Workshop 3, part 2 Yt/Xt

*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 14:48:54 -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/t1256071785cokigdcx3uk9svr.htm/, Retrieved Tue, 20 Oct 2009 22:49:47 +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/t1256071785cokigdcx3uk9svr.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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1.026315789 1.052631579 1.051948052 1.037974684 1.024691358 1 0.975609756 0.975308642 0.938271605 0.938271605 1.012195122 1.037037037 1.024390244 1.012048193 1 1.011764706 1.034883721 1.035294118 1 0.961538462 0.923076923 0.925 1.023255814 1.04494382 1.04494382 1.011627907 0.987951807 1 1.024096386 1.023809524 1 0.976190476 0.941860465 0.929411765 1.011764706 1.023529412 1.023529412 1 0.988235294 1 1.023529412 1.023529412 1.011764706 1 0.965116279 0.952380952 1.012345679 1.0125 1.0125 1 0.9875 1 1.025641026 1.025641026 1 0.987654321 0.9625 0.947368421 1.02739726 1.042857143 1.029411765 1 0.985915493 1 1.028169014 1.028985507 1.014925373 0.955223881 0.924242424 0.942028986 1.054794521 1.053333333 1.02739726 0.971830986 0.956521739 0.971830986 1.026666667 1.038961039 1.025641026 0.987179487 0.948051948 0.961038961 1.038461538

