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 11:54:00 -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/t1256061364e6lbacojuupsiqk.htm/, Retrieved Tue, 20 Oct 2009 19:56:04 +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/t1256061364e6lbacojuupsiqk.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:

SHWWS3V2: Central Tendency Y[t]-X[t]: waarbij Y[t]=werkloosheidsgraad mannen en X[t]= werkloosheidsgraad vrouwen

Dataseries X:

» Textbox « » Textfile « » CSV «

-0,6 -1,5 -1,9 -1,8 -1,2 -1,1 -1,2 -1,7 -1,8 -1,8 -1,5 -1,5 -1,9 -2,8 -3,1 -2,8 -2,3 -1,7 -1,6 -1,7 -1,8 -1,7 -1,6 -1,4 -1,9 -2,6 -2,8 -2,6 -1,9 -1,5 -1,4 -1,3 -1,2 -1 -0,8 -1,1 -1,7 -2,9 -3,4 -3,1 -2,4 -2 -1,9 -1,9 -2 -2,2 -2,2 -2 -1,9 -1,7 -1,5 -1,3 -1,6 -1,7 -1,5 -1,1 -0,8 -0,7 -0,7 -0,7 -0,8 -1 -1,4 -1,4 -1,8 -1,7 -1,6 -1,2 -0,7 -0,3 0 0,2 0,2

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -1.59589041095890 0.0854622660590965 -18.6736262042871 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 1.75292319456027 Winsorized Mean ( 1 / 24 ) -1.59178082191781 0.0843489126119515 -18.8713852096804 Winsorized Mean ( 2 / 24 ) -1.59726027397260 0.0828059247107256 -19.2892027901684 Winsorized Mean ( 3 / 24 ) -1.6013698630137 0.0777218715038722 -20.6038510399729 Winsorized Mean ( 4 / 24 ) -1.61232876712329 0.0729604781747803 -22.0986595408665 Winsorized Mean ( 5 / 24 ) -1.61917808219178 0.0716902248167182 -22.5857581885304 Winsorized Mean ( 6 / 24 ) -1.61917808219178 0.0716902248167182 -22.5857581885304 Winsorized Mean ( 7 / 24 ) -1.6 0.0675174029090723 -23.6975939692877 Winsorized Mean ( 8 / 24 ) -1.6 0.0675174029090723 -23.6975939692877 Winsorized Mean ( 9 / 24 ) -1.58767123287671 0.060406575459546 -26.2830862501048 Winsorized Mean ( 10 / 24 ) -1.57397260273973 0.0579333119623982 -27.1686970660562 Winsorized Mean ( 11 / 24 ) -1.55890410958904 0.0554089410427805 -28.1345227006853 Winsorized Mean ( 12 / 24 ) -1.59178082191781 0.0495318042999165 -32.1365402374508 Winsorized Mean ( 13 / 24 ) -1.55616438356164 0.0439656319600303 -35.3950191134833 Winsorized Mean ( 14 / 24 ) -1.57534246575342 0.0407212758349161 -38.6859800793045 Winsorized Mean ( 15 / 24 ) -1.57534246575342 0.0407212758349161 -38.6859800793045 Winsorized Mean ( 16 / 24 ) -1.55342465753425 0.0377286127275318 -41.1736489955981 Winsorized Mean ( 17 / 24 ) -1.57671232876712 0.0339845378455686 -46.3949910377468 Winsorized Mean ( 18 / 24 ) -1.57671232876712 0.0339845378455686 -46.3949910377468 Winsorized Mean ( 19 / 24 ) -1.57671232876712 0.0339845378455686 -46.3949910377468 Winsorized Mean ( 20 / 24 ) -1.57671232876712 0.0339845378455686 -46.3949910377468 Winsorized Mean ( 21 / 24 ) -1.60547945205479 0.0297049424060102 -54.0475531011283 Winsorized Mean ( 22 / 24 ) -1.60547945205479 0.0297049424060102 -54.0475531011283 Winsorized Mean ( 23 / 24 ) -1.60547945205479 0.0210900088660112 -76.1251198259187 Winsorized Mean ( 24 / 24 ) -1.60547945205479 0.0210900088660112 -76.1251198259187 Trimmed Mean ( 1 / 24 ) -1.59577464788732 0.0801265754128905 -19.9156726674556 Trimmed Mean ( 2 / 24 ) -1.6 0.0750390634274456 -21.3222277427146 Trimmed Mean ( 3 / 24 ) -1.60149253731343 0.0699063318939474 -22.9091198740481 Trimmed Mean ( 4 / 24 ) -1.60153846153846 0.0661979951072011 -24.1931565894848 Trimmed Mean ( 5 / 24 ) -1.5984126984127 0.0635803277940326 -25.1400512370859 Trimmed Mean ( 6 / 24 ) -1.59344262295082 0.060817241787861 -26.2005078840795 Trimmed Mean ( 7 / 24 ) -1.58813559322034 0.0574178826005478 -27.6592504162664 Trimmed Mean ( 8 / 24 ) -1.58596491228070 0.0544647339678221 -29.1191161094754 Trimmed Mean ( 9 / 24 ) -1.58363636363636 0.0507694091437514 -31.192727871864 Trimmed Mean ( 10 / 24 ) -1.58301886792453 0.0480939942854863 -32.915104919914 Trimmed Mean ( 11 / 24 ) -1.58431372549020 0.0453632440846031 -34.9250534757926 Trimmed Mean ( 12 / 24 ) -1.58775510204082 0.0425217684408462 -37.3398181745336 Trimmed Mean ( 13 / 24 ) -1.58723404255319 0.0404206628354523 -39.2678875409498 Trimmed Mean ( 14 / 24 ) -1.59111111111111 0.0390314846005562 -40.7648114693654 Trimmed Mean ( 15 / 24 ) -1.59302325581395 0.0380003131124842 -41.9213192033042 Trimmed Mean ( 16 / 24 ) -1.59512195121951 0.0366178717382172 -43.5612960420832 Trimmed Mean ( 17 / 24 ) -1.6 0.0354268362790828 -45.1635022499791 Trimmed Mean ( 18 / 24 ) -1.60270270270270 0.0347635700568914 -46.102937646503 Trimmed Mean ( 19 / 24 ) -1.60571428571429 0.0337919629306065 -47.5176387063309 Trimmed Mean ( 20 / 24 ) -1.60909090909091 0.0323813792017614 -49.6918583691266 Trimmed Mean ( 21 / 24 ) -1.61290322580645 0.0303180046878961 -53.1995176598931 Trimmed Mean ( 22 / 24 ) -1.61379310344828 0.0288208915789361 -55.9938646945858 Trimmed Mean ( 23 / 24 ) -1.61481481481481 0.0265294029772202 -60.8688712746907 Trimmed Mean ( 24 / 24 ) -1.616 0.0262551582233536 -61.5498099936259 Median -1.6 Midrange -1.6 Midmean - Weighted Average at Xnp -1.6075 Midmean - Weighted Average at X(n+1)p -1.6075 Midmean - Empirical Distribution Function -1.6075 Midmean - Empirical Distribution Function - Averaging -1.6075 Midmean - Empirical Distribution Function - Interpolation -1.6075 Midmean - Closest Observation -1.6075 Midmean - True Basic - Statistics Graphics Toolkit -1.6075 Midmean - MS Excel (old versions) -1.6075 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061364e6lbacojuupsiqk/13jss1256061235.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061364e6lbacojuupsiqk/13jss1256061235.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061364e6lbacojuupsiqk/2bxy71256061235.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256061364e6lbacojuupsiqk/2bxy71256061235.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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