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Type 'q()' to quit R. > x <- c(132.8,132.5,131.4,131.4,130.7,131.5,131.2,130.1,130.5,129,128.2,128.4,127.3,127.7,127,123.9,125.4,124.6,124.5,124.8,124.1,124.2,122.8,122.3,121.1,121.7,122.2,122.2,122.7,121.7,121,119.8,120.2,116.6,116,118,117.1,116.2,113.3,114.3,113.6,113,112.9,112.7,112.5,113,111.9,110.9,109.8,108.3,109.2,109.2,108.7,109.8,110.8,110,109.6,109.5,110.8,111.6,113.1,114.3,114.1,113.8,112.6,112.7,111.5,110.7,110.4,109.7,110,111.3,109,108.2,107.2,108.7,110.3,110.3,109.5,109.5,109.4,109.6,111.3,110,109.5,110.693,109.195,108.095,108.199,106.87,105.278,108.711,111.192,109.641,109.42,109.935,111.126,110.733,110.34,111.766,111.294,111.54,112.008,111.007,114.963,112.045,110.703,108.894,107.51,111.35,112.964,115.203,115.182,115.191,112.346,110.774,113.07,111.138,109.092,107.971,107.051) > 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] 115.1850 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.6634898 > (armose <- arm / armse) [1] 173.6048 > (geo <- geomean(x)) [1] 114.9647 > (har <- harmean(x)) [1] 114.7533 > (qua <- quamean(x)) [1] 115.4141 > (win <- winmean(x)) [,1] [,2] [1,] 115.1957 0.6614364 [2,] 115.1822 0.6576144 [3,] 115.1834 0.6567256 [4,] 115.1936 0.6557061 [5,] 115.2044 0.6521999 [6,] 115.1858 0.6466223 [7,] 115.1802 0.6437716 [8,] 115.1539 0.6385641 [9,] 115.0795 0.6222789 [10,] 115.0629 0.6102025 [11,] 115.0448 0.6069045 [12,] 114.9963 0.5979404 [13,] 114.9730 0.5886788 [14,] 114.9505 0.5816031 [15,] 114.7636 0.5474123 [16,] 114.6978 0.5335546 [17,] 114.6704 0.5290800 [18,] 114.6556 0.5267583 [19,] 114.6399 0.5167763 [20,] 114.6266 0.5139535 [21,] 114.6058 0.5074706 [22,] 114.4058 0.4775414 [23,] 114.3868 0.4747624 [24,] 114.3075 0.4632696 [25,] 114.3075 0.4585253 [26,] 114.3075 0.4585253 [27,] 114.2050 0.4418507 [28,] 114.2187 0.4406798 [29,] 114.0989 0.4184287 [30,] 114.0741 0.4149760 [31,] 113.9037 0.3837264 [32,] 113.8151 0.3678376 [33,] 113.3242 0.3028078 [34,] 113.0713 0.2708291 [35,] 113.0135 0.2449225 [36,] 112.8944 0.2305470 [37,] 112.8455 0.2221256 [38,] 112.6141 0.1913609 [39,] 112.7046 0.1820161 [40,] 112.7040 0.1814644 > (tri <- trimean(x)) [,1] [,2] [1,] 115.1203 0.6527494 [2,] 115.0422 0.6430502 [3,] 114.9686 0.6344343 [4,] 114.8920 0.6251333 [5,] 114.8097 0.6149982 [6,] 114.7221 0.6045089 [7,] 114.6347 0.5939970 [8,] 114.5449 0.5827066 [9,] 114.4555 0.5709520 [10,] 114.3724 0.5606468 [11,] 114.2880 0.5509523 [12,] 114.2022 0.5404139 [13,] 114.1179 0.5297980 [14,] 114.0324 0.5190153 [15,] 113.9452 0.5076475 [16,] 113.8710 0.4996623 [17,] 113.7991 0.4923362 [18,] 113.7262 0.4843974 [19,] 113.6509 0.4754174 [20,] 113.5731 0.4662134 [21,] 113.4925 0.4557474 [22,] 113.4091 0.4442792 [23,] 113.3361 0.4352116 [24,] 113.2603 0.4247847 [25,] 113.1860 0.4140771 [26,] 113.1073 0.4018331 [27,] 113.0239 0.3869690 [28,] 112.9425 0.3717885 [29,] 112.8550 0.3532212 [30,] 112.7699 0.3345243 [31,] 112.7699 0.3117389 [32,] 112.5970 0.2897992 [33,] 112.5132 0.2653135 [34,] 112.4571 0.2501627 [35,] 112.4143 0.2382838 [36,] 112.3720 0.2284123 [37,] 112.3346 0.2190051 [38,] 112.2975 0.2086768 [39,] 112.2741 0.2026336 [40,] 112.2415 0.1961570 > (midr <- midrange(x)) [1] 119.039 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 112.5863 112.7220 112.7220 112.7220 112.7220 112.7220 112.7220 112.7220 > postscript(file="/var/www/html/rcomp/tmp/1cwrd1268602475.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/2zkc71268602475.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/322fb1268602475.tab") > > try(system("convert tmp/1cwrd1268602475.ps tmp/1cwrd1268602475.png",intern=TRUE)) character(0) > try(system("convert tmp/2zkc71268602475.ps tmp/2zkc71268602475.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 0.735 0.332 0.889