 113.3678 0.5113446 [21,] 113.3443 0.4955099 [22,] 113.2632 0.4866025 [23,] 113.1619 0.4728291 [24,] 113.0588 0.4562625 > (midr <- midrange(x)) [1] 116.24 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 113.4985 113.4985 113.4985 113.4985 113.4985 113.4985 113.4985 113.4985 > postscript(file="/var/wessaorg/rcomp/tmp/1iv5v1318964323.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/2qxaf1318964323.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/3amle1318964323.tab") > > try(system("convert tmp/1iv5v1318964323.ps tmp/1iv5v1318964323.png",intern=TRUE)) character(0) > try(system("convert tmp/2qxaf1318964323.ps tmp/2qxaf1318964323.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 0.798 0.122 0.918