Robuustheid consumprijs plat water

*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 12:36:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/20/t1287578204avlj4v6wjgu14o4.htm/, Retrieved Wed, 20 Oct 2010 14:36:46 +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/2010/Oct/20/t1287578204avlj4v6wjgu14o4.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP1W52 - Kristina Henderickx

Dataseries X:

» Textbox « » Textfile « » CSV «

0,65 0,65 0,65 0,65 0,65 0,65 0,66 0,66 0,66 0,65 0,65 0,65 0,65 0,65 0,65 0,65 0,66 0,67 0,66 0,67 0,66 0,66 0,66 0,66 0,71 0,74 0,75 0,75 0,75 0,75 0,7 0,69 0,69 0,68 0,68 0,68 0,67 0,66 0,66 0,67 0,67 0,67 0,67 0,68 0,68 0,67 0,67 0,67 0,67 0,67 0,69 0,69 0,69 0,69 0,69 0,69 0,7 0,69 0,68 0,7 0,7 0,71 0,69 0,7 0,7 0,71 0,71 0,71 0,71 0,7 0,7 0,71 0,71 0,71 0,71 0,7 0,69 0,7 0,7 0,7 0,71 0,7 0,7 0,69

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.684047619047619 0.0028296390867774 241.74376945954 Geometric Mean 0.683568440223214 Harmonic Mean 0.683095711528572 Quadratic Mean 0.684533209045196 Winsorized Mean ( 1 / 28 ) 0.684047619047619 0.0028296390867774 241.74376945954 Winsorized Mean ( 2 / 28 ) 0.684047619047619 0.0028296390867774 241.74376945954 Winsorized Mean ( 3 / 28 ) 0.684047619047619 0.0028296390867774 241.74376945954 Winsorized Mean ( 4 / 28 ) 0.683571428571429 0.00270272623855319 252.919226083865 Winsorized Mean ( 5 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 6 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 7 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 8 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 9 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 10 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 11 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 12 / 28 ) 0.681785714285714 0.00234172358987200 291.146964242258 Winsorized Mean ( 13 / 28 ) 0.683333333333333 0.00211090476188534 323.715851928354 Winsorized Mean ( 14 / 28 ) 0.683333333333333 0.00211090476188534 323.715851928354 Winsorized Mean ( 15 / 28 ) 0.683333333333333 0.00211090476188534 323.715851928354 Winsorized Mean ( 16 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 17 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 18 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 19 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 20 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 21 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 22 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 23 / 28 ) 0.681428571428571 0.00184871648535570 368.59549683599 Winsorized Mean ( 24 / 28 ) 0.684285714285714 0.00147930565388127 462.572229403940 Winsorized Mean ( 25 / 28 ) 0.684285714285714 0.00147930565388127 462.572229403940 Winsorized Mean ( 26 / 28 ) 0.684285714285714 0.00147930565388127 462.572229403940 Winsorized Mean ( 27 / 28 ) 0.684285714285714 0.00147930565388127 462.57222940394 Winsorized Mean ( 28 / 28 ) 0.684285714285714 0.00147930565388127 462.572229403940 Trimmed Mean ( 1 / 28 ) 0.683658536585366 0.00275197881296175 248.424345916237 Trimmed Mean ( 2 / 28 ) 0.68325 0.00266110641308688 256.754106727897 Trimmed Mean ( 3 / 28 ) 0.682820512820513 0.00255409301686053 267.343635612704 Trimmed Mean ( 4 / 28 ) 0.682368421052632 0.00242695694995491 281.162144662397 Trimmed Mean ( 5 / 28 ) 0.682027027027027 0.00232479137399628 293.371282539918 Trimmed Mean ( 6 / 28 ) 0.682083333333333 0.00231462570954223 294.684073766826 Trimmed Mean ( 7 / 28 ) 0.682142857142857 0.00230125411072004 296.4222221115 Trimmed Mean ( 8 / 28 ) 0.682205882352941 0.00228409767856735 298.676317021976 Trimmed Mean ( 9 / 28 ) 0.682272727272727 0.00226244761476996 301.56398884935 Trimmed Mean ( 10 / 28 ) 0.68234375 0.00223542665199917 305.240947802859 Trimmed Mean ( 11 / 28 ) 0.68241935483871 0.00220193516003990 309.918006316927 Trimmed Mean ( 12 / 28 ) 0.6825 0.00216057378861384 315.888308743147 Trimmed Mean ( 13 / 28 ) 0.682586206896552 0.00210952876368506 323.572837046396 Trimmed Mean ( 14 / 28 ) 0.6825 0.00208970885935891 326.600519944861 Trimmed Mean ( 15 / 28 ) 0.682407407407407 0.00206354645748362 330.696410993123 Trimmed Mean ( 16 / 28 ) 0.682307692307692 0.00202948448780179 336.197540019991 Trimmed Mean ( 17 / 28 ) 0.6824 0.00203158729538641 335.894992821465 Trimmed Mean ( 18 / 28 ) 0.6825 0.0020303547536162 336.148152821285 Trimmed Mean ( 19 / 28 ) 0.682608695652174 0.00202484048655918 337.117269327291 Trimmed Mean ( 20 / 28 ) 0.682727272727273 0.00201379062495222 339.025946524838 Trimmed Mean ( 21 / 28 ) 0.682857142857143 0.00199551513077022 342.195923412306 Trimmed Mean ( 22 / 28 ) 0.683 0.00196768769671278 347.107928326746 Trimmed Mean ( 23 / 28 ) 0.683157894736842 0.0019270206795876 354.515082257988 Trimmed Mean ( 24 / 28 ) 0.683333333333333 0.00186870636860462 365.671859856498 Trimmed Mean ( 25 / 28 ) 0.683235294117647 0.00187490169607039 364.411262494264 Trimmed Mean ( 26 / 28 ) 0.683125 0.00187499999999999 364.333333333335 Trimmed Mean ( 27 / 28 ) 0.683 0.00186621505210135 365.981401356155 Trimmed Mean ( 28 / 28 ) 0.682857142857143 0.00184427778390829 370.257207897431 Median 0.685 Midrange 0.7 Midmean - Weighted Average at Xnp 0.68109090909091 Midmean - Weighted Average at X(n+1)p 0.68109090909091 Midmean - Empirical Distribution Function 0.68109090909091 Midmean - Empirical Distribution Function - Averaging 0.68109090909091 Midmean - Empirical Distribution Function - Interpolation 0.68109090909091 Midmean - Closest Observation 0.68109090909091 Midmean - True Basic - Statistics Graphics Toolkit 0.68109090909091 Midmean - MS Excel (old versions) 0.68109090909091 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t1287578204avlj4v6wjgu14o4/1i8gm1287578210.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287578204avlj4v6wjgu14o4/1i8gm1287578210.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287578204avlj4v6wjgu14o4/2tzf71287578210.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287578204avlj4v6wjgu14o4/2tzf71287578210.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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