Tijdsreeks 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: Sat, 07 Aug 2010 11:50:12 +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/07/t1281181795ctznhvo2qvidkus.htm/, Retrieved Sat, 07 Aug 2010 13:49:55 +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/07/t1281181795ctznhvo2qvidkus.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:

Gosselin Claudia

Dataseries X:

» Textbox « » Textfile « » CSV «

166 165 164 162 160 159 160 162 163 163 164 166 163 166 170 171 176 172 169 180 172 170 161 167 158 163 165 169 168 165 156 157 146 150 146 159 146 151 156 152 152 143 127 126 122 122 114 127 125 123 124 123 127 117 104 110 106 107 100 115 117 123 130 129 125 112 90 96 99 108 101 113 113 120 131 135 137 120 102 114 121 134 122 131

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 139.702380952381 2.65191234011230 52.6798638247842 Geometric Mean 137.531037493646 Harmonic Mean 135.300571763967 Quadratic Mean 141.776106187588 Winsorized Mean ( 1 / 28 ) 139.726190476190 2.62836545949420 53.1608684673095 Winsorized Mean ( 2 / 28 ) 139.702380952381 2.59941626804331 53.7437511143765 Winsorized Mean ( 3 / 28 ) 139.738095238095 2.59274989017569 53.8957096353889 Winsorized Mean ( 4 / 28 ) 139.738095238095 2.57699112550565 54.2252916026927 Winsorized Mean ( 5 / 28 ) 139.738095238095 2.55771694352061 54.633917014191 Winsorized Mean ( 6 / 28 ) 139.880952380952 2.53282550481442 55.2272361894119 Winsorized Mean ( 7 / 28 ) 139.964285714286 2.49310273043246 56.1406010293074 Winsorized Mean ( 8 / 28 ) 140.059523809524 2.47763091681872 56.529615794979 Winsorized Mean ( 9 / 28 ) 140.059523809524 2.44564262899425 57.2690065789055 Winsorized Mean ( 10 / 28 ) 140.178571428571 2.39250603258886 58.590686718933 Winsorized Mean ( 11 / 28 ) 140.309523809524 2.33595313487436 60.0652135159681 Winsorized Mean ( 12 / 28 ) 140.452380952381 2.31531883520087 60.6622201733162 Winsorized Mean ( 13 / 28 ) 140.452380952381 2.31531883520087 60.6622201733162 Winsorized Mean ( 14 / 28 ) 140.452380952381 2.26977222805956 61.8795045670528 Winsorized Mean ( 15 / 28 ) 140.452380952381 2.26977222805956 61.8795045670528 Winsorized Mean ( 16 / 28 ) 140.642857142857 2.24328173111851 62.6951377492527 Winsorized Mean ( 17 / 28 ) 140.845238095238 2.16220428735801 65.1396535094915 Winsorized Mean ( 18 / 28 ) 140.845238095238 2.16220428735801 65.1396535094915 Winsorized Mean ( 19 / 28 ) 141.297619047619 2.04543765310600 69.0794064698372 Winsorized Mean ( 20 / 28 ) 141.297619047619 2.04543765310600 69.0794064698372 Winsorized Mean ( 21 / 28 ) 141.547619047619 2.01439204698662 70.2681582065239 Winsorized Mean ( 22 / 28 ) 141.809523809524 1.98253100853237 71.5295363347194 Winsorized Mean ( 23 / 28 ) 141.535714285714 1.94756614580966 72.6731231132966 Winsorized Mean ( 24 / 28 ) 141.535714285714 1.94756614580966 72.6731231132966 Winsorized Mean ( 25 / 28 ) 141.535714285714 1.87438622033325 75.5104325620525 Winsorized Mean ( 26 / 28 ) 141.226190476190 1.83595373081286 76.9225215788327 Winsorized Mean ( 27 / 28 ) 141.226190476190 1.83595373081286 76.9225215788327 Winsorized Mean ( 28 / 28 ) 