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Type 'q()' to quit R. > x <- c(43.31 + ,43.31 + ,44.05 + ,44.05 + ,44.05 + ,43.31 + ,44.05 + ,44.05 + ,44.05 + ,44.05 + ,44.05 + ,44.05 + ,43.31 + ,43.31 + ,43.31 + ,43.31 + ,44.05 + ,44.61 + ,44.61 + ,43.89 + ,43.89 + ,43.89 + ,44.61 + ,44.61 + ,44.61 + ,43.89 + ,43.89 + ,44.61 + ,44.61 + ,44.61 + ,43.89 + ,44.61 + ,44.61 + ,44.61 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,44.61 + ,44.61 + ,44.61 + ,44.61 + ,43.89 + ,44.61 + ,44.61 + ,43.89 + ,44.61 + ,44.61 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,44.61 + ,44.61 + ,44.61 + ,44.61 + ,44.61 + ,44.61 + ,44.61 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,43.89 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,43.58 + ,43.58 + ,44.28 + ,44.28 + ,43.58 + ,43.58 + ,43.58 + ,44.28 + ,44.28 + ,44.28 + ,43.58 + ,43.58 + ,44.28 + ,43.58 + ,44.28 + ,44.28 + ,44.28 + ,43.58 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,44.28 + ,44.28 + ,44.28 + ,44.28 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,43.58 + ,43.33 + ,43.33 + ,44.03 + ,44.03 + ,44.03 + ,43.33 + ,44.03 + ,44.03 + ,44.03 + ,44.03 + ,43.33 + ,43.33 + ,44.03 + ,44.03 + ,44.03 + ,43.33 + ,43.33 + ,44.03 + ,44.03 + ,43.33 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.9 + ,43.9 + ,43.17 + ,43.17 + ,43.17 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.17 + ,43.17 + ,43.17 + ,43.9 + ,43.9 + ,43.17 + ,43.17 + ,43.17 + ,43.9 + ,43.9 + ,43.17 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.17 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.9 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17 + ,43.17) > 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] 43.87124 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.03171813 > (armose <- arm / armse) [1] 1383.16 > (geo <- geomean(x)) [1] 43.86895 > (har <- harmean(x)) [1] 43.86665 > (qua <- quamean(x)) [1] 43.87354 > (win <- winmean(x)) [,1] [,2] [1,] 43.87124 0.031718126 [2,] 43.87124 0.031718126 [3,] 43.87124 0.031718126 [4,] 43.87124 0.031718126 [5,] 43.87124 0.031718126 [6,] 43.87124 0.031718126 [7,] 43.87124 0.031718126 [8,] 43.87124 0.031718126 [9,] 43.87124 0.031718126 [10,] 43.87124 0.031718126 [11,] 43.87124 0.031718126 [12,] 43.87124 0.031718126 [13,] 43.87124 0.031718126 [14,] 43.87124 0.031718126 [15,] 43.87124 0.031718126 [16,] 43.87124 0.031718126 [17,] 43.87124 0.031718126 [18,] 43.87124 0.031718126 [19,] 43.87124 0.031718126 [20,] 43.87124 0.031718126 [21,] 43.87124 0.031718126 [22,] 43.87124 0.031718126 [23,] 43.87124 0.031718126 [24,] 43.87124 0.031718126 [25,] 43.87124 0.031718126 [26,] 43.82856 0.027422837 [27,] 43.82856 0.027422837 [28,] 43.82856 0.027422837 [29,] 43.82856 0.027422837 [30,] 43.84945 0.025036908 [31,] 43.84945 0.025036908 [32,] 43.84945 0.025036908 [33,] 43.84945 0.025036908 [34,] 43.84945 0.025036908 [35,] 43.84945 0.025036908 [36,] 43.84945 0.025036908 [37,] 43.85313 0.024643188 [38,] 43.85313 0.024643188 [39,] 43.85313 0.024643188 [40,] 43.85313 0.024643188 [41,] 43.85313 0.024643188 [42,] 43.85313 0.024643188 [43,] 