paper robuustheidCentral tendency of medical

*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 10:47:42 -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/t1230313702ofudrq4nvc14yq2.htm/, Retrieved Fri, 26 Dec 2008 18:48:24 +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/t1230313702ofudrq4nvc14yq2.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:

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User-defined keywords:

paper robuustheidCentral tendency of medical

Dataseries X:

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96.5 97.3 122.0 91.0 107.9 114.6 98.0 95.5 98.7 115.9 110.4 109.5 92.3 102.1 112.8 110.2 98.9 119.0 104.3 98.8 109.4 170.3 118.0 116.9 111.7 116.8 116.1 114.8 110.8 122.8 104.7 86.0 127.2 126.1 114.6 127.8 105.2 113.1 161.0 126.9 117.7 144.9 119.4 107.1 142.8 126.2 126.9 179.2 105.3 114.8 125.4 113.2 134.4 150.0 100.9 101.8 137.7 138.7 135.4 153.8 119.5 123.3 166.4 137.5 142.2 167.0 112.3 120.6 154.9 153.4 156.2 175.8 131.7 130.1 161.1 128.2 140.3 168.2 110.2 126.2

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 123.7075 2.43521876372846 50.7993375554468 Geometric Mean 121.919878468889 Harmonic Mean 120.235513710664 Quadratic Mean 125.586776772079 Winsorized Mean ( 1 / 26 ) 123.7275 2.41178342476572 51.3012481674297 Winsorized Mean ( 2 / 26 ) 123.6225 2.37033217174943 52.1540826527954 Winsorized Mean ( 3 / 26 ) 123.66375 2.33177842960657 53.0340912454813 Winsorized Mean ( 4 / 26 ) 123.65375 2.30985570248392 53.533105928231 Winsorized Mean ( 5 / 26 ) 123.66625 2.29362141363440 53.9174640003217 Winsorized Mean ( 6 / 26 ) 123.32125 2.19573211872112 56.164068899182 Winsorized Mean ( 7 / 26 ) 123.37375 2.18497729309958 56.4645455994574 Winsorized Mean ( 8 / 26 ) 122.90375 2.08255369325374 59.0158853517853 Winsorized Mean ( 9 / 26 ) 122.76875 2.05160294983357 59.8404043092056 Winsorized Mean ( 10 / 26 ) 122.88125 1.98852729501165 61.7951034960676 Winsorized Mean ( 11 / 26 ) 122.95 1.96060004377373 62.7103933769927 Winsorized Mean ( 12 / 26 ) 122.485 1.85636443729421 65.9811174677163 Winsorized Mean ( 13 / 26 ) 122.01375 1.65678767245955 73.6447717641858 Winsorized Mean ( 14 / 26 ) 121.71625 1.58418054102133 76.8323097325314 Winsorized Mean ( 15 / 26 ) 121.6975 1.55262229690142 78.3819092659384 Winsorized Mean ( 16 / 26 ) 121.3375 1.48747021563629 81.5730619171397 Winsorized Mean ( 17 / 26 ) 121.38 1.38189170470927 87.8361159462465 Winsorized Mean ( 18 / 26 ) 121.335 1.32307909481604 91.706535516586 Winsorized Mean ( 19 / 26 ) 121.64375 1.27097072906718 95.7093245485513 Winsorized Mean ( 20 / 26 ) 121.14375 1.18646219641110 102.105023123741 Winsorized Mean ( 21 / 26 ) 121.065 1.12412567994144 107.697032600756 Winsorized Mean ( 22 / 26 ) 120.3225 1.01557487461505 118.477231967370 Winsorized Mean ( 23 / 26 ) 119.92 0.944230314105594 127.002912540032 Winsorized Mean ( 24 / 26 ) 119.47 0.852936847499734 140.06898676052 Winsorized Mean ( 25 / 26 ) 119.62625 0.80104311691583 149.338091138694 Winsorized Mean ( 26 / 26 ) 119.62625 0.751765314321202 159.127120819634 Trimmed Mean ( 1 / 26 ) 123.479487179487 2.34311637260699 52.6988282029295 Trimmed Mean ( 2 / 26 ) 123.218421052632 2.26245380724489 54.462292515347 Trimmed Mean ( 3 / 26 ) 123 2.19388011506425 56.0650507543333 Trimmed Mean ( 4 / 26 ) 122.754166666667 2.13019037249795 57.6259137453148 Trimmed Mean ( 5 / 26 ) 122.497142857143 2.06244038390891 59.3942708903788 Trimmed Mean ( 6 / 26 ) 122.222058823529 1.98643760357317 61.5282647709036 Trimmed Mean ( 7 / 26 ) 122 1.92373350096904 63.4183476757801 Trimmed Mean ( 8 / 26 ) 121.7546875 1.85060040890785 65.7919921091203 Trimmed Mean ( 9 / 26 ) 121.569354838710 1.78815597506677 67.9858784881281 Trimmed Mean ( 10 / 26 ) 121.391666666667 1.71946531511054 70.5984968698616 Trimmed Mean ( 11 / 26 ) 121.186206896552 1.64935677993355 73.4748287156124 Trimmed Mean ( 12 / 26 ) 120.957142857143 1.56846739891115 77.1180471721073 Trimmed Mean ( 13 / 26 ) 120.768518518519 1.49259486849849 80.9117872956434 Trimmed Mean ( 14 / 26 ) 120.621153846154 1.44290623578507 83.5959751608706 Trimmed Mean ( 15 / 26 ) 120.496 1.39609355864491 86.3094018691394 Trimmed Mean ( 16 / 26 ) 120.3625 1.34305286633589 89.6185868903079 Trimmed Mean ( 17 / 26 ) 120.256521739130 1.28995619209558 93.2252757698456 Trimmed Mean ( 18 / 26 ) 120.136363636364 1.24455724532163 96.529399582031 Trimmed Mean ( 19 / 26 ) 120.009523809524 1.19806177928755 100.169729044265 Trimmed Mean ( 20 / 26 ) 119.8375 1.14690602469739 104.487636667196 Trimmed Mean ( 21 / 26 ) 119.7 1.10031677838806 108.786853341779 Trimmed Mean ( 22 / 26 ) 119.555555555556 1.05226471143324 113.617376175919 Trimmed Mean ( 23 / 26 ) 119.473529411765 1.01675192205752 117.505093248308 Trimmed Mean ( 24 / 26 ) 119.425 0.986082588309794 121.110545319233 Trimmed Mean ( 25 / 26 ) 119.42 0.966798247089181 123.521117626710 Trimmed Mean ( 26 / 26 ) 119.396428571429 0.950737421158403 125.582969507977 Median 118.5 Midrange 132.6 Midmean - Weighted Average at Xnp 119.582926829268 Midmean - Weighted Average at X(n+1)p 119.8375 Midmean - Empirical Distribution Function 119.582926829268 Midmean - Empirical Distribution Function - Averaging 119.8375 Midmean - Empirical Distribution Function - Interpolation 119.8375 Midmean - Closest Observation 119.582926829268 Midmean - True Basic - Statistics Graphics Toolkit 119.8375 Midmean - MS Excel (old versions) 120.009523809524 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t1230313702ofudrq4nvc14yq2/1nwrk1230313660.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t1230313702ofudrq4nvc14yq2/1nwrk1230313660.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t1230313702ofudrq4nvc14yq2/2mw251230313660.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t1230313702ofudrq4nvc14yq2/2mw251230313660.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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