paper robuustheidCentral tendency of electronics

*The author of this computation has been verified*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Fri, 26 Dec 2008 10:43:23 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/26/t123031344730xsapicu92hprj.htm/, Retrieved Fri, 26 Dec 2008 18:44:09 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/26/t123031344730xsapicu92hprj.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

RobuustheidCentral tendency of electronics

Dataseries X:

» Textbox « » Textfile « » CSV «

105.5 106.4 117.9 89.7 88.5 106.4 61.4 92.3 95.5 92.5 89.6 84.3 76.3 80.7 96.3 81.0 82.9 90.3 74.8 70.1 86.7 86.4 89.9 88.1 78.8 81.1 85.4 82.6 80.3 81.2 68.0 67.4 91.3 94.9 82.8 88.6 73.1 76.7 93.2 84.9 83.8 93.5 91.9 69.6 87.0 90.2 82.7 91.4 74.6 76.1 87.1 78.4 81.3 99.3 71.0 73.2 95.6 84.0 90.8 93.6 80.9 84.4 97.3 83.5 88.8 100.7 69.4 74.6 96.6 96.6 93.1 91.8 85.7 79.1 91.3 84.2 85.8 90.0 76.6 81.3

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 85.8825 1.10716420602995 77.5697945546453 Geometric Mean 85.3179405010884 Harmonic Mean 84.7493592799855 Quadratic Mean 86.4444503713223 Winsorized Mean ( 1 / 26 ) 85.81375 1.04372862480955 82.2184502371567 Winsorized Mean ( 2 / 26 ) 85.82875 1.04042681381492 82.4937889531056 Winsorized Mean ( 3 / 26 ) 85.8475 1.02104125153775 84.0783855409451 Winsorized Mean ( 4 / 26 ) 85.6175 0.965863185465713 88.6435069566478 Winsorized Mean ( 5 / 26 ) 85.56125 0.942612001453838 90.7703804619871 Winsorized Mean ( 6 / 26 ) 85.47875 0.902443402184076 94.7192364564094 Winsorized Mean ( 7 / 26 ) 85.60125 0.856713055055502 99.9182275732384 Winsorized Mean ( 8 / 26 ) 85.61125 0.854870620439066 100.145271054033 Winsorized Mean ( 9 / 26 ) 85.735 0.82137215389242 104.380212542766 Winsorized Mean ( 10 / 26 ) 85.6475 0.80742004933984 106.075518028103 Winsorized Mean ( 11 / 26 ) 85.66125 0.800534816781723 107.005027394526 Winsorized Mean ( 12 / 26 ) 85.76625 0.754037536733947 113.742679670152 Winsorized Mean ( 13 / 26 ) 85.5875 0.71758291321754 119.271931401262 Winsorized Mean ( 14 / 26 ) 85.6225 0.706567238596744 121.180965268143 Winsorized Mean ( 15 / 26 ) 85.585 0.695669470839585 123.025378556155 Winsorized Mean ( 16 / 26 ) 85.905 0.640052658039392 134.215519490450 Winsorized Mean ( 17 / 26 ) 85.8625 0.609646543685641 140.839804456062 Winsorized Mean ( 18 / 26 ) 85.885 0.593634748974379 144.676503773378 Winsorized Mean ( 19 / 26 ) 86.075 0.540714190162454 159.187610693441 Winsorized Mean ( 20 / 26 ) 86.15 0.523957675360921 164.421677649167 Winsorized Mean ( 21 / 26 ) 86.0975 0.502890301222136 171.205330050637 Winsorized Mean ( 22 / 26 ) 86.0975 0.495639131560632 173.710053378761 Winsorized Mean ( 23 / 26 ) 86.12625 0.491908398613586 175.085951455071 Winsorized Mean ( 24 / 26 ) 86.00625 0.468310131169181 183.652336935947 Winsorized Mean ( 25 / 26 ) 85.88125 0.444274738773946 193.306624268137 Winsorized Mean ( 26 / 26 ) 85.84875 0.440195561222797 195.024115557924 Trimmed Mean ( 1 / 26 ) 85.7858974358974 1.00960212530077 84.9700048029721 Trimmed Mean ( 2 / 26 ) 85.7565789473684 0.969612575055816 88.4441695101075 Trimmed Mean ( 3 / 26 ) 85.7175675675676 0.924519663968112 92.715786270744 Trimmed Mean ( 4 / 26 ) 85.6694444444444 0.880086687669206 97.342052373646 Trimmed Mean ( 5 / 26 ) 85.6842857142857 0.848253926283044 101.012542423169 Trimmed Mean ( 6 / 26 ) 85.7132352941177 0.817799957754504 104.809537444178 Trimmed Mean ( 7 / 26 ) 85.760606060606 0.792764125944187 108.17922160449 Trimmed Mean ( 8 / 26 ) 85.7890625 0.774456149384165 110.773298873304 Trimmed Mean ( 9 / 26 ) 85.8177419354839 0.752733513907152 114.008132160925 Trimmed Mean ( 10 / 26 ) 85.83 0.733998029523672 116.934918824918 Trimmed Mean ( 11 / 26 ) 85.8551724137931 0.714041912266386 120.238281449455 Trimmed Mean ( 12 / 26 ) 85.880357142857 0.69092174290852 124.298240754927 Trimmed Mean ( 13 / 26 ) 85.8944444444444 0.672222222222222 127.776859504132 Trimmed Mean ( 14 / 26 ) 85.9307692307692 0.65615509275104 130.961064205857 Trimmed Mean ( 15 / 26 ) 85.966 0.63803659289852 134.735218883712 Trimmed Mean ( 16 / 26 ) 86.0083333333333 0.617094206784735 139.376342198163 Trimmed Mean ( 17 / 26 ) 86.0195652173913 0.60229528416365 142.819589459078 Trimmed Mean ( 18 / 26 ) 86.0363636363636 0.589182711506336 146.02662630137 Trimmed Mean ( 19 / 26 ) 86.052380952381 0.57504469447301 149.644682890679 Trimmed Mean ( 20 / 26 ) 86.05 0.567348759921633 151.670376457482 Trimmed Mean ( 21 / 26 ) 86.0394736842105 0.559700939675087 153.724011494706 Trimmed Mean ( 22 / 26 ) 86.0333333333333 0.552986121700763 155.579552464589 Trimmed Mean ( 23 / 26 ) 86.0264705882353 0.544152333046766 158.092624737202 Trimmed Mean ( 24 / 26 ) 86.015625 0.531414526231186 161.861636733994 Trimmed Mean ( 25 / 26 ) 86.0166666666667 0.518687187491105 165.835341109408 Trimmed Mean ( 26 / 26 ) 86.0321428571429 0.50586647263189 170.068876890655 Median 85.75 Midrange 89.65 Midmean - Weighted Average at Xnp 85.909756097561 Midmean - Weighted Average at X(n+1)p 86.05 Midmean - Empirical Distribution Function 85.909756097561 Midmean - Empirical Distribution Function - Averaging 86.05 Midmean - Empirical Distribution Function - Interpolation 86.05 Midmean - Closest Observation 85.909756097561 Midmean - True Basic - Statistics Graphics Toolkit 86.05 Midmean - MS Excel (old versions) 86.052380952381 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t123031344730xsapicu92hprj/1le781230313396.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t123031344730xsapicu92hprj/1le781230313396.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t123031344730xsapicu92hprj/2umwe1230313396.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t123031344730xsapicu92hprj/2umwe1230313396.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

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)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') 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() bitmap(file='test2.png') 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() load(file='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='mytable.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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