taak 3 task 2 verbetering (3)

*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: Tue, 28 Oct 2008 13:23:37 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/28/t1225221853yijoc4nca43m6ts.htm/, Retrieved Tue, 28 Oct 2008 19:24:15 +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/Oct/28/t1225221853yijoc4nca43m6ts.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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1.506206897 1.491582492 1.100350058 1.114512472 1.375796178 0.926436782 1.314393939 0.966071429 1.179292929 0.544284633 2.346633416 1.375362319 1.622895623 1.234417344 1.470383275 1.065351418 1.888412017 1.814009662 1.540730337 1.516936672 1.140277778 0.467353952 2.428211587 1.816955684 1.221166893 1.241184767 1.251644737 1.352459016 1.493577982 1.700767263 1.459459459 1.608547009 1.349498328 0.87144623 2.353887399 2.006726457 2.045174538 1.559259259 1.517171717 1.493506494 2.308571429 2.047619048 1.945419103 1.836734694 2.002409639 0.99862069 1.871733967 1.979591837 2.017738359 1.592445328 1.799511002 1.830508475 2.01897019 1.740831296 2.412532637 1.760259179 3.003521127 0.891581633 2.288043478 1.788954635 2.343457944

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.22007403326527e-16 0.0630127827147049 1.93623258758345e-15 Geometric Mean NaN Harmonic Mean -0.121321190943761 Quadratic Mean 0.488094916104477 Winsorized Mean ( 1 / 20 ) -0.00817014522950808 0.0597963719696704 -0.136632791595652 Winsorized Mean ( 2 / 20 ) 0.00204240057377061 0.0569207386385893 0.0358814840183042 Winsorized Mean ( 3 / 20 ) 0.000148474262295203 0.0560508678132905 0.00264891995588332 Winsorized Mean ( 4 / 20 ) 0.00195838678688537 0.0554657748195696 0.0353080218072498 Winsorized Mean ( 5 / 20 ) 0.00494684375409847 0.054752034822883 0.0903499526565722 Winsorized Mean ( 6 / 20 ) 0.00471694991803292 0.0533755169535665 0.0883729130368214 Winsorized Mean ( 7 / 20 ) 0.0100189079344264 0.0514386610679398 0.194773886536305 Winsorized Mean ( 8 / 20 ) -0.0169221792786884 0.0444577478149292 -0.380635099851051 Winsorized Mean ( 9 / 20 ) -0.0151933081967212 0.0440128011342553 -0.345202027709530 Winsorized Mean ( 10 / 20 ) -0.0152652822950818 0.0425288842818287 -0.358939166941754 Winsorized Mean ( 11 / 20 ) -0.00845189672131135 0.0412630387235077 -0.204829721289922 Winsorized Mean ( 12 / 20 ) -0.00238067140983595 0.0395226040118848 -0.0602356921907287 Winsorized Mean ( 13 / 20 ) -0.000476782409835916 0.0389102459643072 -0.0122533897697093 Winsorized Mean ( 14 / 20 ) -0.00416047595081952 0.0377892541126443 -0.110096799963761 Winsorized Mean ( 15 / 20 ) -0.00999148349180317 0.0360121240579178 -0.277447769416044 Winsorized Mean ( 16 / 20 ) -0.00848535470491792 0.0310634637250768 -0.273161897849399 Winsorized Mean ( 17 / 20 ) -0.00335014547540976 0.0288672361056626 -0.116053558544615 Winsorized Mean ( 18 / 20 ) -0.0128041541639343 0.0271912441056325 -0.470892545931063 Winsorized Mean ( 19 / 20 ) -0.00760965259016384 0.0258464563924137 -0.294417636005119 Winsorized Mean ( 20 / 20 ) -0.0119109417704916 0.0251787233952615 -0.473055825091322 Trimmed Mean ( 1 / 20 ) -0.00422911796526801 0.0574242027234319 -0.0736469600742462 Trimmed Mean ( 2 / 20 ) -1.15273842391616e-05 0.0544960899522023 -0.000211526813194709 Trimmed Mean ( 3 / 20 ) -0.00115052379731731 0.0528327850684075 -0.0217767016413695 Trimmed Mean ( 4 / 20 ) -0.00164888154345796 0.0511856498087598 -0.0322137464234317 Trimmed Mean ( 5 / 20 ) -0.00272752550498219 0.0493510343330067 -0.0552678488271923 Trimmed Mean ( 6 / 20 ) -0.00463828683071248 0.0472789744982266 -0.0981046412266506 Trimmed Mean ( 7 / 20 ) -0.00666193733310067 0.045085630905696 -0.147761874443661 Trimmed Mean ( 8 / 20 ) -0.00989219625792337 0.0428540241110905 -0.230834710697876 Trimmed Mean ( 9 / 20 ) -0.00864560043156679 0.0420017049405637 -0.205839273519994 Trimmed Mean ( 10 / 20 ) -0.00756318803678516 0.0409635764071163 -0.184632024353012 Trimmed Mean ( 11 / 20 ) -0.00635850149894901 0.039945420450988 -0.159179736429380 Trimmed Mean ( 12 / 20 ) -0.0060447493894549 0.0388765570563548 -0.155485718056065 Trimmed Mean ( 13 / 20 ) -0.00657691309601861 0.0378456816139299 -0.173782392483000 Trimmed Mean ( 14 / 20 ) -0.00744429764580216 0.0365289841316416 -0.203791532197411 Trimmed Mean ( 15 / 20 ) -0.00790584862136423 0.0349555747374989 -0.226168463277566 Trimmed Mean ( 16 / 20 ) -0.00761338028321073 0.0332118863039276 -0.229236611661843 Trimmed Mean ( 17 / 20 ) -0.00749025426533078 0.0322672589943648 -0.232131717994357 Trimmed Mean ( 18 / 20 ) -0.00808448164459003 0.0314754229374968 -0.256850612004294 Trimmed Mean ( 19 / 20 ) -0.00738907095937264 0.0307038914712922 -0.240655845409086 Trimmed Mean ( 20 / 20 ) -0.00735534795316146 0.0298185609799701 -0.246670117920923 Median -0.05141930052459 Midrange 0.12475897997541 Midmean - Weighted Average at Xnp -0.0193273950245900 Midmean - Weighted Average at X(n+1)p -0.00790584862136422 Midmean - Empirical Distribution Function -0.00790584862136422 Midmean - Empirical Distribution Function - Averaging -0.00790584862136422 Midmean - Empirical Distribution Function - Interpolation -0.00790584862136422 Midmean - Closest Observation -0.0192054718683400 Midmean - True Basic - Statistics Graphics Toolkit -0.00790584862136422 Midmean - MS Excel (old versions) -0.00790584862136422 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221853yijoc4nca43m6ts/14wwc1225221815.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221853yijoc4nca43m6ts/14wwc1225221815.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221853yijoc4nca43m6ts/2c5fi1225221815.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221853yijoc4nca43m6ts/2c5fi1225221815.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 36 ;

Parameters (R input):

par1 = 0 ; par2 = 36 ;

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

x <- x-1.61067855952459 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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