JJ Workshop 3, deel 3, Central Tendency e2(t)

*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, 20 Oct 2009 09:38:48 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256054479cohfyf8xosp4qlz.htm/, Retrieved Tue, 20 Oct 2009 18:01:19 +0200

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/2009/Oct/20/t1256054479cohfyf8xosp4qlz.htm/}, year = {2009}, } @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 = {2009}, 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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0.049411765 -0.02566077 -0.041514085 -0.06 -0.088237585 -0.161123596 -0.126827697 -0.13385399 -0.095361842 -0.12870229 -0.047432675 -0.051803279 0.019913607 0.020076263 -0.042543641 -0.02883593 0.059226638 -0.000435281 0.036351731 0.010519099 -0.023867188 -0.011456311 -0.013280318 -0.035845411 0.028580576 0.040389864 0.017705828 0.024041549 0.093846154 -0.01599022 0.044046243 0.087181628 0.026299892 0.082433234 0.084318182 0.006810345 0.080468227 0.078075314 0.052394958 0.108214654 0.148333333 0.040680272 0.082427282 0.057312073 0.065958379 0.055015974 0.005555556 -0.006547884 0.082857143 -0.062879079 -0.064512635 -0.027420814 0.051366246 -0.080179372 0.094404145 -0.039035639 -0.041188119 -0.01260223 -0.025884861 -0.046140725

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00325087811666667 0.00859252610424447 0.378337880761378 Geometric Mean NaN Harmonic Mean -0.0272331412674854 Quadratic Mean 0.0660804584942073 Winsorized Mean ( 1 / 20 ) 0.0030367269 0.00828701298617212 0.366444086073854 Winsorized Mean ( 2 / 20 ) 0.00274809993333333 0.00814602685963234 0.337354636890722 Winsorized Mean ( 3 / 20 ) 0.00281393003333333 0.00811520698317739 0.346747783410397 Winsorized Mean ( 4 / 20 ) 0.00446735196666667 0.00750928942820567 0.594910078959912 Winsorized Mean ( 5 / 20 ) 0.00482241955 0.00733433251873396 0.6575130780725 Winsorized Mean ( 6 / 20 ) 0.00548213695 0.00713883689762871 0.767931391151546 Winsorized Mean ( 7 / 20 ) 0.00726046688333333 0.00677922469135397 1.07098779195107 Winsorized Mean ( 8 / 20 ) 0.00747748075 0.00674026519461069 1.10937485901575 Winsorized Mean ( 9 / 20 ) 0.00761548435 0.00660947119556836 1.15220781279842 Winsorized Mean ( 10 / 20 ) 0.00858278568333334 0.00630548051532758 1.36116282692017 Winsorized Mean ( 11 / 20 ) 0.007162625 0.00577644184406758 1.23997180156086 Winsorized Mean ( 12 / 20 ) 0.0060746668 0.0055086220697371 1.10275613812256 Winsorized Mean ( 13 / 20 ) 0.00643921258333333 0.00531758767617127 1.21092739329681 Winsorized Mean ( 14 / 20 ) 0.00614368588333333 0.00519398695113818 1.18284584484507 Winsorized Mean ( 15 / 20 ) 0.00556992338333333 0.0050778221454523 1.09691186965297 Winsorized Mean ( 16 / 20 ) 0.00586959485 0.00494603449231989 1.18672743975284 Winsorized Mean ( 17 / 20 ) 0.00621972316666667 0.00472212020630764 1.31714630185792 Winsorized Mean ( 18 / 20 ) 0.00671291086666667 0.00416355949137358 1.61230093639230 Winsorized Mean ( 19 / 20 ) 0.00609514011666667 0.00393844992260211 1.54759873464118 Winsorized Mean ( 20 / 20 ) 0.00651032178333333 0.00385059724019907 1.69073039251354 Trimmed Mean ( 1 / 20 ) 0.00358349913793103 0.00803217259958166 0.446143193949502 Trimmed Mean ( 2 / 20 ) 0.00416932653571429 0.0077172698673196 0.540259263625103 Trimmed Mean ( 3 / 20 ) 0.00495889687037037 0.00742072967777157 0.66824922692232 Trimmed Mean ( 4 / 20 ) 0.00578388411538462 0.0070630207478136 0.818896662193021 Trimmed Mean ( 5 / 20 ) 0.00617884376 0.00686411897433671 0.900165597813967 Trimmed Mean ( 6 / 20 ) 0.0065179498125 0.00667138946996406 0.977000344807499 Trimmed Mean ( 7 / 20 ) 0.00674312652173913 0.00648529918686577 1.03975565774907 Trimmed Mean ( 8 / 20 ) 0.00664234593181818 0.00634855802817611 1.04627632012469 Trimmed Mean ( 9 / 20 ) 0.00649321471428571 0.00617580262355978 1.05139608728994 Trimmed Mean ( 10 / 20 ) 0.006306169775 0.00597982489644238 1.05457432018649 Trimmed Mean ( 11 / 20 ) 0.00594670410526316 0.00579709845166704 1.0258069885898 Trimmed Mean ( 12 / 20 ) 0.00576247366666667 0.00569032509715835 1.01267916477116 Trimmed Mean ( 13 / 20 ) 0.00571656291176471 0.00560478827243933 1.01994270503937 Trimmed Mean ( 14 / 20 ) 0.00561233459375 0.00552255506179497 1.01625688308227 Trimmed Mean ( 15 / 20 ) 0.00553642726666667 0.00542374871710663 1.02077503133666 Trimmed Mean ( 16 / 20 ) 0.00553164210714286 0.00529723995467085 1.04424986492547 Trimmed Mean ( 17 / 20 ) 0.00548289892307692 0.00513312210096186 1.06814114592161 Trimmed Mean ( 18 / 20 ) 0.00537454241666667 0.00494329372317141 1.08723914006441 Trimmed Mean ( 19 / 20 ) 0.00517175931818182 0.00483985860171174 1.06857653162691 Trimmed Mean ( 20 / 20 ) 0.00502596235 0.00472909232694528 1.06277526479304 Median 0.0061829505 Midrange -0.0063951315 Midmean - Weighted Average at Xnp 0.00401866880645161 Midmean - Weighted Average at X(n+1)p 0.00553642726666666 Midmean - Empirical Distribution Function 0.00401866880645161 Midmean - Empirical Distribution Function - Averaging 0.00553642726666666 Midmean - Empirical Distribution Function - Interpolation 0.00553642726666666 Midmean - Closest Observation 0.00401866880645161 Midmean - True Basic - Statistics Graphics Toolkit 0.00553642726666666 Midmean - MS Excel (old versions) 0.00561233459375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256054479cohfyf8xosp4qlz/124vh1256053123.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256054479cohfyf8xosp4qlz/124vh1256053123.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256054479cohfyf8xosp4qlz/2n15u1256053123.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256054479cohfyf8xosp4qlz/2n15u1256053123.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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