Tijdreeks 2 - 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: Sat, 14 Aug 2010 10:06:08 +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/14/t1281780343q3jcl2ew0t0v5lr.htm/, Retrieved Sat, 14 Aug 2010 12:05:44 +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/14/t1281780343q3jcl2ew0t0v5lr.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:

Reuben Vermoet

Dataseries X:

» Textbox « » Textfile « » CSV «

172 171 170 168 166 165 166 168 169 169 170 172 173 172 165 152 148 145 141 149 146 144 149 150 149 156 150 137 130 126 125 123 117 111 114 121 122 131 125 116 106 98 99 96 95 83 85 98 102 110 101 90 88 83 88 85 86 80 79 97 105 116 99 87 82 81 85 84 78 77 79 85 96 108 98 86 80 74 75 82 71 66 71 75

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 116.690476190476 3.70196239653167 31.5212483789144 Geometric Mean 111.920723445256 Harmonic Mean 107.421450009335 Quadratic Mean 121.466632690393 Winsorized Mean ( 1 / 28 ) 116.738095238095 3.69044287735043 31.632543604606 Winsorized Mean ( 2 / 28 ) 116.738095238095 3.69044287735043 31.632543604606 Winsorized Mean ( 3 / 28 ) 116.845238095238 3.67491746476176 31.7953366886876 Winsorized Mean ( 4 / 28 ) 116.845238095238 3.65974261670746 31.9271736656606 Winsorized Mean ( 5 / 28 ) 116.785714285714 3.64920756369978 32.0030341511487 Winsorized Mean ( 6 / 28 ) 116.928571428571 3.62988589813408 32.2127402100098 Winsorized Mean ( 7 / 28 ) 116.928571428571 3.6043491337063 32.4409670348264 Winsorized Mean ( 8 / 28 ) 117.02380952381 3.59207932879061 32.5782920733016 Winsorized Mean ( 9 / 28 ) 116.916666666667 3.57351320877366 32.7175694718615 Winsorized Mean ( 10 / 28 ) 117.035714285714 3.55843951809645 32.8896173984492 Winsorized Mean ( 11 / 28 ) 116.77380952381 3.51373630974364 33.2335153323811 Winsorized Mean ( 12 / 28 ) 116.916666666667 3.49588760670737 33.4440576528676 Winsorized Mean ( 13 / 28 ) 116.916666666667 3.45079369807613 33.8810942919739 Winsorized Mean ( 14 / 28 ) 116.916666666667 3.45079369807613 33.8810942919739 Winsorized Mean ( 15 / 28 ) 115.488095238095 3.16977505656828 36.434161155627 Winsorized Mean ( 16 / 28 ) 114.72619047619 3.05506695122084 37.5527581908948 Winsorized Mean ( 17 / 28 ) 114.52380952381 2.97100523633123 38.5471584241401 Winsorized Mean ( 18 / 28 ) 114.738095238095 2.94470552086202 38.9642001297662 Winsorized Mean ( 19 / 28 ) 114.511904761905 2.91225150854136 39.320746998002 Winsorized Mean ( 20 / 28 ) 114.511904761905 2.91225150854136 39.320746998002 Winsorized Mean ( 21 / 28 ) 114.511904761905 2.91225150854136 39.320746998002 Winsorized Mean ( 22 / 28 ) 114.511904761905 2.84317049920607 40.2761300435135 Winsorized Mean ( 23 / 28 ) 113.964285714286 2.76609909373785 41.2003626234102 Winsorized Mean ( 24 / 28 ) 113.964285714286 2.69167382551308 42.339560103484 Winsorized Mean ( 25 / 28 ) 113.964285714286 2.61463764486272 43.5870285652027 Winsorized Mean ( 26 / 28 ) 113.035714285714 2.48745829607063 45.4422550377121 Winsorized Mean ( 27 / 28 ) 112.392857142857 2.23735163914478 50.2347754266374 Winsorized Mean ( 28 / 