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: Thu, 29 Jul 2010 12:32:48 +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/Jul/29/t1280406760v2okhzvf8c32pbb.htm/, Retrieved Thu, 29 Jul 2010 14:32:41 +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/2010/Jul/29/t1280406760v2okhzvf8c32pbb.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:

Van de Walle Mathias

Dataseries X:

» Textbox « » Textfile « » CSV «

239 238 237 235 233 232 233 235 236 236 237 239 238 237 244 230 237 244 239 240 230 228 231 228 225 227 238 214 222 233 228 218 203 209 207 203 195 199 207 182 181 189 186 174 153 158 153 147 143 156 168 142 146 150 145 133 111 115 109 105 96 112 127 107 116 125 120 107 86 87 79 83 75 89 104 86 98 98 85 74 49 54 47 56

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 168.928571428571 6.81795042487593 24.7770313512723 Geometric Mean 155.03448878726 Harmonic Mean 138.971428473394 Quadratic Mean 179.986309003133 Winsorized Mean ( 1 / 28 ) 168.952380952381 6.81286001668698 24.7990389555282 Winsorized Mean ( 2 / 28 ) 168.97619047619 6.77572817558184 24.9384547457411 Winsorized Mean ( 3 / 28 ) 169.011904761905 6.75674572189312 25.0138027562995 Winsorized Mean ( 4 / 28 ) 169.869047619048 6.59518722109742 25.7565163693385 Winsorized Mean ( 5 / 28 ) 169.928571428571 6.58480547490701 25.8061642179295 Winsorized Mean ( 6 / 28 ) 170.142857142857 6.52696737940915 26.0676738908812 Winsorized Mean ( 7 / 28 ) 170.47619047619 6.47178164025208 26.3414620505568 Winsorized Mean ( 8 / 28 ) 170.666666666667 6.44101025609673 26.4968785766367 Winsorized Mean ( 9 / 28 ) 170.666666666667 6.41047473038347 26.6230932722915 Winsorized Mean ( 10 / 28 ) 170.666666666667 6.41047473038347 26.6230932722915 Winsorized Mean ( 11 / 28 ) 170.797619047619 6.38970997041312 26.7301050968635 Winsorized Mean ( 12 / 28 ) 171.083333333333 6.34486995430509 26.9640409599334 Winsorized Mean ( 13 / 28 ) 172.011904761905 6.16049203315279 27.9217802468082 Winsorized Mean ( 14 / 28 ) 172.345238095238 6.11128612841205 28.2011403939976 Winsorized Mean ( 15 / 28 ) 172.166666666667 6.08898051295366 28.2751219683493 Winsorized Mean ( 16 / 28 ) 173.309523809524 5.9245344048838 29.2528512732847 Winsorized Mean ( 17 / 28 ) 173.107142857143 5.8456926161164 29.6127686187076 Winsorized Mean ( 18 / 28 ) 173.535714285714 5.78592190259506 29.9927508886494 Winsorized Mean ( 19 / 28 ) 173.535714285714 5.78592190259506 29.9927508886494 Winsorized Mean ( 20 / 28 ) 173.77380952381 5.69086371067836 30.5355774375232 Winsorized Mean ( 21 / 28 ) 174.02380952381 5.59187530933761 31.1208315452269 Winsorized Mean ( 22 / 28 ) 174.02380952381 5.5243158362928 31.5014229238189 Winsorized Mean ( 23 / 28 ) 174.845238095238 5.41405212634132 32.2947090303311 Winsorized Mean ( 24 / 28 ) 174.559523809524 5.30629128951027 32.8967096387266 Winsorized Mean ( 25 / 28 ) 175.75 5.1494830659244 34.1296393735107 Winsorized Mean ( 26 / 28 ) 177.297619047619 4.95000187653623 35.817687239279 Winsorized Mean ( 27 / 28 ) 177.619047619048 4.8288523977862 36.782869507562 Winsorized Mean ( 28 / 28 ) 178.952380952381 4.49714337716325 39.7924562203445 Trimmed Mean ( 