central tendency residuals

*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 03:05:00 -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/t1230026762jk2cg1220mys8b4.htm/, Retrieved Tue, 23 Dec 2008 11:06:04 +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/t1230026762jk2cg1220mys8b4.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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0.0116336809818516 -0.154699100737743 0.300072012027226 -0.0281009082456990 -0.0251835401949439 0.149430781746124 -0.0474303009483888 0.189500500437989 -0.0206213472278605 0.099262365402598 -0.0336852870542978 -0.00660697294658047 -0.014407402190082 -0.162817662318404 0.0701902317692395 0.0869287301407032 0.0475463983256501 -0.0657098624738588 -0.173657662369991 -0.276407781076756 0.284286042426195 0.184763450923668 0.215844788210768 0.0791703148704692 -0.0757752611799243 -0.239844929271474 0.0580807137132677 0.0780992335812968 -0.262896297845741 0.0382739239466598 0.254506443794837 0.103225582875943 0.200928813722370 -0.0827196042197738 -0.180839166769625 0.0232745881765549 0.0423530836184901 -0.19423864986694 0.138244493738257 -0.0229304392309003 0.0671664871834856 0.0981295220879554 -0.0131126113391596 0.247873123505392 -0.0717314714408619 -0.0434772582819433 -0.228142684103270 0.0112903158271855 -0.0415097429872191 -0.216120288055151 0.0630033449128768 -0.105144089112524 -0.0273518411019308 0.145131569120259 0.0462387733804017 0.245764427953454 -0.0644763533124804 -0.210903939526438 0.257806389487202 -0.149938534530506 -0.314604118193826 0.231052233386827 -0.0162174883775465 0.0233245255900905 0.0318802978158298 -0.0521300406332036 0.0532608736670998 0.0333126331974996 -0.0654063687086189 0.291433563336759 -0.0165545860799951 0.0756034704157121

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 0.0121179740742296 0.0173105100472849 0.700035645462117 Geometric Mean NaN Harmonic Mean -0.285510539337426 Quadratic Mean 0.146363458966238 Winsorized Mean ( 1 / 24 ) 0.0125285003023768 0.0171492192966730 0.730558055479962 Winsorized Mean ( 2 / 24 ) 0.0127052770335005 0.0170168184540838 0.746630580080697 Winsorized Mean ( 3 / 24 ) 0.0125624318516369 0.0165649633088822 0.758373659958601 Winsorized Mean ( 4 / 24 ) 0.0130292262669613 0.0163896823568272 0.794965148396173 Winsorized Mean ( 5 / 24 ) 0.0134034676390914 0.0161244795804679 0.83124962714006 Winsorized Mean ( 6 / 24 ) 0.0136624387204893 0.0160019974988637 0.853795829018193 Winsorized Mean ( 7 / 24 ) 0.0138523229656296 0.0153993192587382 0.89954125457651 Winsorized Mean ( 8 / 24 ) 0.0136514382902136 0.0147890517719927 0.923077321026522 Winsorized Mean ( 9 / 24 ) 0.0126846295291181 0.01427052563579 0.888869117568132 Winsorized Mean ( 10 / 24 ) 0.0126029193578967 0.0137045124252063 0.919618222587514 Winsorized Mean ( 11 / 24 ) 0.0131195392569209 0.0133515800640548 0.982620723088897 Winsorized Mean ( 12 / 24 ) 0.00802418876186969 0.0121925999609800 0.658119579708147 Winsorized Mean ( 13 / 24 ) 0.0153358280160019 0.0106759515258796 1.43648348147951 Winsorized Mean ( 14 / 24 ) 0.0183569909764252 0.00978060101436578 1.87687760184291 Winsorized Mean ( 15 / 24 ) 0.0125081226800784 0.00837621201309049 1.49329107961099 Winsorized Mean ( 16 / 24 ) 0.0125260276280156 0.00811023607011634 1.54447139635924 Winsorized Mean ( 17 / 24 ) 0.0136803195181563 0.00786473106544354 1.73945166138809 Winsorized Mean ( 18 / 24 ) 0.0109559949726532 0.00744047075334415 1.47248680034513 