Central Tendency 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 12:41:52 -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/t12560642251nnx9lx41r6ruh0.htm/, Retrieved Tue, 20 Oct 2009 20:43:46 +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/t12560642251nnx9lx41r6ruh0.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 «

0,924050633 0,835164835 0,79787234 0,808510638 0,868131868 0,877777778 0,870967742 0,828282828 0,816326531 0,806451613 0,819277108 0,8125 0,776470588 0,730769231 0,720720721 0,743119266 0,77 0,815217391 0,826086957 0,821052632 0,8125 0,821052632 0,824175824 0,842696629 0,788888889 0,742574257 0,72815534 0,745098039 0,802083333 0,836956522 0,849462366 0,861702128 0,872340426 0,891304348 0,911111111 0,877777778 0,811111111 0,704081633 0,66 0,683673469 0,741935484 0,777777778 0,788888889 0,791208791 0,78021978 0,758241758 0,760869565 0,772727273 0,771084337 0,797619048 0,814814815 0,831168831 0,797468354 0,784810127 0,8125 0,860759494 0,894736842 0,901408451 0,897058824 0,892307692 0,884057971 0,87804878 0,83908046 0,831325301 0,772151899 0,773333333 0,794871795 0,855421687 0,916666667 0,963414634 1 1,027777778 1,02739726

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.823652742917808 0.00830987850898789 99.117302620845 Geometric Mean 0.820702152032003 Harmonic Mean 0.81780695978677 Quadratic Mean 0.826665430955043 Winsorized Mean ( 1 / 24 ) 0.823971824438356 0.00822529962801727 100.175295940797 Winsorized Mean ( 2 / 24 ) 0.823780342356164 0.00785357575374289 104.892391464304 Winsorized Mean ( 3 / 24 ) 0.82296063230137 0.00727722884562075 113.087089846928 Winsorized Mean ( 4 / 24 ) 0.821211077123288 0.0066756750681226 123.015435703978 Winsorized Mean ( 5 / 24 ) 0.820884359657534 0.0065355937185284 125.602109771654 Winsorized Mean ( 6 / 24 ) 0.821345512835617 0.00627505648649772 130.890536938263 Winsorized Mean ( 7 / 24 ) 0.820476372986301 0.00608578097325832 134.818583940430 Winsorized Mean ( 8 / 24 ) 0.820059428547945 0.00598854795079840 136.937941431798 Winsorized Mean ( 9 / 24 ) 0.820017115109589 0.00589448264749585 139.116045317049 Winsorized Mean ( 10 / 24 ) 0.821484864287671 0.00553328508188082 148.462414665329 Winsorized Mean ( 11 / 24 ) 0.821729646383562 0.00544425508018644 150.935184755418 Winsorized Mean ( 12 / 24 ) 0.822039354547945 0.00501092101945965 164.049553236940 Winsorized Mean ( 13 / 24 ) 0.821162325753425 0.00480293439985485 170.970964287632 Winsorized Mean ( 14 / 24 ) 0.821315090684931 0.00476488800020644 172.368183816566 Winsorized Mean ( 15 / 24 ) 0.821433318219178 0.00474799447803294 173.006376064593 Winsorized Mean ( 16 / 24 ) 0.82037440490411 0.0045358618824479 180.864062038276 Winsorized Mean ( 17 / 24 ) 0.82078533239726 0.00438104142472611 187.349365784318 Winsorized Mean ( 18 / 24 ) 0.820408396616438 0.00422533379828138 194.164162119010 Winsorized Mean ( 19 / 24 ) 0.81937049220548 0.0038779326745208 211.290540856728 Winsorized Mean ( 20 / 24 ) 0.820369865630137 0.00366560731814208 223.801895410320 Winsorized Mean ( 21 / 24 ) 0.82000767460274 0.00327618716298701 250.293293334045 Winsorized Mean ( 22 / 24 ) 0.818211714849315 0.00301173149448443 271.674854264982 Winsorized Mean ( 23 / 24 ) 0.816810972315068 0.00261176797898301 312.742547916957 Winsorized Mean ( 24 / 24 ) 0.816826370123288 0.00228713860284457 357.13898978723 Trimmed Mean ( 1 / 24 ) 0.823082710633803 0.00769744696418569 106.929312337377 Trimmed Mean ( 2 / 24 ) 0.822142054 0.00705047419994018 116.608050846704 Trimmed Mean ( 3 / 24 ) 0.821249553626866 0.00651357038557073 126.082855486777 Trimmed Mean ( 4 / 24 ) 0.820608995969231 0.00614853787411064 133.464087360433 Trimmed Mean ( 5 / 24 ) 0.820434583571429 0.0059442931023747 138.020546672517 Trimmed Mean ( 6 / 24 ) 0.820326932245902 0.0057430364432034 142.838538525507 Trimmed Mean ( 7 / 24 ) 0.820116885966102 0.00557417025810062 147.128065342869 Trimmed Mean ( 8 / 24 ) 0.820051115157895 0.00541813121607276 151.353129419463 Trimmed Mean ( 9 / 24 ) 0.82004973589091 0.00524985556610916 156.204247062491 Trimmed Mean ( 10 / 24 ) 0.820054728169811 0.00506346510212991 161.955244408589 Trimmed Mean ( 11 / 24 ) 0.819850022411765 0.0049156304402528 166.784308213699 Trimmed Mean ( 12 / 24 ) 0.81959545367347 0.00474830515929861 172.607999312861 Trimmed Mean ( 13 / 24 ) 0.819279133170213 0.00463313236385911 176.830504468429 Trimmed Mean ( 14 / 24 ) 0.819044136488889 0.00452993491669799 180.807042827431 Trimmed Mean ( 15 / 24 ) 0.818768755 0.00440089786260374 186.045843498759 Trimmed Mean ( 16 / 24 ) 0.818452473512195 0.00423202416204785 193.395037970707 Trimmed Mean ( 17 / 24 ) 0.818227632179487 0.0040601771381053 201.525106996025 Trimmed Mean ( 18 / 24 ) 0.817930792567568 0.00386545460642487 211.600154664361 Trimmed Mean ( 19 / 24 ) 0.817643705114286 0.00364000871975235 224.626853413119 Trimmed Mean ( 20 / 24 ) 0.817442659727273 0.00343004645196437 238.318247631640 Trimmed Mean ( 21 / 24 ) 0.81709800483871 0.00319259192698207 255.935623320048 Trimmed Mean ( 22 / 24 ) 0.816749226689655 0.00298005926496864 274.071471091448 Trimmed Mean ( 23 / 24 ) 0.816569493296296 0.00276422802282160 295.405981906941 Trimmed Mean ( 24 / 24 ) 0.81653883596 0.0025942679021203 314.747307050533 Median 0.815217391 Midrange 0.843888889 Midmean - Weighted Average at Xnp 0.81653631825 Midmean - Weighted Average at X(n+1)p 0.817930792567568 Midmean - Empirical Distribution Function 0.817930792567568 Midmean - Empirical Distribution Function - Averaging 0.817930792567568 Midmean - Empirical Distribution Function - Interpolation 0.817930792567568 Midmean - Closest Observation 0.816839734552632 Midmean - True Basic - Statistics Graphics Toolkit 0.817930792567568 Midmean - MS Excel (old versions) 0.817930792567568 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560642251nnx9lx41r6ruh0/1jg1k1256064106.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560642251nnx9lx41r6ruh0/1jg1k1256064106.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560642251nnx9lx41r6ruh0/2yzcw1256064106.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560642251nnx9lx41r6ruh0/2yzcw1256064106.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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