R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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Type 'license()' or 'licence()' for distribution details.

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> x <- c(20.98,20.1,20.61,20.27,20.08,23.58,22.31,22.89,21.78,22.19,22.58,22.78,25.06,25.16,25.47,25.34,24.2,25.32,25.57,25.76,24.79,23.14,22.66,22.06,24.26,23.15,22.92,21.43,21.56,23.48,24.35,24.83,24.19,23.58,23.58,24.35,27.18,25.69,24.81,23.26,23.49,26.86,27.12,27.66,26.26,25.51,24.63,23.57,27.63,25.85,26.09,24.47,24.19,25.09,25.26,25.58,24.76,25.02,24.24,24.14,28.69,26.74,26.48,24.45,23.88,26.58,26.23,28.63,26.81,26.56,26.64,26.8,28.37,27.13,28.44,28.62,27.28,31.32,31.26,31.41,31.76,32.72,32.15,33.62,35.97,33.78,33.77,32.75,32.55,33.22,32.88,31.56,30.27,28.65,27.89,27.07,30.8,28.38,27.5,28,28.02,29.2,27.59,27.22,27.16,26.31,25.67,26.41,28.34,25.43,23.72,23.33,23.8,27.7,26.28,27.51,27.93,28.76,28.65,29.52,31.23,27.9,27.87,27.52,27.59,31.2,30.22,30.62,31.52,30.59,31.42,31.95)
> 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] 26.67053
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.2917147
> (armose <- arm / armse)
[1] 91.42675
> (geo <- geomean(x))
[1] 26.46487
> (har <- harmean(x))
[1] 26.26241
> (qua <- quamean(x))
[1] 26.87871
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 26.65409 0.2881008
 [2,] 26.65652 0.2876302
 [3,] 26.66083 0.2857119
 [4,] 26.65992 0.2817381
 [5,] 26.66409 0.2769480
 [6,] 26.66409 0.2750981
 [7,] 26.67417 0.2732054
 [8,] 26.68083 0.2692054
 [9,] 26.66242 0.2636132
[10,] 26.65636 0.2600634
[11,] 26.66303 0.2548123
[12,] 26.65212 0.2511820
[13,] 26.66000 0.2491756
[14,] 26.66106 0.2462282
[15,] 26.66333 0.2456630
[16,] 26.67909 0.2410107
[17,] 26.67265 0.2397340
[18,] 26.68356 0.2374695
[19,] 26.68932 0.2357361
[20,] 26.65144 0.2245715
[21,] 26.62439 0.2203985
[22,] 26.63273 0.2182686
[23,] 26.57871 0.2104878
[24,] 26.56962 0.2092740
[25,] 26.43705 0.1923052
[26,] 26.40159 0.1816194
[27,] 26.32795 0.1695329
[28,] 26.33008 0.1659922
[29,] 26.37841 0.1587399
[30,] 26.38977 0.1575225
[31,] 26.38508 0.1570090
[32,] 26.38508 0.1564860
[33,] 26.35008 0.1505801
[34,] 26.33977 0.1483993
[35,] 26.36098 0.1455857
[36,] 26.35280 0.1447259
[37,] 26.29114 0.1325846
[38,] 26.29114 0.1314025
[39,] 26.31773 0.1244029
[40,] 26.34803 0.1194631
[41,] 26.35424 0.1182116
[42,] 26.35424 0.1169391
[43,] 26.30538 0.1108794
[44,] 26.35538 0.1032503
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 26.64969 0.2828358
 [2,] 26.64516 0.2770539
 [3,] 26.63921 0.2709632
 [4,] 26.63153 0.2650272
 [5,] 26.62385 0.2597426
 [6,] 26.61500 0.2551722
 [7,] 26.60585 0.2505405
 [8,] 26.59474 0.2457928
 [9,] 26.58228 0.2412701
[10,] 26.57179 0.2372172
[11,] 26.56164 0.2332771
[12,] 26.55037 0.2296747
[13,] 26.53981 0.2261719
[14,] 26.52808 0.2225162
[15,] 26.51578 0.2188031
[16,] 26.50280 0.2146894
[17,] 26.48796 0.2106393
[18,] 26.47302 0.2062178
[19,] 26.45660 0.2014752
[20,] 26.43902 0.1962847
[21,] 26.42344 0.1918300
[22,] 26.40909 0.1872795
[23,] 26.39349 0.1823101
[24,] 26.38083 0.1776390
[25,] 26.36817 0.1723986
[26,] 26.36362 0.1686220
[27,] 26.36115 0.1655799
[28,] 26.36329 0.1634875
[29,] 26.36541 0.1614275
[30,] 26.36458 0.1598353
[31,] 26.36300 0.1580457
[32,] 26.36162 0.1559365
[33,] 26.36015 0.1534464
[34,] 26.36078 0.1512109
[35,] 26.36210 0.1487654
[36,] 26.36217 0.1461558
[37,] 26.36276 0.1430579
[38,] 26.36732 0.1410224
[39,] 26.37222 0.1386091
[40,] 26.37577 0.1366529
[41,] 26.37760 0.1349063
[42,] 26.37917 0.1327915
[43,] 26.38087 0.1302105
[44,] 26.38614 0.1278994
> (midr <- midrange(x))
[1] 28.025
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 26.32791 26.36015 26.32791 26.36015 26.36015 26.32791 26.36015 26.36162
> postscript(file="/var/wessaorg/rcomp/tmp/1kfdx1318948166.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/26dxf1318948166.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/3dpck1318948166.tab") 
> 
> try(system("convert tmp/1kfdx1318948166.ps tmp/1kfdx1318948166.png",intern=TRUE))
character(0)
> try(system("convert tmp/26dxf1318948166.ps tmp/26dxf1318948166.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.977   0.161   1.139