Tijdreeks B stap 9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 04 Aug 2010 14:08:48 +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/Aug/04/t1280930924xl8awq235gj7z4t.htm/, Retrieved Wed, 04 Aug 2010 16:08:46 +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/Aug/04/t1280930924xl8awq235gj7z4t.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:

Bogaerts Yannik

Dataseries X:

» Textbox « » Textfile « » CSV «

83 82 81 79 77 76 77 79 80 80 81 83 83 76 77 72 64 70 69 78 84 91 96 101 99 98 98 97 92 106 100 107 111 115 117 120 117 108 111 118 113 129 122 135 146 151 147 151 156 144 151 159 148 170 163 179 184 192 197 199 205 194 200 211 211 230 229 236 239 250 254 254 264 258 264 277 274 284 279 290 287 297 302 294

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 153 7.97181998927975 19.1926059802842 Geometric Mean 137.019039179835 Harmonic Mean 123.508343847617 Quadratic Mean 169.362459999679 Winsorized Mean ( 1 / 28 ) 153 7.9508314045104 19.2432705733397 Winsorized Mean ( 2 / 28 ) 152.952380952381 7.93237165115332 19.2820492633048 Winsorized Mean ( 3 / 28 ) 152.880952380952 7.89320943841234 19.3686679130743 Winsorized Mean ( 4 / 28 ) 152.928571428571 7.84052511710523 19.5048889129806 Winsorized Mean ( 5 / 28 ) 152.75 7.80403772906368 19.5732011175613 Winsorized Mean ( 6 / 28 ) 152.464285714286 7.72416847729794 19.7386017876737 Winsorized Mean ( 7 / 28 ) 152.297619047619 7.69144228987895 19.8009181253333 Winsorized Mean ( 8 / 28 ) 152.011904761905 7.63603901308882 19.9071671191495 Winsorized Mean ( 9 / 28 ) 151.047619047619 7.42193846743764 20.3515051640905 Winsorized Mean ( 10 / 28 ) 151.166666666667 7.40789366192621 20.4061604506564 Winsorized Mean ( 11 / 28 ) 150.380952380952 7.2656720192656 20.6974595030169 Winsorized Mean ( 12 / 28 ) 149.952380952381 7.14769008424541 20.9791386007206 Winsorized Mean ( 13 / 28 ) 149.952380952381 7.14769008424541 20.9791386007206 Winsorized Mean ( 14 / 28 ) 149.452380952381 7.01200521149487 21.3137863485015 Winsorized Mean ( 15 / 28 ) 147.488095238095 6.68003881313036 22.0789278870942 Winsorized Mean ( 16 / 28 ) 147.107142857143 6.56345123384095 22.4130777568154 Winsorized Mean ( 17 / 28 ) 146.095238095238 6.34336447156931 23.0311909003543 Winsorized Mean ( 18 / 28 ) 145.880952380952 6.30928349058998 23.1216353803926 Winsorized Mean ( 19 / 28 ) 141.809523809524 5.68645450417214 24.9381268601514 Winsorized Mean ( 20 / 28 ) 142.047619047619 5.65690254497108 25.110494288769 Winsorized Mean ( 21 / 28 ) 142.297619047619 5.22644923344333 27.2264424070315 Winsorized Mean ( 22 / 28 ) 141.25 5.00822258486506 28.2036186703962 Winsorized Mean ( 23 / 28 ) 142.071428571429 4.84178201128803 29.3427973915815 Winsorized Mean ( 24 / 28 ) 141.785714285714 4.7284272155194 29.9858087738672 Winsorized Mean ( 25 / 28 ) 141.190476190476 4.56952024377966 30.8983150654982 Winsorized Mean ( 26 / 28 ) 140.571428571429 4.48364420115095 31.3520480807429 Winsorized Mean ( 27 / 28 ) 138.321428571429 4.09602751434192 33.7696531791124 Winsorized Mean ( 28 / 28 ) 136.988095238095 