W3: Part 2 Yt= c+et (variabiliteit)

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 20 Oct 2009 09:08:56 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t125605147021xe8ol05zcb103.htm/, Retrieved Tue, 20 Oct 2009 17:11:10 +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/2009/Oct/20/t125605147021xe8ol05zcb103.htm/}, year = {2009}, } @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 = {2009}, 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:

cvm Variabiliteit

Dataseries X:

» Textbox « » Textfile « » CSV «

0.659038902 0.626033058 0.797546012 0.773345422 0.744947064 0.760826772 0.721987315 0.728884254 0.780324737 0.730544747 0.712538226 0.737489025 0.671199011 0.626959248 0.794169611 0.727101039 0.784007353 0.758553275 0.698989899 0.749751738 0.741991342 0.716981132 0.727024568 0.744328098 0.611241218 0.608955224 0.717770035 0.73304721 0.692648361 0.688235294 0.662264151 0.658119658 0.652356902 0.622997172 0.631290027 0.675767918 0.607567568 0.607485605 0.691555556 0.751633987 0.689320388 0.651 0.642276423 0.628546099 0.655737705 0.698209719 0.647112741 0.625539258 0.678125 0.5501002 0.684931507 0.668971478 0.599597586 0.608695652 0.558241758 0.61695279 0.646944714 0.643995749 0.650326797 0.679649464 0.56779661

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 0.680648678229508 0.00775425382737473 87.7774565267163 Geometric Mean 0.677979523067663 Harmonic Mean 0.675293125834904 Quadratic Mean 0.683293736485809 Winsorized Mean ( 1 / 20 ) 0.680726795557377 0.0077040959955911 88.3590749579111 Winsorized Mean ( 2 / 20 ) 0.680706880606557 0.00754456325468546 90.2248225149167 Winsorized Mean ( 3 / 20 ) 0.682089750770492 0.00715672127492864 95.307575154559 Winsorized Mean ( 4 / 20 ) 0.682149337918033 0.00695837157791916 98.0328989734728 Winsorized Mean ( 5 / 20 ) 0.681129937344262 0.00674386614024326 100.999919509033 Winsorized Mean ( 6 / 20 ) 0.681017273770492 0.006680114586085 101.946944920538 Winsorized Mean ( 7 / 20 ) 0.680253044065574 0.00652548252846113 104.245631046995 Winsorized Mean ( 8 / 20 ) 0.680305994229508 0.00642659951839576 105.857847883966 Winsorized Mean ( 9 / 20 ) 0.680439798852459 0.00615279507729106 110.590356139740 Winsorized Mean ( 10 / 20 ) 0.681329211311475 0.00596904077921331 114.143835921535 Winsorized Mean ( 11 / 20 ) 0.681366238032787 0.00582142937823588 117.044490925228 Winsorized Mean ( 12 / 20 ) 0.680577677311475 0.0056546714596624 120.356714296556 Winsorized Mean ( 13 / 20 ) 0.679828445754098 0.00546666526746918 124.358893857942 Winsorized Mean ( 14 / 20 ) 0.679618305295082 0.00531569446649504 127.851273164538 Winsorized Mean ( 15 / 20 ) 0.679884723737705 0.00514351696290633 132.182848553014 Winsorized Mean ( 16 / 20 ) 0.682298672852459 0.00463340535098995 147.256417508708 Winsorized Mean ( 17 / 20 ) 0.682756517688525 0.00456154046891318 149.676742394702 Winsorized Mean ( 18 / 20 ) 0.682140301557377 0.00420133793954979 162.362635753713 Winsorized Mean ( 19 / 20 ) 0.680879058819672 0.00398886743848926 170.694832385191 Winsorized Mean ( 20 / 20 ) 0.68167419095082 0.00380213366928869 179.287276630216 Trimmed Mean ( 1 / 20 ) 0.680880053559322 0.00743880323328766 91.5308594953115 Trimmed Mean ( 2 / 20 ) 0.681044066508772 0.00711265588183165 95.751021534503 Trimmed Mean ( 3 / 20 ) 0.681231051418182 0.00681784470504846 99.9188278538738 Trimmed Mean ( 4 / 20 ) 0.680901613301887 0.00664148231235289 102.522536578233 Trimmed Mean ( 5 / 20 ) 0.68052851917647 0.00649652482097244 104.752700548384 Trimmed Mean ( 6 / 20 ) 0.68037877832653 0.00638377647552355 106.579354859183 Trimmed Mean ( 7 / 20 ) 0.68024066406383 0.00625541397457219 108.744308023251 Trimmed Mean ( 8 / 20 ) 0.680238266666667 0.00613076693053104 110.954840458720 Trimmed Mean ( 9 / 20 ) 0.680226256837209 0.00599132626218509 113.535171858447 Trimmed Mean ( 10 / 20 ) 0.680190955853659 0.00587656533626324 115.746344494176 Trimmed Mean ( 11 / 20 ) 0.680012921025641 0.00576472210088554 117.961093201905 Trimmed Mean ( 12 / 20 ) 0.67981008972973 0.00564460651341292 120.435337363967 Trimmed Mean ( 13 / 20 ) 0.679698606771429 0.00551699927827665 123.200778627571 Trimmed Mean ( 14 / 20 ) 0.679680144818182 0.00538242437872969 126.277695141273 Trimmed Mean ( 15 / 20 ) 0.679688836548387 0.00522513970763014 130.080509724143 Trimmed Mean ( 16 / 20 ) 0.679661367310345 0.00504026683243287 134.846306734574 Trimmed Mean ( 17 / 20 ) 0.67928897 0.00491760926877235 138.133986023168 Trimmed Mean ( 18 / 20 ) 0.67879127492 0.00473390098672557 143.389411148102 Trimmed Mean ( 19 / 20 ) 0.678297819304348 0.00456836288171336 148.477219710259 Trimmed Mean ( 20 / 20 ) 0.677903193714286 0.00437154056662358 155.071921072866 Median 0.678125 Midrange 0.673823106 Midmean - Weighted Average at Xnp 0.6780489893 Midmean - Weighted Average at X(n+1)p 0.679688836548387 Midmean - Empirical Distribution Function 0.679688836548387 Midmean - Empirical Distribution Function - Averaging 0.679688836548387 Midmean - Empirical Distribution Function - Interpolation 0.679688836548387 Midmean - Closest Observation 0.678090626 Midmean - True Basic - Statistics Graphics Toolkit 0.679688836548387 Midmean - MS Excel (old versions) 0.679688836548387 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t125605147021xe8ol05zcb103/13ttq1256051331.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t125605147021xe8ol05zcb103/13ttq1256051331.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t125605147021xe8ol05zcb103/2cb2n1256051331.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t125605147021xe8ol05zcb103/2cb2n1256051331.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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