141.226190476190 1.75543996627046 80.4505954004421 Trimmed Mean ( 1 / 28 ) 139.817073170732 2.60105183648108 53.754051038017 Trimmed Mean ( 2 / 28 ) 139.9125 2.56887367268274 54.4645310852852 Trimmed Mean ( 3 / 28 ) 140.025641025641 2.54829962040758 54.9486567059352 Trimmed Mean ( 4 / 28 ) 140.131578947368 2.52623720638014 55.4704754539514 Trimmed Mean ( 5 / 28 ) 140.243243243243 2.50477594978312 55.9903344869574 Trimmed Mean ( 6 / 28 ) 140.361111111111 2.48401033368508 56.5058483081599 Trimmed Mean ( 7 / 28 ) 140.457142857143 2.46471460845947 56.987183171253 Trimmed Mean ( 8 / 28 ) 140.544117647059 2.44961821966071 57.373886477104 Trimmed Mean ( 9 / 28 ) 140.621212121212 2.43342738441179 57.787305683339 Trimmed Mean ( 10 / 28 ) 140.703125 2.41878803521015 58.1709198787959 Trimmed Mean ( 11 / 28 ) 140.774193548387 2.40937479737913 58.4276857637584 Trimmed Mean ( 12 / 28 ) 140.833333333333 2.40587401066201 58.5372852897567 Trimmed Mean ( 13 / 28 ) 140.879310344828 2.40249386287784 58.6387805278613 Trimmed Mean ( 14 / 28 ) 140.928571428571 2.39545797791011 58.8315773969547 Trimmed Mean ( 15 / 28 ) 140.981481481481 2.39153099575613 58.9503049434271 Trimmed Mean ( 16 / 28 ) 141.038461538462 2.38331960123166 59.1773178324784 Trimmed Mean ( 17 / 28 ) 141.08 2.37432525323791 59.4189864289262 Trimmed Mean ( 18 / 28 ) 141.104166666667 2.37324768938130 59.456148339684 Trimmed Mean ( 19 / 28 ) 141.130434782609 2.36737256173183 59.6147970386908 Trimmed Mean ( 20 / 28 ) 141.113636363636 2.37548613230841 59.4041086766975 Trimmed Mean ( 21 / 28 ) 141.095238095238 2.37969769496193 59.2912445954592 Trimmed Mean ( 22 / 28 ) 141.05 2.38422970412905 59.1595682898034 Trimmed Mean ( 23 / 28 ) 140.973684210526 2.38877378035085 59.015083542076 Trimmed Mean ( 24 / 28 ) 140.916666666667 2.39389932291522 58.8649093626303 Trimmed Mean ( 25 / 28 ) 140.852941176471 2.39173128209292 58.8916247536032 Trimmed Mean ( 26 / 28 ) 140.78125 2.39570111252729 58.7641126281758 Trimmed Mean ( 27 / 28 ) 140.733333333333 2.39920165521273 58.6584012342452 Trimmed Mean ( 28 / 28 ) 140.678571428571 2.39104013774073 58.8357214118108 Median 140 Midrange 135 Midmean - Weighted Average at Xnp 141.130434782609 Midmean - Weighted Average at X(n+1)p 142.090909090909 Midmean - Empirical Distribution Function 141.130434782609 Midmean - Empirical Distribution Function - Averaging 142.090909090909 Midmean - Empirical Distribution Function - Interpolation 142.090909090909 Midmean - Closest Observation 141.130434782609 Midmean - True Basic - Statistics Graphics Toolkit 142.090909090909 Midmean - MS Excel (old versions) 141.130434782609 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/07/t1281181795ctznhvo2qvidkus/1p1yu1281181809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t1281181795ctznhvo2qvidkus/1p1yu1281181809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t1281181795ctznhvo2qvidkus/2p1yu1281181809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t1281181795ctznhvo2qvidkus/2p1yu1281181809.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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