central tendency paper - totaal na arima

*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: Thu, 10 Dec 2009 08:49:24 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t12604602282zm2eo3axrefj2f.htm/, Retrieved Thu, 10 Dec 2009 16:50:31 +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/2009/Dec/10/t12604602282zm2eo3axrefj2f.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:

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Dataseries X:

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9.21658481064732e-06 -0.00029788936701127 -0.000237595445619398 0.000176386639516741 -0.000354517420077153 -0.000704448564633498 0.000513049322447122 -0.000153768338800356 -0.000165495788075780 0.000140072526121174 0.000346620687208592 0.000161916908058288 -0.000165099254299721 -1.69432824053433e-06 -0.000354149939969856 -0.000342774975550734 -4.96908925173395e-06 0.000111232688614015 -5.71770531287065e-05 -0.000121692129730065 0.000224672210051711 -0.000246864010604340 0.000322726843768265 -4.30529292240296e-05 -0.000418419406504748 -0.000378004975610374 -3.24021390863647e-05 -2.7363752224343e-05 -0.000183622849538695 9.90770631009303e-05 0.000173737572911515 -0.000202839888158976 -0.000286608152931299 4.11099519259386e-05 3.30589617581101e-05 -0.00050937217008082 -1.86226730255005e-05 -0.000118364395817495 -0.000351397442503670 -0.000205285906638802 -0.000344501241171445 4.54893857804128e-05 0.000109739140624292 -2.35892220696581e-05 -0.000303095753286898 0.00012 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -5.45689180983375e-05 3.61690667128068e-05 -1.50871789232581 Geometric Mean NaN Harmonic Mean -6.74243809774903e-05 Quadratic Mean 0.000285429238227185 Winsorized Mean ( 1 / 20 ) -5.87814059111168e-05 3.29673404849238e-05 -1.78301934722329 Winsorized Mean ( 2 / 20 ) -6.01883942136255e-05 3.18749612007567e-05 -1.88826564633424 Winsorized Mean ( 3 / 20 ) -5.894561177178e-05 3.01123083702865e-05 -1.95752550906874 Winsorized Mean ( 4 / 20 ) -5.73320969999217e-05 2.93675126483139e-05 -1.95222856244223 Winsorized Mean ( 5 / 20 ) -5.86490656511966e-05 2.88107004595516e-05 -2.03566955039973 Winsorized Mean ( 6 / 20 ) -6.16780184331329e-05 2.75637340501096e-05 -2.23765104978176 Winsorized Mean ( 7 / 20 ) -6.1727606821995e-05 2.75375304983576e-05 -2.24158106064291 Winsorized Mean ( 8 / 20 ) -6.80289111935293e-05 2.61707544869581e-05 -2.59942491254621 Winsorized Mean ( 9 / 20 ) -7.41355394365572e-05 2.47187906739629e-05 -2.99915721664517 Winsorized Mean ( 10 / 20 ) -7.42868182864777e-05 2.45940774430600e-05 -3.02051656373231 Winsorized Mean ( 11 / 20 ) -6.92631439993187e-05 2.29769479668386e-05 -3.01446232542644 Winsorized Mean ( 12 / 20 ) -7.31330234552958e-05 2.21996558869410e-05 -3.29433139989871 Winsorized Mean ( 13 / 20 ) -7.52653945065742e-05 2.16500965561174e-05 -3.47644613553963 Winsorized Mean ( 14 / 20 ) -7.63025399285903e-05 2.06514911772830e-05 -3.69477144645732 Winsorized Mean ( 15 / 20 ) -6.74538957395549e-05 1.90799299707527e-05 -3.53533245892169 Winsorized Mean ( 16 / 20 ) -6.96561172621437e-05 1.85570678404221e-05 -3.75361656599729 