Winsorized Mean ( 19 / 24 ) 0.00915405611698913 0.0071156439984362 1.28646909808879 Winsorized Mean ( 20 / 24 ) 0.0122860648364626 0.00658749614742697 1.86505837142105 Winsorized Mean ( 21 / 24 ) 0.0129288913212380 0.00629831815391198 2.05275297393602 Winsorized Mean ( 22 / 24 ) 0.0124827203273408 0.00590639339662823 2.11342514612502 Winsorized Mean ( 23 / 24 ) 0.0121453137482619 0.00569047663958909 2.13432274965616 Winsorized Mean ( 24 / 24 ) 0.0133657516356994 0.00516106084767392 2.58972952076768 Trimmed Mean ( 1 / 24 ) 0.0126718034215876 0.0166696292623035 0.760173080168222 Trimmed Mean ( 2 / 24 ) 0.0128235361360460 0.0160993608495215 0.796524548763509 Trimmed Mean ( 3 / 24 ) 0.0128880411010708 0.0155036156595722 0.831292608386707 Trimmed Mean ( 4 / 24 ) 0.0130101445696085 0.0150007729361677 0.867298280226635 Trimmed Mean ( 5 / 24 ) 0.0130046047219900 0.0144603100694716 0.899330972815382 Trimmed Mean ( 6 / 24 ) 0.0129088776218856 0.0138917969344652 0.929244624204017 Trimmed Mean ( 7 / 24 ) 0.0127529684290710 0.0132320837772433 0.963791390967748 Trimmed Mean ( 8 / 24 ) 0.0125510461672542 0.0125917242643651 0.996769457759962 Trimmed Mean ( 9 / 24 ) 0.0123676474800943 0.0119632669957167 1.03380184397141 Trimmed Mean ( 10 / 24 ) 0.0123188810110137 0.0113135733852083 1.08885854111485 Trimmed Mean ( 11 / 24 ) 0.0122779794890625 0.0106403481881464 1.15390767970737 Trimmed Mean ( 12 / 24 ) 0.0121632213389000 0.00986945953120538 1.23241007275446 Trimmed Mean ( 13 / 24 ) 0.0127030951532953 0.00918451985802356 1.38309844713308 Trimmed Mean ( 14 / 24 ) 0.0123717022055420 0.0086993960053532 1.42213346741878 Trimmed Mean ( 15 / 24 ) 0.0116388097029849 0.00828768172626515 1.40435046704308 Trimmed Mean ( 16 / 24 ) 0.0115344921457337 0.00809585715845709 1.42474007630983 Trimmed Mean ( 17 / 24 ) 0.0114170734702003 0.00789408030966904 1.44628291356703 Trimmed Mean ( 18 / 24 ) 0.0111508092292643 0.00767116013559348 1.45360141519215 Trimmed Mean ( 19 / 24 ) 0.0111737285535715 0.0074661163660255 1.4965918029911 Trimmed Mean ( 20 / 24 ) 0.0114129002894825 0.00725369938099941 1.57339030610751 Trimmed Mean ( 21 / 24 ) 0.0113081205438449 0.00708812538803562 1.59536124501020 Trimmed Mean ( 22 / 24 ) 0.0111096588160009 0.00691261850431974 1.60715636325922 Trimmed Mean ( 23 / 24 ) 0.0109368258984896 0.00675436092026964 1.61922438371163 Trimmed Mean ( 24 / 24 ) 0.0107791970485192 0.00655811405764902 1.64364281465142 Median 0.0114619984045185 Midrange -0.0072660530833 Midmean - Weighted Average at Xnp 0.00907349377782853 Midmean - Weighted Average at X(n+1)p 0.0111508092292643 Midmean - Empirical Distribution Function 0.00907349377782853 Midmean - Empirical Distribution Function - Averaging 0.0111508092292643 Midmean - Empirical Distribution Function - Interpolation 0.0111508092292643 Midmean - Closest Observation 0.00907349377782853 Midmean - True Basic - Statistics Graphics Toolkit 0.0111508092292643 Midmean - MS Excel (old versions) 0.0114170734702003 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230026762jk2cg1220mys8b4/1uwnb1230026697.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230026762jk2cg1220mys8b4/1uwnb1230026697.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230026762jk2cg1220mys8b4/2cpb11230026697.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230026762jk2cg1220mys8b4/2cpb11230026697.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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