central tendency residuals export

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 23 Dec 2008 03:31:31 -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/23/t1230028344kzeechug5s4fzj7.htm/, Retrieved Tue, 23 Dec 2008 11:32:26 +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/23/t1230028344kzeechug5s4fzj7.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:

Dataseries X:

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0.0149994435710854 -0.187272889456763 0.783610541316898 0.820253359437909 -0.128480187064758 0.0973604964959972 -0.000555424984621835 -0.108798129324484 -0.411259536814343 -0.412967982493527 -0.775180072815647 0.0513699485461512 0.171091997313326 -0.559987647777577 0.350298858460566 0.0248441904146359 -0.244826657610183 1.06340098337485 -0.064430759914597 0.109951554465647 1.50429932801390 0.63402991841865 -0.505156450025503 1.22453590536772 0.334342185134797 0.387623702787292 0.609800320816726 -0.00684756070541829 0.710259001142361 0.717745165814745 -0.38479617444722 -0.532103579474728 -0.34112865179578 -0.193930196585549 -0.0736614923676532 -0.367047391683380 -1.05336791990604 -0.237345748394650 0.776921090951805 -1.23329471813023 0.500914642312414 1.39368409436530 0.359974890816273 0.0321277650951418 1.39795292628765 -1.49091899243776 0.306194045706259 1.09684993392529 -0.138783333463160 0.161299798351927 -0.594652246674679 0.512191518507154 0.626101389245217 -1.54333588056056 0.0206384486198507 0.179085634154539 -0.37975488705151 0.15080216195892 0.0890102756063935 0.0419478410965998 0.765059089089874 0.774437669297186 -0.85186048667728 0.505328816512842 0.188557358188863 -0.949944839369926 1.30814280572219 2.03149903031633 -0.8170352751667 1.82633654903848 0.862775217520398 -0.222242407311244 1.57724133026930 -1.02736312888576

