Paper - Central tendency - Residuwaardes Medische apparatuur

*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: Sat, 27 Dec 2008 06:07:36 -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/27/t123038330294vklifi5rj3wxv.htm/, Retrieved Sat, 27 Dec 2008 14:08:24 +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/27/t123038330294vklifi5rj3wxv.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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Dataseries X:

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-0.385868851153837 4.81234262686034 -5.86804122114596 16.0725680225492 -8.57525163788969 5.08247518971098 0.092732021505415 3.83298655010795 5.81986266263392 37.1247698411582 -0.456916305824569 -3.62813490741323 -3.87648507892191 4.61958462101272 -12.967748044016 3.19886759717217 -5.74783565702396 -0.568909646003526 -7.15658094463292 -18.0497313555278 15.6314099338156 -18.6819481453537 -0.704909311621681 2.59171945848611 2.56763423323193 0.363060127151921 32.5587282582796 8.52568321864334 1.42269516052334 3.53469472344553 0.904411865388995 -1.1005444418027 13.3248076718110 -33.5907843348750 -0.845486516554237 42.0892768528428 -6.25360506437205 -11.0785340316643 -29.2902232669615 -11.1727173982373 13.9239510644368 13.5369579913798 -16.4941540115674 -9.38355957013267 -2.83541693438183 -2.88173330956316 6.18397479401454 3.71189006095175 3.17508248559435 -4.18249526402528 13.6042900329871 4.81933405297545 10.0482983006261 9.69015652302726 -13.6259654676286 2.81390485024080 2.39082408194279 9.1175078099302 14.2141474796521 3.49385172983141 5.51425675339953 -6.1504957612917 2.72297593670155 -11.1163190852539 -4.69675096946234 1.81576665288666 -10.4353591925503 6.036622781552

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.01737644546483 1.5175745907115 0.670396336161532 Geometric Mean NaN Harmonic Mean 7.96341855770884 Quadratic Mean 12.4634763048994 Winsorized Mean ( 1 / 22 ) 1.00761253452702 1.46889604556303 0.685965856855988 Winsorized Mean ( 2 / 22 ) 1.18532528566611 1.33744765229883 0.886259199475025 Winsorized Mean ( 3 / 22 ) 0.485886604229147 1.12383073802566 0.432348562633862 Winsorized Mean ( 4 / 22 ) 0.551440678066018 1.09659611296017 0.502865796758527 Winsorized Mean ( 5 / 22 ) 0.65812641996126 1.0292553520356 0.639419963821084 Winsorized Mean ( 6 / 22 ) 0.690598861878669 1.01237685884819 0.682155914413516 Winsorized Mean ( 7 / 22 ) 0.842475145706654 0.970223360683964 0.868331128527711 Winsorized Mean ( 8 / 22 ) 0.841188824692078 0.967444814836406 0.869495408721915 Winsorized Mean ( 9 / 22 ) 0.818111068900713 0.96104473461145 0.851272619719909 Winsorized Mean ( 10 / 22 ) 0.430855990654993 0.855782496857848 0.503464364177761 Winsorized Mean ( 11 / 22 ) 0.543065347905091 0.814454042219873 0.666784520370129 Winsorized Mean ( 12 / 22 ) 0.584652268930842 0.772032215296287 0.757289990426716 Winsorized Mean ( 13 / 22 ) 0.742725788425089 0.706700373846262 1.05097692871274 Winsorized Mean ( 14 / 22 ) 0.446516146937574 0.601353637810312 0.742518409905123 Winsorized Mean ( 15 / 22 ) 0.436756725750326 0.592971623006038 0.736555863392267 Winsorized Mean ( 16 / 22 ) 0.452214236627423 0.574859194031402 0.786652177302952 Winsorized Mean ( 17 / 22 ) 0.405864150349325 0.559394428839911 0.725541995816831 Winsorized Mean ( 18 / 22 ) 0.569797330198079 0.49908430922144 1.14168552220556 Winsorized Mean ( 19 / 22 ) 0.63996169498233 0.466807899860999 1.37093158700376 Winsorized Mean ( 20 / 22 ) 0.727908388802406 0.452761123996056 1.60770956299850 Winsorized Mean ( 21 / 22 ) 0.745076557609499 0.433179416031154 1.72001838045765 Winsorized Mean ( 22 / 22 ) 0.732071816327096 0.363816602577752 2.01220013363915 Trimmed Mean ( 1 / 22 ) 0.919440996570309 1.33164443229392 0.690455330471706 Trimmed Mean ( 2 / 22 ) 0.825758737491308 1.15548924312828 0.714639917595178 Trimmed Mean ( 3 / 22 ) 0.62857708204061 1.02756868250965 0.611712961614812 Trimmed Mean ( 4 / 22 ) 0.682482373658273 0.98086689828355 0.695795091925898 Trimmed Mean ( 5 / 22 ) 0.72089114650428 0.934523166346016 0.771399974302362 Trimmed Mean ( 6 / 22 ) 0.736134008664727 0.900816267399576 0.817185518629405 Trimmed Mean ( 7 / 22 ) 0.745690767866739 0.864229682231229 0.862838644862959 Trimmed Mean ( 8 / 22 ) 0.727610169808733 0.830734691199086 0.87586347063284 Trimmed Mean ( 9 / 22 ) 0.708301798478564 0.789166929590321 0.897531019002866 Trimmed Mean ( 10 / 22 ) 0.691017005912115 0.737695107244752 0.936724398909223 Trimmed Mean ( 11 / 22 ) 0.729475590776211 0.700682492451417 1.04109293244085 Trimmed Mean ( 12 / 22 ) 0.755665459609343 0.663803412617555 1.13838742803318 Trimmed Mean ( 13 / 22 ) 0.77873866787549 0.626863115419305 1.24227865497334 Trimmed Mean ( 14 / 22 ) 0.783448044419005 0.595758108389474 1.31504386325000 Trimmed Mean ( 15 / 22 ) 0.826514527555729 0.581195953865686 1.42209270738787 Trimmed Mean ( 16 / 22 ) 0.875595139634928 0.562745778900153 1.55593373147324 Trimmed Mean ( 17 / 22 ) 0.928517752510866 0.541506039009414 1.71469510147923 Trimmed Mean ( 18 / 22 ) 0.993849452781058 0.515156786217708 1.92921743315840 Trimmed Mean ( 19 / 22 ) 1.04724860895817 0.496051170645965 2.11117052217502 Trimmed Mean ( 20 / 22 ) 1.09930783856411 0.477570115137428 2.30187736568852 Trimmed Mean ( 21 / 22 ) 1.14787545891756 0.453731331532554 2.52985716247635 Trimmed Mean ( 22 / 22 ) 1.20222134242738 0.423244361576156 2.84048991922852 Median 1.619230906705 Midrange 4.2492462589839 Midmean - Weighted Average at Xnp 0.734330353263527 Midmean - Weighted Average at X(n+1)p 0.928517752510866 Midmean - Empirical Distribution Function 0.734330353263527 Midmean - Empirical Distribution Function - Averaging 0.928517752510866 Midmean - Empirical Distribution Function - Interpolation 0.928517752510866 Midmean - Closest Observation 0.734330353263527 Midmean - True Basic - Statistics Graphics Toolkit 0.928517752510866 Midmean - MS Excel (old versions) 0.875595139634927 Number of observations 68

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t123038330294vklifi5rj3wxv/1t18h1230383254.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t123038330294vklifi5rj3wxv/1t18h1230383254.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t123038330294vklifi5rj3wxv/2lxt91230383254.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t123038330294vklifi5rj3wxv/2lxt91230383254.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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