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.00053300933735 0.00378780021288363 264.146193860539 Geometric Mean 0.999936167793501 Harmonic Mean 0.999330415142547 Quadratic Mean 1.00112076797496 Winsorized Mean ( 1 / 27 ) 1.00052944684337 0.00378128503950549 264.600376959210 Winsorized Mean ( 2 / 27 ) 1.00053079195181 0.0037739483052071 265.115129047032 Winsorized Mean ( 3 / 27 ) 1.00066554754217 0.00373176803451438 268.147842600937 Winsorized Mean ( 4 / 27 ) 1.00075497443373 0.00358283475969367 279.319321586379 Winsorized Mean ( 5 / 27 ) 1.00075497443373 0.00358283475969367 279.319321586379 Winsorized Mean ( 6 / 27 ) 1.00086356597590 0.0035062518525044 285.451133597554 Winsorized Mean ( 7 / 27 ) 1.00054919150602 0.00345705582990661 289.422341071377 Winsorized Mean ( 8 / 27 ) 1.00101569116867 0.00334704596859357 299.074377992275 Winsorized Mean ( 9 / 27 ) 1.00103701715663 0.00332542432805424 301.025348468041 Winsorized Mean ( 10 / 27 ) 1.00144561438554 0.00321083023998222 311.896157546805 Winsorized Mean ( 11 / 27 ) 1.00159139884337 0.00311058536438730 321.994506342911 Winsorized Mean ( 12 / 27 ) 1.00171970645783 0.00306884768417609 326.415583159438 Winsorized Mean ( 13 / 27 ) 1.00157016980723 0.00283557938109942 353.215352207455 Winsorized Mean ( 14 / 27 ) 1.00158252404819 0.00281234453341830 356.137917010761 Winsorized Mean ( 15 / 27 ) 1.001608737 0.00276485744278535 362.264152032000 Winsorized Mean ( 16 / 27 ) 1.00196430808434 0.00266137782909710 376.483300164962 Winsorized Mean ( 17 / 27 ) 1.00333960951807 0.00243648441633555 411.798082019784 Winsorized Mean ( 18 / 27 ) 1.00318116766265 0.00241755922225695 414.956191528625 Winsorized Mean ( 19 / 27 ) 1.00389693612048 0.00228423299487178 439.489727350179 Winsorized Mean ( 20 / 27 ) 1.00380690021687 0.00225382495951155 445.379263363208 Winsorized Mean ( 21 / 27 ) 1.00395382937349 0.00223146944102372 449.907048206277 Winsorized Mean ( 22 / 27 ) 1.00653154472289 0.00185973721563082 541.222456733748 Winsorized Mean ( 23 / 27 ) 1.00661864710843 0.00177994336717960 565.534087021804 Winsorized Mean ( 24 / 27 ) 1.00662425645783 0.00175686051237034 572.967659851211 Winsorized Mean ( 25 / 27 ) 1.00658222724096 0.00173980087317306 578.561743911045 Winsorized Mean ( 26 / 27 ) 1.00658555524096 0.00171643593071635 586.439340512331 Winsorized Mean ( 27 / 27 ) 1.00658665313253 0.00169310104160941 594.522493575281 Trimmed Mean ( 1 / 27 ) 1.00081936211111 0.00369972915408022 270.511521365655 Trimmed Mean ( 2 / 27 ) 1.00112395663291 0.00360472162404070 277.725733370419 Trimmed Mean ( 3 / 27 ) 1.00144364928571 0.00349820228312299 286.273796720435 Trimmed Mean ( 4 / 27 ) 1.00173068237333 0.00339230478114727 295.29501238817 Trimmed Mean ( 5 / 27 ) 1.00200802401370 0.00332097785144492 301.720778889789 Trimmed Mean ( 6 / 27 ) 1.00230099053521 0.00323636153084396 309.699945751684 Trimmed Mean ( 7 / 27 ) 1.00230099053521 0.00315662370140221 317.523114994663 Trimmed Mean ( 8 / 27 ) 1.00295018947761 0.00307280821079863 326.395310307031 Trimmed Mean ( 9 / 27 ) 1.00325896516923 0.00299826081435675 334.613640136063 Trimmed Mean ( 10 / 27 ) 1.00358422387302 0.00291266201519171 344.559107317833 Trimmed Mean ( 11 / 27 ) 1.003875215 0.0028337790074575 354.253176538522 Trimmed Mean ( 12 / 27 ) 1.00416729010169 0.00275811208529548 364.07776734502 Trimmed Mean ( 13 / 27 ) 1.00446429221053 0.00267338315118338 375.727770920489 Trimmed Mean ( 14 / 27 ) 1.00446429221053 0.00261430978354247 384.217776536584 Trimmed Mean ( 15 / 27 ) 1.00516018794340 0.00254391281439852 395.12367808134 Trimmed Mean ( 16 / 27 ) 1.00554550876471 0.00246374203542373 408.137497476179 Trimmed Mean ( 17 / 27 ) 1.00592464097959 0.00238328739474915 422.074418383549 Trimmed Mean ( 18 / 27 ) 1.00619317365957 0.00232954106019658 431.92764053477 Trimmed Mean ( 19 / 27 ) 1.00650181131111 0.00226172009597892 445.016080062495 Trimmed Mean ( 20 / 27 ) 1.00676644367442 0.00220236322324165 457.130065127296 Trimmed Mean ( 21 / 27 ) 1.00706600721951 0.00212837406273786 473.162131060768 Trimmed Mean ( 22 / 27 ) 1.00738140497436 0.00203328437078688 495.445408152378 Trimmed Mean ( 23 / 27 ) 1.00746806148649 0.00200083965104817 503.5226390874 Trimmed Mean ( 24 / 27 ) 1.00755564085714 0.00197120829456343 511.136059865398 Trimmed Mean ( 25 / 27 ) 1.00765324806061 0.00193110282061751 521.801965852025 Trimmed Mean ( 26 / 27 ) 1.00776795093548 0.00187434554298881 537.663908720112 Trimmed Mean ( 27 / 27 ) 1.00789810855172 0.00179515848385205 561.453552774335 Median 1.011627907 Midrange 0.988935722 Midmean - Weighted Average at Xnp 1.00676644367442 Midmean - Weighted Average at X(n+1)p 1.00676644367442 Midmean - Empirical Distribution Function 1.00676644367442 Midmean - Empirical Distribution Function - Averaging 1.00676644367442 Midmean - Empirical Distribution Function - Interpolation 1.00750826957143 Midmean - Closest Observation 1.00676644367442 Midmean - True Basic - Statistics Graphics Toolkit 1.00676644367442 Midmean - MS Excel (old versions) 1.00676644367442 Number of observations 83

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071785cokigdcx3uk9svr/1y1k41256071732.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071785cokigdcx3uk9svr/1y1k41256071732.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071785cokigdcx3uk9svr/2rczm1256071732.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071785cokigdcx3uk9svr/2rczm1256071732.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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