43.85313 0.024643188 [44,] 43.85313 0.024643188 [45,] 43.90910 0.019203829 [46,] 43.90910 0.019203829 [47,] 43.90910 0.019203829 [48,] 43.90910 0.019203829 [49,] 43.90910 0.019203829 [50,] 43.90910 0.019203829 [51,] 43.90910 0.019203829 [52,] 43.90910 0.019203829 [53,] 43.84846 0.013971561 [54,] 43.84846 0.013971561 [55,] 43.84846 0.013971561 [56,] 43.84846 0.013971561 [57,] 43.84846 0.013971561 [58,] 43.84846 0.013971561 [59,] 43.84846 0.013971561 [60,] 43.84846 0.013971561 [61,] 43.84846 0.013971561 [62,] 43.84846 0.013971561 [63,] 43.84219 0.013527783 [64,] 43.84219 0.013527783 [65,] 43.84219 0.013527783 [66,] 43.94398 0.004699465 [67,] 43.94398 0.004699465 > (tri <- trimean(x)) [,1] [,2] [1,] 43.87106 0.031624092 [2,] 43.87086 0.031522600 [3,] 43.87067 0.031413192 [4,] 43.87047 0.031295372 [5,] 43.87026 0.031168608 [6,] 43.87005 0.031032324 [7,] 43.86984 0.030885898 [8,] 43.86962 0.030728653 [9,] 43.86940 0.030559856 [10,] 43.86917 0.030378710 [11,] 43.86894 0.030184345 [12,] 43.86870 0.029975808 [13,] 43.86846 0.029752059 [14,] 43.86821 0.029511951 [15,] 43.86821 0.029254223 [16,] 43.86769 0.028977479 [17,] 43.86743 0.028680171 [18,] 43.86715 0.028360576 [19,] 43.86687 0.028016766 [20,] 43.86658 0.027646575 [21,] 43.86629 0.027247557 [22,] 43.86599 0.026816934 [23,] 43.86568 0.026351531 [24,] 43.86536 0.025847690 [25,] 43.86503 0.025301166 [26,] 43.86470 0.024706982 [27,] 43.86660 0.024426799 [28,] 43.86855 0.024121535 [29,] 43.87056 0.023788642 [30,] 43.87056 0.023425202 [31,] 43.87374 0.023227999 [32,] 43.87489 0.023011776 [33,] 43.87607 0.022774666 [34,] 43.87729 0.022514553 [35,] 43.87855 0.022229023 [36,] 43.87984 0.021915310 [37,] 43.88118 0.021570223 [38,] 43.88240 0.021224271 [39,] 43.88366 0.020842660 [40,] 43.88496 0.020420889 [41,] 43.88630 0.019953609 [42,] 43.88769 0.019434377 [43,] 43.88913 0.018855331 [44,] 43.89062 0.018206692 [45,] 43.89216 0.017476042 [46,] 43.89147 0.017196386 [47,] 43.89075 0.016883693 [48,] 43.89000 0.016533350 [49,] 43.88922 0.016139791 [50,] 43.88842 0.015696208 [51,] 43.88758 0.015194127 [52,] 43.88670 0.014622778 [53,] 43.88579 0.013968112 [54,] 43.88731 0.013767029 [55,] 43.88731 0.013535510 [56,] 43.89056 0.013268616 [57,] 43.89230 0.012960266 [58,] 43.89412 0.012602848 [59,] 43.89602 0.012186642 [60,] 43.89602 0.011698923 [61,] 43.90013 0.011122483 [62,] 43.90234 0.010433030 [63,] 43.90467 0.009594167 [64,] 43.90740 0.008605216 [65,] 43.91028 0.007321235 [66,] 43.91333 0.005507751 [67,] 43.91194 0.005381169 > (midr <- midrange(x)) [1] 43.89 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 43.94885 43.94885 43.94885 43.94885 43.94885 43.94885 43.94885 43.94885 > postscript(file="/var/www/html/rcomp/tmp/1byre1290438074.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/2byre1290438074.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/3pszg1290438074.tab") > > try(system("convert tmp/1byre1290438074.ps tmp/1byre1290438074.png",intern=TRUE)) character(0) > try(system("convert tmp/2byre1290438074.ps tmp/2byre1290438074.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.012 0.361 2.195