Workshop 3

*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: Mon, 19 Oct 2009 01:14:44 -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/19/t1255936558brvlxcckc9askpt.htm/, Retrieved Mon, 19 Oct 2009 09:15:59 +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/19/t1255936558brvlxcckc9askpt.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:

Vraag 2

Dataseries X:

» Textbox « » Textfile « » CSV «

-0.37 -0.35 -0.36 -0.36 -0.18 0.14 -0.25 -1.00 -1.23 -1.06 -0.72 -0.92 -0.53 -0.67 -0.43 -0.21 -0.25 -0.37 -0.39 -0.37 -0.15 0.00 -0.21 -0.17 0.20 0.08 -0.30 -0.05 0.00 -0.14 0.16 0.09 0.12 0.00 -0.24 -0.34 -0.27 -0.56 -0.59 -0.67 -0.56 -0.63 -1.13 -1.21 -1.22 -1.35 -3.00 -19.00 -3.14 -5.50 3.13 1.14 2.20 1.91 1.00 0.88 0.63 0.57 -0.88 -1.50

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.676333333333333 0.345786581143169 -1.95592706662409 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 2.74079550495837 Winsorized Mean ( 1 / 20 ) -0.466833333333333 0.169691227008176 -2.75107524156708 Winsorized Mean ( 2 / 20 ) -0.397833333333333 0.132713763536474 -2.99767953776698 Winsorized Mean ( 3 / 20 ) -0.429333333333333 0.12021893085991 -3.57126228175853 Winsorized Mean ( 4 / 20 ) -0.338666666666667 0.0875622350640743 -3.86772524044007 Winsorized Mean ( 5 / 20 ) -0.336166666666667 0.082299951488843 -4.08465206340054 Winsorized Mean ( 6 / 20 ) -0.349166666666667 0.0738762485116966 -4.72637246342286 Winsorized Mean ( 7 / 20 ) -0.355 0.0720920237405335 -4.92426181955553 Winsorized Mean ( 8 / 20 ) -0.403 0.0623042924585222 -6.46825417796517 Winsorized Mean ( 9 / 20 ) -0.397 0.0587421349465534 -6.75835157100113 Winsorized Mean ( 10 / 20 ) -0.388666666666667 0.0557817917088753 -6.96762607940445 Winsorized Mean ( 11 / 20 ) -0.381333333333333 0.0529819640277808 -7.19741784455902 Winsorized Mean ( 12 / 20 ) -0.371333333333333 0.0489144685691759 -7.59148252440248 Winsorized Mean ( 13 / 20 ) -0.364833333333333 0.0469369643802771 -7.77283614631533 Winsorized Mean ( 14 / 20 ) -0.346166666666667 0.0372865614502521 -9.28395253417303 Winsorized Mean ( 15 / 20 ) -0.333666666666667 0.0352112002810953 -9.476151451895 Winsorized Mean ( 16 / 20 ) -0.333666666666667 0.0352112002810953 -9.476151451895 Winsorized Mean ( 17 / 20 ) -0.3365 0.0311437572527659 -10.8047335865397 Winsorized Mean ( 18 / 20 ) -0.3515 0.0251760187659597 -13.9616991577421 Winsorized Mean ( 19 / 20 ) -0.345166666666667 0.0232166067422704 -14.8672314821193 Winsorized Mean ( 20 / 20 ) -0.351833333333333 0.0222803042745995 -15.7912265917498 Trimmed Mean ( 1 / 20 ) -0.426034482758621 0.144879727672063 -2.94060797603758 Trimmed Mean ( 2 / 20 ) -0.382321428571429 0.109076998620309 -3.50506003472161 Trimmed Mean ( 3 / 20 ) -0.373703703703704 0.091156210253638 -4.0995967544492 Trimmed Mean ( 4 / 20 ) -0.352307692307692 0.0741190674029694 -4.7532666647338 Trimmed Mean ( 5 / 20 ) -0.3564 0.0682801910497907 -5.21966905072232 Trimmed Mean ( 6 / 20 ) -0.361458333333333 0.0628278560995723 -5.75315402710032 Trimmed Mean ( 7 / 20 ) -0.364130434782609 0.058843587058151 -6.1881073705239 Trimmed Mean ( 8 / 20 ) -0.365909090909091 0.0542207123053389 -6.74851132254604 Trimmed Mean ( 9 / 20 ) -0.359285714285714 0.0512768361025739 -7.00678399047478 Trimmed Mean ( 10 / 20 ) -0.353 0.0484532552953664 -7.2853722179892 Trimmed Mean ( 11 / 20 ) -0.347368421052632 0.0455590908097292 -7.62456877165009 Trimmed Mean ( 12 / 20 ) -0.342222222222222 0.0424733550670601 -8.0573390466069 Trimmed Mean ( 13 / 20 ) -0.337941176470588 0.0395130326922995 -8.55265094689753 Trimmed Mean ( 14 / 20 ) -0.3340625 0.03595993339087 -9.28985313651378 Trimmed Mean ( 15 / 20 ) -0.332333333333333 0.034276372792359 -9.6956972473884 Trimmed Mean ( 16 / 20 ) -0.332142857142857 0.0324826251596726 -10.2252467437643 Trimmed Mean ( 17 / 20 ) -0.331923076923077 0.0296959941912359 -11.1773687314714 Trimmed Mean ( 18 / 20 ) -0.33125 0.0270822184831859 -12.2312727151824 Trimmed Mean ( 19 / 20 ) -0.328181818181818 0.0255301906300916 -12.8546560006881 Trimmed Mean ( 20 / 20 ) -0.3255 0.0238136957497814 -13.6686049666603 Median -0.345 Midrange -7.935 Midmean - Weighted Average at Xnp -0.3340625 Midmean - Weighted Average at X(n+1)p -0.321612903225807 Midmean - Empirical Distribution Function -0.3340625 Midmean - Empirical Distribution Function - Averaging -0.321612903225807 Midmean - Empirical Distribution Function - Interpolation -0.321612903225807 Midmean - Closest Observation -0.3340625 Midmean - True Basic - Statistics Graphics Toolkit -0.321612903225807 Midmean - MS Excel (old versions) -0.3340625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t1255936558brvlxcckc9askpt/17rfb1255936479.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255936558brvlxcckc9askpt/17rfb1255936479.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255936558brvlxcckc9askpt/2j20y1255936479.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255936558brvlxcckc9askpt/2j20y1255936479.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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