28 ) 112.059523809524 1.77881580108266 62.9966991193353 Trimmed Mean ( 1 / 28 ) 116.621951219512 3.67710758857791 31.7156755439443 Trimmed Mean ( 2 / 28 ) 116.5 3.65995261780217 31.8310131757823 Trimmed Mean ( 3 / 28 ) 116.371794871795 3.63837855730545 31.9845208624962 Trimmed Mean ( 4 / 28 ) 116.197368421053 3.61803570515884 32.1161475148989 Trimmed Mean ( 5 / 28 ) 116.013513513514 3.59745545657345 32.2487699747687 Trimmed Mean ( 6 / 28 ) 115.833333333333 3.57438286037616 32.4065266251706 Trimmed Mean ( 7 / 28 ) 115.614285714286 3.54989824933018 32.5683379054881 Trimmed Mean ( 8 / 28 ) 115.382352941176 3.52459248086557 32.7363669892528 Trimmed Mean ( 9 / 28 ) 115.121212121212 3.49475231982613 32.9411648053329 Trimmed Mean ( 10 / 28 ) 114.859375 3.4607254483302 33.1893924308326 Trimmed Mean ( 11 / 28 ) 114.564516129032 3.42036556008917 33.4948163043852 Trimmed Mean ( 12 / 28 ) 114.283333333333 3.37823639901181 33.8292883727033 Trimmed Mean ( 13 / 28 ) 113.965517241379 3.32782050336648 34.2462933701171 Trimmed Mean ( 14 / 28 ) 113.625 3.27223289465819 34.7239954055498 Trimmed Mean ( 15 / 28 ) 113.259259259259 3.2013913363722 35.3781363660476 Trimmed Mean ( 16 / 28 ) 113.019230769231 3.16626857678139 35.6947706830727 Trimmed Mean ( 17 / 28 ) 112.84 3.1405653982059 35.9298360939918 Trimmed Mean ( 18 / 28 ) 112.666666666667 3.11927963436308 36.1194506018285 Trimmed Mean ( 19 / 28 ) 112.45652173913 3.09194160998469 36.3708426368657 Trimmed Mean ( 20 / 28 ) 112.25 3.05847261829676 36.7013257952629 Trimmed Mean ( 21 / 28 ) 112.02380952381 3.01014314993278 37.2154425700024 Trimmed Mean ( 22 / 28 ) 111.775 2.94206614560723 37.9920078163062 Trimmed Mean ( 23 / 28 ) 111.5 2.86285625659863 38.9471178453344 Trimmed Mean ( 24 / 28 ) 111.25 2.77184684292529 40.1356951896344 Trimmed Mean ( 25 / 28 ) 110.970588235294 2.66203428776365 41.686385763468 Trimmed Mean ( 26 / 28 ) 110.65625 2.52591782065323 43.8083333888445 Trimmed Mean ( 27 / 28 ) 110.4 2.37157496531144 46.5513431431851 Trimmed Mean ( 28 / 28 ) 110.178571428571 2.23254758235586 49.351051820498 Median 109 Midrange 119.5 Midmean - Weighted Average at Xnp 111.872340425532 Midmean - Weighted Average at X(n+1)p 111.872340425532 Midmean - Empirical Distribution Function 111.872340425532 Midmean - Empirical Distribution Function - Averaging 111.872340425532 Midmean - Empirical Distribution Function - Interpolation 111.872340425532 Midmean - Closest Observation 111.872340425532 Midmean - True Basic - Statistics Graphics Toolkit 111.872340425532 Midmean - MS Excel (old versions) 111.872340425532 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/14/t1281780343q3jcl2ew0t0v5lr/1mr1g1281780364.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281780343q3jcl2ew0t0v5lr/1mr1g1281780364.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281780343q3jcl2ew0t0v5lr/2x1ij1281780364.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281780343q3jcl2ew0t0v5lr/2x1ij1281780364.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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