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.152115683438895 0.087201596754712 1.74441396832192 Geometric Mean NaN Harmonic Mean -0.0429691622105088 Quadratic Mean 0.76042082423997 Winsorized Mean ( 1 / 24 ) 0.150051553801664 0.0862363247332366 1.74000404430307 Winsorized Mean ( 2 / 24 ) 0.150282068816214 0.0828373563894369 1.81418233712946 Winsorized Mean ( 3 / 24 ) 0.154619290274409 0.0805642320810543 1.91920516438174 Winsorized Mean ( 4 / 24 ) 0.150276500506518 0.0789944766252863 1.90236718978925 Winsorized Mean ( 5 / 24 ) 0.155219031424997 0.0778891854252387 1.99281877936678 Winsorized Mean ( 6 / 24 ) 0.156236036618203 0.0748958674550502 2.08604348847378 Winsorized Mean ( 7 / 24 ) 0.151621552538375 0.0726577631076988 2.08679081289126 Winsorized Mean ( 8 / 24 ) 0.142342550474443 0.0691293146797332 2.05907654565789 Winsorized Mean ( 9 / 24 ) 0.160230521830047 0.0645935882941192 2.48059484016365 Winsorized Mean ( 10 / 24 ) 0.137803337106081 0.0589443399149738 2.33785529373745 Winsorized Mean ( 11 / 24 ) 0.135627449436135 0.057226295442855 2.37001973282666 Winsorized Mean ( 12 / 24 ) 0.134055175597467 0.0555699084208891 2.41236992118336 Winsorized Mean ( 13 / 24 ) 0.149075273207865 0.0529239901678983 2.81678068367355 Winsorized Mean ( 14 / 24 ) 0.148928656131431 0.0528006925491445 2.82058149129039 Winsorized Mean ( 15 / 24 ) 0.152391787650312 0.0517207023976777 2.94643693116500 Winsorized Mean ( 16 / 24 ) 0.143251758270978 0.0499282976152234 2.86914966288175 Winsorized Mean ( 17 / 24 ) 0.144451253160541 0.0492402335409803 2.93360211300219 Winsorized Mean ( 18 / 24 ) 0.132213602200406 0.0454792965033605 2.90711625652866 Winsorized Mean ( 19 / 24 ) 0.154904086460286 0.0417792984674413 3.70767562267718 Winsorized Mean ( 20 / 24 ) 0.152520259645973 0.0408363199147511 3.73491685745363 Winsorized Mean ( 21 / 24 ) 0.129106547676386 0.0361276880088598 3.57361776498746 Winsorized Mean ( 22 / 24 ) 0.135483428650581 0.0347227899050991 3.90185895260347 Winsorized Mean ( 23 / 24 ) 0.1361806186148 0.0342543576737272 3.97557063868839 Winsorized Mean ( 24 / 24 ) 0.115163953685659 0.0269861801921349 4.26751592354754 Trimmed Mean ( 1 / 24 ) 0.149561075343367 0.0823537974777366 1.81607988852972 Trimmed Mean ( 2 / 24 ) 0.149042569544596 0.0777099383252157 1.91793447217592 Trimmed Mean ( 3 / 24 ) 0.148368136117392 0.074396801291986 1.99428111882243 Trimmed Mean ( 4 / 24 ) 0.146031846179921 0.0715037490785009 2.04229635595190 Trimmed Mean ( 5 / 24 ) 0.144804875788639 0.0686274051244498 2.11001531423268 Trimmed Mean ( 6 / 24 ) 0.142318916056089 0.065510715007135 2.17245249178839 Trimmed Mean ( 7 / 24 ) 0.139458174607210 0.0626239010114739 2.22691611916126 Trimmed Mean ( 8 / 24 ) 0.137241204245373 0.0597191629627485 2.29810997737829 Trimmed Mean ( 9 / 24 ) 0.136398571162892 0.0570857347088711 2.38936350488445 Trimmed Mean ( 10 / 24 ) 0.132769837933737 0.0549523838852959 2.41608877625532 Trimmed Mean ( 11 / 24 ) 0.132053532282288 0.0536373728449354 2.46196868485808 Trimmed Mean ( 12 / 24 ) 0.131572677974316 0.0523527411223809 2.51319558734754 Trimmed Mean ( 13 / 24 ) 0.131253745988008 0.0510718493432886 2.56998224414712 Trimmed Mean ( 14 / 24 ) 0.129048406499263 0.0499812221268958 2.58193779599119 Trimmed Mean ( 15 / 24 ) 0.126660194692802 0.0485650474825828 2.60805252456979 Trimmed Mean ( 16 / 24 ) 0.123637753615253 0.0469318725440937 2.63440913206887 Trimmed Mean ( 17 / 24 ) 0.121369884326935 0.0451940604803919 2.68552732453843 Trimmed Mean ( 18 / 24 ) 0.118725888516274 0.0430082972384981 2.76053450472339 Trimmed Mean ( 19 / 24 ) 0.117185624916543 0.0410536574688276 2.85445030093903 Trimmed Mean ( 20 / 24 ) 0.112864934275309 0.0393000778438541 2.87187559077466 Trimmed Mean ( 21 / 24 ) 0.108279787279326 0.0370627681136688 2.92152455928925 Trimmed Mean ( 22 / 24 ) 0.105833469391417 0.0353974225980502 2.98986371389782 Trimmed Mean ( 23 / 24 ) 0.102271623636258 0.0333388969851342 3.06763669121569 Trimmed Mean ( 24 / 24 ) 0.0980755272676758 0.0303079162598093 3.23597064301421 Median 0.0701901120762723 Midrange 0.244081574877885 Midmean - Weighted Average at Xnp 0.104798752572966 Midmean - Weighted Average at X(n+1)p 0.118725888516274 Midmean - Empirical Distribution Function 0.118725888516274 Midmean - Empirical Distribution Function - Averaging 0.118725888516274 Midmean - Empirical Distribution Function - Interpolation 0.117185624916543 Midmean - Closest Observation 0.118725888516274 Midmean - True Basic - Statistics Graphics Toolkit 0.118725888516274 Midmean - MS Excel (old versions) 0.118725888516274 Number of observations 74

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230028344kzeechug5s4fzj7/13z951230028283.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230028344kzeechug5s4fzj7/13z951230028283.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230028344kzeechug5s4fzj7/2l4251230028283.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230028344kzeechug5s4fzj7/2l4251230028283.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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We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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