Central Tendency e[t]: Y[t]/X[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 12:55:54 -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/t1256065044kck8hxmyz6yjadh.htm/, Retrieved Tue, 20 Oct 2009 20:57:26 +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/t1256065044kck8hxmyz6yjadh.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:

Y[t]: werkloosheidsgraad mannen X[t]: werkloosheidsgraad vrouwen

Dataseries X:

» Textbox « » Textfile « » CSV «

0.104050633 0.015164835 -0.02212766 -0.011489362 0.048131868 0.057777778 0.050967742 0.008282828 -0.003673469 -0.013548387 -0.000722892 -0.0075 -0.043529412 -0.089230769 -0.099279279 -0.076880734 -0.05 -0.004782609 0.006086957 0.001052632 -0.0075 0.001052632 0.004175824 0.022696629 -0.031111111 -0.077425743 -0.09184466 -0.074901961 -0.017916667 0.016956522 0.029462366 0.041702128 0.052340426 0.071304348 0.091111111 0.057777778 -0.008888889 -0.115918367 -0.16 -0.136326531 -0.078064516 -0.042222222 -0.031111111 -0.028791209 -0.03978022 -0.061758242 -0.059130435 -0.047272727 -0.048915663 -0.022380952 -0.005185185 0.011168831 -0.022531646 -0.035189873 -0.0075 0.040759494 0.074736842 0.081408451 0.077058824 0.072307692 0.064057971 0.05804878 0.01908046 0.011325301 -0.047848101 -0.046666667 -0.025128205 0.035421687 0.096666667 0.143414634 0.18 0.207777778 0.20739726

