Workshop3/part2(2)

*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, 26 Oct 2009 16:16:38 -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/26/t1256595487z39dh6o619eo72q.htm/, Retrieved Mon, 26 Oct 2009 23:18:10 +0100

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/26/t1256595487z39dh6o619eo72q.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:

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Dataseries X:

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184.7926685 206.6394558 173.6951794 124.9389196 268.8268257 230.6534475 261.7017449 238.1689001 200.5998747 242.1128021 160.6903335 167.5762727 176.1747069 176.6360146 165.1975684 95.4837558 285.6785267 263.3523742 338.9254494 267.056626 262.6842209 232.1736574 177.3837436 168.9547582 177.2811374 204.2911355 169.003403 91.03012634 302.9984424 258.3033369 297.8717201 251.2778156 243.0051312 249.4242864 198.2907643 181.3488598 197.9453382 240.0542583 191.773132 123.2988094 304.6911197 290.4224537 289.2839934 307.5900597 248.6616599 258.2771896 194.9724983 171.6256633 197.8784957 216.9991327 149.8172022 110.6315486 244.6121311 230.9905072 266.2769526 250.2627305 195.8942041 217.04177 182.8736185 162.9476716

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 215.650768764 7.16558273943858 30.0953567358984 Geometric Mean 207.890572110914 Harmonic Mean 199.180338832809 Quadratic Mean 222.563795466048 Winsorized Mean ( 1 / 20 ) 215.202739426667 7.00922088455688 30.7028046299431 Winsorized Mean ( 2 / 20 ) 215.61103452 6.84901308546927 31.4805990044662 Winsorized Mean ( 3 / 20 ) 216.159763695 6.67329147421208 32.3917761617811 Winsorized Mean ( 4 / 20 ) 215.927322888333 6.57376292738344 32.8468375378847 Winsorized Mean ( 5 / 20 ) 217.379740905 6.00102989955618 36.2237390153775 Winsorized Mean ( 6 / 20 ) 218.353208005 5.78158852178601 37.7669920960663 Winsorized Mean ( 7 / 20 ) 218.195926335 5.65119073815274 38.6106108332 Winsorized Mean ( 8 / 20 ) 216.249019108333 5.17911394790013 41.7540570228255 Winsorized Mean ( 9 / 20 ) 216.340294798333 5.07490944048599 42.6293902059493 Winsorized Mean ( 10 / 20 ) 216.440096815 5.01581928862854 43.1514941747792 Winsorized Mean ( 11 / 20 ) 215.912842321667 4.92546026103509 43.8360743725283 Winsorized Mean ( 12 / 20 ) 216.303663721667 4.82011833727315 44.8751770364282 Winsorized Mean ( 13 / 20 ) 216.539189076667 4.71572863484746 45.9185007967853 Winsorized Mean ( 14 / 20 ) 216.324783626667 4.50034152965171 48.0685259554975 Winsorized Mean ( 15 / 20 ) 216.433573726667 4.48190961357697 48.2904815998582 Winsorized Mean ( 16 / 20 ) 214.73910674 4.16924218676474 51.5055487593619 Winsorized Mean ( 17 / 20 ) 214.480571051667 4.122293226433 52.0294310158173 Winsorized Mean ( 18 / 20 ) 215.418572681667 3.9065259079346 55.1432597040063 Winsorized Mean ( 19 / 20 ) 215.659914545 3.79993927136616 56.7535160811834 Winsorized Mean ( 20 / 20 ) 214.949754945 3.51047395318127 61.2309784410187 Trimmed Mean ( 1 / 20 ) 215.673975001724 6.75910705992063 31.9086490404335 Trimmed Mean ( 2 / 20 ) 216.178870260714 6.44980180636932 33.5171338206444 Trimmed Mean ( 3 / 20 ) 216.494334561111 6.17550774595259 35.0569286716547 Trimmed Mean ( 4 / 20 ) 216.623015663462 5.92113097616761 36.5847363511065 Trimmed Mean ( 5 / 20 ) 216.831723496 5.64128604133462 38.4365766790123 Trimmed Mean ( 6 / 20 ) 216.69471914375 5.49264589271615 39.4517912452924 Trimmed Mean ( 7 / 20 ) 216.334178086957 5.36809095345285 40.3000209874996 Trimmed Mean ( 8 / 20 ) 215.971499856818 5.24179635308314 41.2018104689983 Trimmed Mean ( 9 / 20 ) 215.921942847619 5.20283263710146 41.5008434651304 Trimmed Mean ( 10 / 20 ) 215.8522175225 5.16778537353555 41.7688046078478 Trimmed Mean ( 11 / 20 ) 215.759394476316 5.1242746306494 42.1053534456979 Trimmed Mean ( 12 / 20 ) 215.736144802778 5.07622703219203 42.4993097106648 Trimmed Mean ( 13 / 20 ) 215.652686138235 5.02380151831599 42.9261955019519 Trimmed Mean ( 14 / 20 ) 215.5248251375 4.96319288327382 43.4246321282069 Trimmed Mean ( 15 / 20 ) 215.410545353333 4.91974588842601 43.7848926018922 Trimmed Mean ( 16 / 20 ) 215.264398442857 4.84082358640095 44.4685485022811 Trimmed Mean ( 17 / 20 ) 215.340161669231 4.79999000118306 44.8626271338389 Trimmed Mean ( 18 / 20 ) 215.466572054167 4.72337668821664 45.6170630201248 Trimmed Mean ( 19 / 20 ) 215.473844686364 4.65198668037207 46.3186718903352 Trimmed Mean ( 20 / 20 ) 215.444465235 4.54043520556476 47.4501794389558 Median 211.81929425 Midrange 214.97778787 Midmean - Weighted Average at Xnp 214.144873145161 Midmean - Weighted Average at X(n+1)p 215.410545353333 Midmean - Empirical Distribution Function 214.144873145161 Midmean - Empirical Distribution Function - Averaging 215.410545353333 Midmean - Empirical Distribution Function - Interpolation 215.410545353333 Midmean - Closest Observation 214.144873145161 Midmean - True Basic - Statistics Graphics Toolkit 215.410545353333 Midmean - MS Excel (old versions) 215.5248251375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/26/t1256595487z39dh6o619eo72q/13oes1256595396.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256595487z39dh6o619eo72q/13oes1256595396.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256595487z39dh6o619eo72q/2sq5i1256595396.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256595487z39dh6o619eo72q/2sq5i1256595396.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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