Winsorized Mean ( 17 / 20 ) -6.86178350634164e-05 1.79148615287793e-05 -3.83021855643067 Winsorized Mean ( 18 / 20 ) -7.72966126410159e-05 1.51087265087535e-05 -5.11602434501894 Winsorized Mean ( 19 / 20 ) -7.30368005818847e-05 1.43362402958805e-05 -5.09455750423433 Winsorized Mean ( 20 / 20 ) -7.36707072620972e-05 1.40160717559334e-05 -5.25615939650926 Trimmed Mean ( 1 / 20 ) -6.01240441606977e-05 3.15584320829115e-05 -1.90516575737152 Trimmed Mean ( 2 / 20 ) -6.15609026383193e-05 2.98182376508132e-05 -2.06453860081300 Trimmed Mean ( 3 / 20 ) -6.23220209465585e-05 2.84134228247542e-05 -2.19340068005684 Trimmed Mean ( 4 / 20 ) -6.3617372894115e-05 2.75409734893860e-05 -2.30991736434561 Trimmed Mean ( 5 / 20 ) -6.54967936271827e-05 2.67385703222047e-05 -2.44952489373718 Trimmed Mean ( 6 / 20 ) -6.72017381436526e-05 2.59138638760297e-05 -2.59327356449588 Trimmed Mean ( 7 / 20 ) -6.83965853150771e-05 2.52539663804341e-05 -2.70835021654533 Trimmed Mean ( 8 / 20 ) -6.96880382931025e-05 2.44005657947030e-05 -2.85600091733244 Trimmed Mean ( 9 / 20 ) -6.99822439706431e-05 2.36818101201624e-05 -2.95510535789075 Trimmed Mean ( 10 / 20 ) -6.92956558312915e-05 2.31218665602290e-05 -2.99697499121824 Trimmed Mean ( 11 / 20 ) -6.85149868318906e-05 2.23893005219065e-05 -3.0601664739304 Trimmed Mean ( 12 / 20 ) -6.84028551679763e-05 2.18301292848066e-05 -3.13341502817317 Trimmed Mean ( 13 / 20 ) -6.77158545357703e-05 2.12473708080215e-05 -3.18702276849264 Trimmed Mean ( 14 / 20 ) -6.66423768243041e-05 2.05576025404489e-05 -3.24173875300777 Trimmed Mean ( 15 / 20 ) -6.52846119640242e-05 1.98434689725479e-05 -3.28997979407436 Trimmed Mean ( 16 / 20 ) -6.49804135495245e-05 1.92777426208107e-05 -3.37074806047969 Trimmed Mean ( 17 / 20 ) -6.43201868678815e-05 1.85575411049552e-05 -3.46598649595377 Trimmed Mean ( 18 / 20 ) -6.37033479504047e-05 1.76448573180922e-05 -3.61030677675621 Trimmed Mean ( 19 / 20 ) -6.1700475616764e-05 1.72202965788766e-05 -3.58300888339225 Trimmed Mean ( 20 / 20 ) -5.99673532536753e-05 1.67530394153573e-05 -3.57949096679758 Median -2.7363752224343e-05 Midrange 0.000109307300741286 Midmean - Weighted Average at Xnp -7.11187370503014e-05 Midmean - Weighted Average at X(n+1)p -6.52846119640242e-05 Midmean - Empirical Distribution Function -6.52846119640242e-05 Midmean - Empirical Distribution Function - Averaging -6.52846119640242e-05 Midmean - Empirical Distribution Function - Interpolation -6.52846119640242e-05 Midmean - Closest Observation -7.22009726192516e-05 Midmean - True Basic - Statistics Graphics Toolkit -6.52846119640242e-05 Midmean - MS Excel (old versions) -6.52846119640242e-05 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604602282zm2eo3axrefj2f/17mqr1260460160.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604602282zm2eo3axrefj2f/17mqr1260460160.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604602282zm2eo3axrefj2f/2js4c1260460160.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604602282zm2eo3axrefj2f/2js4c1260460160.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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