1 / 28 ) 169.5 6.76041246922033 25.0724346734347 Trimmed Mean ( 2 / 28 ) 170.075 6.69715070247382 25.395128100847 Trimmed Mean ( 3 / 28 ) 170.666666666667 6.64339929063082 25.6896596456813 Trimmed Mean ( 4 / 28 ) 171.276315789474 6.58583271278398 26.0067820212019 Trimmed Mean ( 5 / 28 ) 171.675675675676 6.56985103741873 26.1308322970937 Trimmed Mean ( 6 / 28 ) 172.083333333333 6.54937160253611 26.2747853957008 Trimmed Mean ( 7 / 28 ) 172.471428571429 6.53475250025386 26.392954984099 Trimmed Mean ( 8 / 28 ) 172.823529411765 6.5245514976921 26.4881853523413 Trimmed Mean ( 9 / 28 ) 173.166666666667 6.51301667197207 26.587781881761 Trimmed Mean ( 10 / 28 ) 173.53125 6.49896850599117 26.7013526592763 Trimmed Mean ( 11 / 28 ) 173.91935483871 6.47573261056386 26.8570932893361 Trimmed Mean ( 12 / 28 ) 174.316666666667 6.44522736169016 27.045852207292 Trimmed Mean ( 13 / 28 ) 174.706896551724 6.41001789967091 27.2552899673952 Trimmed Mean ( 14 / 28 ) 175.017857142857 6.39299998026599 27.3764832915853 Trimmed Mean ( 15 / 28 ) 175.314814814815 6.37259287526907 27.5107508429075 Trimmed Mean ( 16 / 28 ) 175.653846153846 6.342409425986 27.6951288313493 Trimmed Mean ( 17 / 28 ) 175.9 6.32521678260427 27.8093235450464 Trimmed Mean ( 18 / 28 ) 176.1875 6.30663392209386 27.9368522378899 Trimmed Mean ( 19 / 28 ) 176.45652173913 6.28284271499697 28.085459041961 Trimmed Mean ( 20 / 28 ) 176.75 6.240690741435 28.3221853674739 Trimmed Mean ( 21 / 28 ) 177.047619047619 6.19279416979487 28.589294943979 Trimmed Mean ( 22 / 28 ) 177.35 6.1374794375341 28.8962271572604 Trimmed Mean ( 23 / 28 ) 177.684210526316 6.06485869933495 29.2973372233388 Trimmed Mean ( 24 / 28 ) 177.972222222222 5.97926126337794 29.7649181701216 Trimmed Mean ( 25 / 28 ) 178.323529411765 5.87294479366519 30.3635630295916 Trimmed Mean ( 26 / 28 ) 178.59375 5.75260448991052 31.0457203016886 Trimmed Mean ( 27 / 28 ) 178.733333333333 5.62362286249859 31.7825959712244 Trimmed Mean ( 28 / 28 ) 178.857142857143 5.45634776334757 32.7796450326345 Median 181.5 Midrange 145.5 Midmean - Weighted Average at Xnp 175.46511627907 Midmean - Weighted Average at X(n+1)p 177.047619047619 Midmean - Empirical Distribution Function 175.46511627907 Midmean - Empirical Distribution Function - Averaging 177.047619047619 Midmean - Empirical Distribution Function - Interpolation 177.047619047619 Midmean - Closest Observation 175.46511627907 Midmean - True Basic - Statistics Graphics Toolkit 177.047619047619 Midmean - MS Excel (old versions) 176.75 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/29/t1280406760v2okhzvf8c32pbb/1plnv1280406764.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280406760v2okhzvf8c32pbb/1plnv1280406764.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280406760v2okhzvf8c32pbb/2plnv1280406764.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280406760v2okhzvf8c32pbb/2plnv1280406764.ps (open in new window)

Parameters (Session):

par1 = 0.1 ; par2 = 0.99 ; par3 = 0.1 ;

Parameters (R input):

par1 = 0.1 ; par2 = 0.99 ; par3 = 0.1 ;

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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