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00365274291780822 0.00830987850898789 0.439566344304245 Geometric Mean NaN Harmonic Mean -0.328093011070996 Quadratic Mean 0.070606206178222 Winsorized Mean ( 1 / 24 ) 0.00397182443835616 0.00822529962801727 0.482878997480799 Winsorized Mean ( 2 / 24 ) 0.00378034235616438 0.00785357575374289 0.481353013544529 Winsorized Mean ( 3 / 24 ) 0.00296063230136986 0.00727722884562075 0.406835124217854 Winsorized Mean ( 4 / 24 ) 0.00121107712328767 0.0066756750681226 0.181416427691449 Winsorized Mean ( 5 / 24 ) 0.000884359657534247 0.0065355937185284 0.135314356372411 Winsorized Mean ( 6 / 24 ) 0.00134551283561644 0.00627505648649772 0.214422426078814 Winsorized Mean ( 7 / 24 ) 0.00047637298630137 0.00608578097325832 0.078276393513768 Winsorized Mean ( 8 / 24 ) 5.94285479452043e-05 0.00598854795079839 0.0099236991059379 Winsorized Mean ( 9 / 24 ) 1.71151095890409e-05 0.00589448264749585 0.00290358130010135 Winsorized Mean ( 10 / 24 ) 0.00148486428767123 0.00553328508188082 0.268351307712942 Winsorized Mean ( 11 / 24 ) 0.00172964638356164 0.00544425508018644 0.317701202108703 Winsorized Mean ( 12 / 24 ) 0.00203935454794521 0.00501092101945965 0.406981977968816 Winsorized Mean ( 13 / 24 ) 0.00116232575342466 0.00480293439985485 0.242003253981521 Winsorized Mean ( 14 / 24 ) 0.00131509068493151 0.00476488800020644 0.275996137763265 Winsorized Mean ( 15 / 24 ) 0.00143331821917808 0.00474799447803294 0.301878661782247 Winsorized Mean ( 16 / 24 ) 0.000374404904109589 0.0045358618824479 0.0825432770689947 Winsorized Mean ( 17 / 24 ) 0.000785332397260273 0.00438104142472610 0.179257012460084 Winsorized Mean ( 18 / 24 ) 0.000408396616438359 0.00422533379828138 0.0966542848293953 Winsorized Mean ( 19 / 24 ) -0.000629507794520548 0.0038779326745208 -0.162330769344348 Winsorized Mean ( 20 / 24 ) 0.000369865630136986 0.00366560731814208 0.100901596389341 Winsorized Mean ( 21 / 24 ) 7.67460273972508e-06 0.00327618716298701 0.00234254099595698 Winsorized Mean ( 22 / 24 ) -0.00178828515068493 0.00301173149448443 -0.593773101606144 Winsorized Mean ( 23 / 24 ) -0.00318902768493151 0.00261176797898301 -1.22102258339704 Winsorized Mean ( 24 / 24 ) -0.00317362987671233 0.00228713860284458 -1.38759840473385 Trimmed Mean ( 1 / 24 ) 0.00308271063380282 0.00769744696418568 0.400484816348317 Trimmed Mean ( 2 / 24 ) 0.002142054 0.00705047419994018 0.303817011346297 Trimmed Mean ( 3 / 24 ) 0.00124955362686567 0.00651357038557073 0.191838508359987 Trimmed Mean ( 4 / 24 ) 0.000608995969230769 0.00614853787411064 0.0990472827361185 Trimmed Mean ( 5 / 24 ) 0.000434583571428572 0.0059442931023747 0.0731093780108116 Trimmed Mean ( 6 / 24 ) 0.000326932245901639 0.0057430364432034 0.0569267231951049 Trimmed Mean ( 7 / 24 ) 0.000116885966101695 0.00557417025810062 0.0209692134774376 Trimmed Mean ( 8 / 24 ) 5.1115157894737e-05 0.00541813121607276 0.00943409375969063 Trimmed Mean ( 9 / 24 ) 4.97358909090912e-05 0.00524985556610916 0.00947376366507395 Trimmed Mean ( 10 / 24 ) 5.47281698113212e-05 0.00506346510212991 0.0108084421848390 Trimmed Mean ( 11 / 24 ) -0.000149977588235294 0.0049156304402528 -0.0305103465482610 Trimmed Mean ( 12 / 24 ) -0.000404546326530612 0.00474830515929861 -0.0851980470838923 Trimmed Mean ( 13 / 24 ) -0.000720866829787234 0.00463313236385911 -0.155589517668517 Trimmed Mean ( 14 / 24 ) -0.00095586351111111 0.00452993491669799 -0.211010429220001 Trimmed Mean ( 15 / 24 ) -0.001231245 0.00440089786260374 -0.279771319044325 Trimmed Mean ( 16 / 24 ) -0.00154752648780488 0.00423202416204785 -0.36567052279211 Trimmed Mean ( 17 / 24 ) -0.00177236782051282 0.0040601771381053 -0.436524752548088 Trimmed Mean ( 18 / 24 ) -0.00206920743243243 0.00386545460642487 -0.535307652816088 Trimmed Mean ( 19 / 24 ) -0.00235629488571429 0.00364000871975235 -0.647332209103773 Trimmed Mean ( 20 / 24 ) -0.00255734027272727 0.00343004645196437 -0.745570157297052 Trimmed Mean ( 21 / 24 ) -0.00290199516129032 0.00319259192698207 -0.908977792233396 Trimmed Mean ( 22 / 24 ) -0.00325077331034483 0.00298005926496864 -1.09084183276437 Trimmed Mean ( 23 / 24 ) -0.00343050670370370 0.00276422802282160 -1.24103607784209 Trimmed Mean ( 24 / 24 ) -0.00346116404 0.0025942679021203 -1.33415829458908 Median -0.004782609 Midrange 0.023888889 Midmean - Weighted Average at Xnp -0.00346368175000000 Midmean - Weighted Average at X(n+1)p -0.00206920743243243 Midmean - Empirical Distribution Function -0.00206920743243243 Midmean - Empirical Distribution Function - Averaging -0.00206920743243243 Midmean - Empirical Distribution Function - Interpolation -0.00206920743243243 Midmean - Closest Observation -0.00316026544736842 Midmean - True Basic - Statistics Graphics Toolkit -0.00206920743243243 Midmean - MS Excel (old versions) -0.00206920743243243 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256065044kck8hxmyz6yjadh/1tfey1256064952.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256065044kck8hxmyz6yjadh/1tfey1256064952.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256065044kck8hxmyz6yjadh/2iu0w1256064952.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256065044kck8hxmyz6yjadh/2iu0w1256064952.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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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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