WS3 deel 2 verschil tussen y(t) en 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 15:31:01 -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/t12560744797tbj9lr7nidlc2i.htm/, Retrieved Tue, 20 Oct 2009 23:34:41 +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/t12560744797tbj9lr7nidlc2i.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:

WS3 deel 2 verschil

Dataseries X:

» Textbox « » Textfile « » CSV «

-2,30 -2,00 -1,50 -0,90 -0,80 -0,90 -1,00 -0,90 -0,80 -0,60 -1,10 -1,80 -2,00 -1,80 -1,10 -0,70 -0,60 -0,50 -0,40 -0,20 0,00 -0,30 -0,90 -2,10 -2,60 -2,30 -1,60 -1,20 -1,10 -1,10 -1,20 -1,40 -1,40 -1,20 -1,10 -0,90 -0,70 -0,50 -0,80 -0,90 -0,70 -0,30 0,00 0,10 0,10 0,10 0,00 -0,20 -0,60 -0,60 -1,00 -0,90 -0,80 -0,40 0,10 0,50 0,80 1,00 1,00 0,70 0,40

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.752459016393443 0.102685432889692 -7.32780682924869 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 1.09492121132819 Winsorized Mean ( 1 / 20 ) -0.747540983606557 0.101319344664054 -7.37806769363928 Winsorized Mean ( 2 / 20 ) -0.754098360655738 0.099522734599392 -7.57714670613909 Winsorized Mean ( 3 / 20 ) -0.749180327868852 0.0958317899848072 -7.81765975557406 Winsorized Mean ( 4 / 20 ) -0.755737704918033 0.0911530446111342 -8.2908662913243 Winsorized Mean ( 5 / 20 ) -0.763934426229508 0.0893214489347888 -8.55264256614597 Winsorized Mean ( 6 / 20 ) -0.773770491803279 0.0789584396228393 -9.799718630451 Winsorized Mean ( 7 / 20 ) -0.773770491803279 0.0789584396228393 -9.799718630451 Winsorized Mean ( 8 / 20 ) -0.747540983606558 0.0735741162825612 -10.1603800545239 Winsorized Mean ( 9 / 20 ) -0.732786885245902 0.0708157507515838 -10.3477951934233 Winsorized Mean ( 10 / 20 ) -0.732786885245902 0.0647703514222587 -11.3136160165108 Winsorized Mean ( 11 / 20 ) -0.732786885245902 0.0647703514222587 -11.3136160165108 Winsorized Mean ( 12 / 20 ) -0.69344262295082 0.0585278810052722 -11.8480732779024 Winsorized Mean ( 13 / 20 ) -0.736065573770492 0.0505182316754394 -14.5702957003609 Winsorized Mean ( 14 / 20 ) -0.736065573770492 0.0505182316754394 -14.5702957003609 Winsorized Mean ( 15 / 20 ) -0.736065573770492 0.0425956196525016 -17.2803114445892 Winsorized Mean ( 16 / 20 ) -0.736065573770492 0.0425956196525016 -17.2803114445892 Winsorized Mean ( 17 / 20 ) -0.763934426229508 0.0379842350736069 -20.1118812778284 Winsorized Mean ( 18 / 20 ) -0.763934426229508 0.0379842350736069 -20.1118812778284 Winsorized Mean ( 19 / 20 ) -0.795081967213115 0.0331766450795332 -23.9651105561485 Winsorized Mean ( 20 / 20 ) -0.762295081967213 0.0283579707500619 -26.8811576359197 Trimmed Mean ( 1 / 20 ) -0.750847457627119 0.0968641242678067 -7.75155366656907 Trimmed Mean ( 2 / 20 ) -0.75438596491228 0.0913581105178117 -8.25746023682486 Trimmed Mean ( 3 / 20 ) -0.754545454545455 0.0857456178977948 -8.79981360032697 Trimmed Mean ( 4 / 20 ) -0.756603773584906 0.0806140005362266 -9.38551329238276 Trimmed Mean ( 5 / 20 ) -0.75686274509804 0.076145109248313 -9.93974206051596 Trimmed Mean ( 6 / 20 ) -0.755102040816327 0.0711339892451818 -10.6152072845749 Trimmed Mean ( 7 / 20 ) -0.751063829787234 0.0682727525195185 -11.0009308555783 Trimmed Mean ( 8 / 20 ) -0.746666666666667 0.0645575461714335 -11.5659084173349 Trimmed Mean ( 9 / 20 ) -0.746511627906977 0.0613929158214515 -12.1595727767362 Trimmed Mean ( 10 / 20 ) -0.748780487804878 0.0580287934436917 -12.9036025629493 Trimmed Mean ( 11 / 20 ) -0.751282051282051 0.0553326091612931 -13.5775641645975 Trimmed Mean ( 12 / 20 ) -0.754054054054054 0.0516389920934108 -14.6024161875590 Trimmed Mean ( 13 / 20 ) -0.762857142857143 0.0483484749502195 -15.7783082846480 Trimmed Mean ( 14 / 20 ) -0.766666666666667 0.0463980363569169 -16.5236877864633 Trimmed Mean ( 15 / 20 ) -0.770967741935484 0.0435503782898022 -17.7028942620233 Trimmed Mean ( 16 / 20 ) -0.775862068965517 0.0420107810505549 -18.4681657794427 Trimmed Mean ( 17 / 20 ) -0.781481481481481 0.0395980650182801 -19.735345177112 Trimmed Mean ( 18 / 20 ) -0.784 0.0377182537595084 -20.7856918562239 Trimmed Mean ( 19 / 20 ) -0.78695652173913 0.0346092517880913 -22.7383280793696 Trimmed Mean ( 20 / 20 ) -0.785714285714286 0.0318371707627558 -24.6791491483107 Median -0.8 Midrange -0.8 Midmean - Weighted Average at Xnp -0.770967741935484 Midmean - Weighted Average at X(n+1)p -0.770967741935484 Midmean - Empirical Distribution Function -0.770967741935484 Midmean - Empirical Distribution Function - Averaging -0.770967741935484 Midmean - Empirical Distribution Function - Interpolation -0.770967741935484 Midmean - Closest Observation -0.808823529411765 Midmean - True Basic - Statistics Graphics Toolkit -0.770967741935484 Midmean - MS Excel (old versions) -0.770967741935484 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560744797tbj9lr7nidlc2i/1ve1p1256074259.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560744797tbj9lr7nidlc2i/1ve1p1256074259.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560744797tbj9lr7nidlc2i/27ibb1256074259.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560744797tbj9lr7nidlc2i/27ibb1256074259.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 36 ;

Parameters (R input):

par1 = 0 ; par2 = 36 ;

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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