3.83537801417957 35.7169735894725 Trimmed Mean ( 1 / 28 ) 152.268292682927 7.88451821329195 19.3123141533529 Trimmed Mean ( 2 / 28 ) 151.5 7.80473728261451 19.4112875954806 Trimmed Mean ( 3 / 28 ) 150.717948717949 7.72034296193176 19.5221830767265 Trimmed Mean ( 4 / 28 ) 149.921052631579 7.63573691931667 19.6341301718126 Trimmed Mean ( 5 / 28 ) 149.067567567568 7.55121550739036 19.7408705157038 Trimmed Mean ( 6 / 28 ) 148.208333333333 7.45917258634806 19.8692725791849 Trimmed Mean ( 7 / 28 ) 147.357142857143 7.36788497971015 19.9999244373302 Trimmed Mean ( 8 / 28 ) 146.485294117647 7.26385608342018 20.1663265950438 Trimmed Mean ( 9 / 28 ) 145.606060606061 7.14896046978474 20.3674452001054 Trimmed Mean ( 10 / 28 ) 144.8125 7.05392617653235 20.5293472565357 Trimmed Mean ( 11 / 28 ) 143.951612903226 6.93783026976863 20.7487942636029 Trimmed Mean ( 12 / 28 ) 143.133333333333 6.82250623576848 20.9795826323948 Trimmed Mean ( 13 / 28 ) 142.310344827586 6.70117536694716 21.236624477777 Trimmed Mean ( 14 / 28 ) 141.428571428571 6.54796771995675 21.5988498229044 Trimmed Mean ( 15 / 28 ) 140.537037037037 6.38217473997496 22.0202427484128 Trimmed Mean ( 16 / 28 ) 139.788461538462 6.24133405476373 22.3972087236329 Trimmed Mean ( 17 / 28 ) 139.02 6.08380184571779 22.8508428652804 Trimmed Mean ( 18 / 28 ) 138.291666666667 5.92655688715151 23.3342342442500 Trimmed Mean ( 19 / 28 ) 137.521739130435 5.72845589049169 24.0067728126699 Trimmed Mean ( 20 / 28 ) 137.090909090909 5.61011414695634 24.4363849825204 Trimmed Mean ( 21 / 28 ) 136.595238095238 5.45577292560886 25.0368261212034 Trimmed Mean ( 22 / 28 ) 136.025 5.3400383533627 25.4726634902057 Trimmed Mean ( 23 / 28 ) 135.5 5.22900190112172 25.9131670942657 Trimmed Mean ( 24 / 28 ) 134.833333333333 5.10485296649412 26.4127751021071 Trimmed Mean ( 25 / 28 ) 134.117647058824 4.95267527156802 27.0798386134373 Trimmed Mean ( 26 / 28 ) 133.375 4.77450174735374 27.9348520657518 Trimmed Mean ( 27 / 28 ) 132.6 4.53684786010586 29.2273411162846 Trimmed Mean ( 28 / 28 ) 131.964285714286 4.32247789962468 30.5297768499277 Median 125.5 Midrange 183 Midmean - Weighted Average at Xnp 135.372093023256 Midmean - Weighted Average at X(n+1)p 136.595238095238 Midmean - Empirical Distribution Function 135.372093023256 Midmean - Empirical Distribution Function - Averaging 136.595238095238 Midmean - Empirical Distribution Function - Interpolation 136.595238095238 Midmean - Closest Observation 135.372093023256 Midmean - True Basic - Statistics Graphics Toolkit 136.595238095238 Midmean - MS Excel (old versions) 138.733333333333 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/04/t1280930924xl8awq235gj7z4t/1djvm1280930926.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280930924xl8awq235gj7z4t/1djvm1280930926.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280930924xl8awq235gj7z4t/2otup1280930926.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280930924xl8awq235gj7z4t/2otup1280930926.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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