Robuustheid eigen reeks - Robbert Van Hees

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 08 Nov 2008 11:11:14 -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/Nov/08/t1226167953vn5sfp2ddm3dxtp.htm/, Retrieved Sat, 08 Nov 2008 18:12:35 +0000

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/Nov/08/t1226167953vn5sfp2ddm3dxtp.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}, }

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Dataseries X:

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18,33 18,22 18,21 18,06 18,26 18,21 18,05 18,25 18,27 18,28 18,13 18,01 18,02 17,97 18,06 18,08 18,23 18,06 18,23 18,17 18,27 18,33 18,18 18,29 18,33 18,31 18,44 18,63 18,37 18,59 18,72 18,75 18,87 18,83 18,89 18,78 19,27 19,19 19,43 19,36 19,39 19,07 19,31 19,19 19,06 19,05 19,49 19,25 19,76 20,35 19,61 19,33 18,95 18,97 19,28 19,41 18,99 19,37 19,63 19,53 19,86 20,13 19,47 19,49 18,95 19,33 19,65 19,44 19,73 18,89 19,56 19,56

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 18.8608333333333 0.0723995580745468 260.510337838155 Geometric Mean 18.8510050792795 Harmonic Mean 18.8412177528031 Quadratic Mean 18.8706967132760 Winsorized Mean ( 1 / 24 ) 18.8583333333333 0.071479173893306 263.829760560501 Winsorized Mean ( 2 / 24 ) 18.8511111111111 0.0697265942677751 270.357548781403 Winsorized Mean ( 3 / 24 ) 18.8481944444444 0.0687051394081909 274.334563713838 Winsorized Mean ( 4 / 24 ) 18.8470833333333 0.0683071166644513 275.916833467249 Winsorized Mean ( 5 / 24 ) 18.8415277777778 0.067331386727028 279.832759930585 Winsorized Mean ( 6 / 24 ) 18.8398611111111 0.0670521405785389 280.97329851899 Winsorized Mean ( 7 / 24 ) 18.8398611111111 0.0664160468381241 283.664295121773 Winsorized Mean ( 8 / 24 ) 18.8398611111111 0.0646488931383993 291.418154225457 Winsorized Mean ( 9 / 24 ) 18.8448611111111 0.0638902475700939 294.956770834804 Winsorized Mean ( 10 / 24 ) 18.8420833333333 0.0630354799551558 298.912348200376 Winsorized Mean ( 11 / 24 ) 18.8405555555556 0.0614403564904092 306.647887996818 Winsorized Mean ( 12 / 24 ) 18.8405555555556 0.0614403564904092 306.647887996818 Winsorized Mean ( 13 / 24 ) 18.83875 0.0606465998579879 310.631594254475 Winsorized Mean ( 14 / 24 ) 18.8348611111111 0.0595224188953736 316.433059352282 Winsorized Mean ( 15 / 24 ) 18.8327777777778 0.0592253138625822 317.985276050620 Winsorized Mean ( 16 / 24 ) 18.8327777777778 0.0579647045425093 324.900781025572 Winsorized Mean ( 17 / 24 ) 18.8304166666667 0.0569732240530447 330.513446968258 Winsorized Mean ( 18 / 24 ) 18.8279166666667 0.0559342118244789 336.608241227185 Winsorized Mean ( 19 / 24 ) 18.8252777777778 0.0555752996996567 338.734615548894 Winsorized Mean ( 20 / 24 ) 18.8197222222222 0.0540658947855316 348.088611071291 Winsorized Mean ( 21 / 24 ) 18.8226388888889 0.0536569528197241 350.795896892038 Winsorized Mean ( 22 / 24 ) 18.8226388888889 0.0519950164096331 362.008519058793 Winsorized Mean ( 23 / 24 ) 18.8194444444444 0.0498534192915417 377.495560222033 Winsorized Mean ( 24 / 24 ) 18.8161111111111 0.0494209646911089 380.731360237819 Trimmed Mean ( 1 / 24 ) 18.8522857142857 0.0701657816329026 268.682045229941 Trimmed Mean ( 2 / 24 ) 18.8458823529412 0.0685905498851216 274.759167035474 Trimmed Mean ( 3 / 24 ) 18.8430303030303 0.0678050715271391 277.900013651462 Trimmed Mean ( 4 / 24 ) 18.84109375 0.0672840155562966 280.023324919358 Trimmed Mean ( 5 / 24 ) 18.8393548387097 0.0667540340049617 282.220469811748 Trimmed Mean ( 6 / 24 ) 18.8388333333333 0.066358933112027 283.892950803318 Trimmed Mean ( 7 / 24 ) 18.8386206896552 0.0658966946542529 285.881117232021 Trimmed Mean ( 8 / 24 ) 18.8383928571429 0.065429041957986 287.920964351573 Trimmed Mean ( 9 / 24 ) 18.8381481481481 0.0651901878519956 288.972140882878 Trimmed Mean ( 10 / 24 ) 18.8371153846154 0.0649726340689899 289.923837236052 Trimmed Mean ( 11 / 24 ) 18.8364 0.064786468730841 290.745897546243 Trimmed Mean ( 12 / 24 ) 18.8358333333333 0.0647682949682708 290.818730716330 Trimmed Mean ( 13 / 24 ) 18.8352173913043 0.064621334125787 291.470574634704 Trimmed Mean ( 14 / 24 ) 18.8347727272727 0.0644651836120529 292.169690241156 Trimmed Mean ( 15 / 24 ) 18.8347619047619 0.064349905577856 292.692922167135 Trimmed Mean ( 16 / 24 ) 18.835 0.0641042820282622 293.818125779742 Trimmed Mean ( 17 / 24 ) 18.8352631578947 0.0638819332833233 294.844914513753 Trimmed Mean ( 18 / 24 ) 18.8358333333333 0.0636151312239071 296.090457898084 Trimmed Mean ( 19 / 24 ) 18.8367647058824 0.0632846054054647 297.651610295982 Trimmed Mean ( 20 / 24 ) 18.838125 0.0626891291638557 300.500664967944 Trimmed Mean ( 21 / 24 ) 18.8403333333333 0.0620057159644217 303.848331404539 Trimmed Mean ( 22 / 24 ) 18.8425 0.0608811510261145 309.496448119348 Trimmed Mean ( 23 / 24 ) 18.845 0.0594830292539879 316.813051324830 Trimmed Mean ( 24 / 24 ) 18.8483333333333 0.0578155070049684 326.008268537948 Median 18.89 Midrange 19.16 Midmean - Weighted Average at Xnp 18.8202702702703 Midmean - Weighted Average at X(n+1)p 18.8358333333333 Midmean - Empirical Distribution Function 18.8202702702703 Midmean - Empirical Distribution Function - Averaging 18.8358333333333 Midmean - Empirical Distribution Function - Interpolation 18.8358333333333 Midmean - Closest Observation 18.8202702702703 Midmean - True Basic - Statistics Graphics Toolkit 18.8358333333333 Midmean - MS Excel (old versions) 18.8352631578947 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226167953vn5sfp2ddm3dxtp/13zky1226167871.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226167953vn5sfp2ddm3dxtp/13zky1226167871.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226167953vn5sfp2ddm3dxtp/28rdm1226167871.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226167953vn5sfp2ddm3dxtp/28rdm1226167871.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')

Copyright

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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