workshop 3/part 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: Thu, 22 Oct 2009 09:44:00 -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/22/t12562262804nydrrk8tou5hcm.htm/, Retrieved Thu, 22 Oct 2009 17:44:43 +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/22/t12562262804nydrrk8tou5hcm.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:

Dataseries X:

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1.436908929 1.411717837 1.377545552 1.348943246 1.320311666 1.285253017 1.254095745 1.220260273 1.202206488 1.188118812 1.299190218 1.359671133 1.419631059 1.396021307 1.365642626 1.340841502 1.299472705 1.285594244 1.247119212 1.230448329 1.211402173 1.206059338 1.29726206 1.355737705 1.410891576 1.413686003 1.354369179 1.304479295 1.304147696 1.289441991 1.262425237 1.259654419 1.204585727 1.198638691 1.314828123 1.354351739 1.435689999 1.407968081 1.347733625 1.356390977 1.334319012 1.321790492 1.292481913 1.290630619 1.214534007 1.183867141 1.296155497 1.332478319 1.416671793 1.360303256 1.33168649 1.314907675 1.30101151 1.279733914 1.285324542 1.265348075 1.221352518 1.208470561 1.291576557 1.324770741

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.30743586943333 0.00884337137834611 147.843600986239 Geometric Mean 1.30566839080629 Harmonic Mean 1.30389873648609 Quadratic Mean 1.30919924400516 Winsorized Mean ( 1 / 20 ) 1.30748641511667 0.00882183177585481 148.210309189440 Winsorized Mean ( 2 / 20 ) 1.30730177975 0.0086189971825614 151.676784672239 Winsorized Mean ( 3 / 20 ) 1.3073322063 0.00854896467456687 152.922869150379 Winsorized Mean ( 4 / 20 ) 1.30729176956667 0.00847338325411776 154.282148034714 Winsorized Mean ( 5 / 20 ) 1.30725055665 0.00841354056625121 155.374606725462 Winsorized Mean ( 6 / 20 ) 1.30740905285 0.00834736780737484 156.625307883871 Winsorized Mean ( 7 / 20 ) 1.30740999983333 0.0082078564744961 159.287629345833 Winsorized Mean ( 8 / 20 ) 1.3062346745 0.00780393419940299 167.381559239688 Winsorized Mean ( 9 / 20 ) 1.30432225115 0.0071193846886792 183.207160195185 Winsorized Mean ( 10 / 20 ) 1.30252047098333 0.00675213599527249 192.904952135931 Winsorized Mean ( 11 / 20 ) 1.30320915183333 0.00626467763145658 208.024934162547 Winsorized Mean ( 12 / 20 ) 1.30641690383333 0.00561666378206303 232.596600851454 Winsorized Mean ( 13 / 20 ) 1.30721778551667 0.00523764233093304 249.581338877677 Winsorized Mean ( 14 / 20 ) 1.30836237931667 0.00499448523409686 261.961407030419 Winsorized Mean ( 15 / 20 ) 1.30871295231667 0.00482598040608103 271.180743019099 Winsorized Mean ( 16 / 20 ) 1.30948772511667 0.00469982498015231 278.624785103004 Winsorized Mean ( 17 / 20 ) 1.31203130648333 0.00383194091369375 342.393407423033 Winsorized Mean ( 18 / 20 ) 1.31332415108333 0.00354273403026071 370.709214935529 Winsorized Mean ( 19 / 20 ) 1.31116429505 0.00318741247820061 411.356956157175 Winsorized Mean ( 20 / 20 ) 1.30908003238333 0.00283914866019595 461.081890756994 Trimmed Mean ( 1 / 20 ) 1.30733407062069 0.00860530240231495 151.921920869277 Trimmed Mean ( 2 / 20 ) 1.307170844375 0.00833791898181543 156.774231942751 Trimmed Mean ( 3 / 20 ) 1.3070981025 0.00814134259462198 160.550681574737 Trimmed Mean ( 4 / 20 ) 1.30700806257692 0.00792804343304749 164.858842363142 Trimmed Mean ( 5 / 20 ) 1.30692295048 0.00768825211249966 169.989606396386 Trimmed Mean ( 6 / 20 ) 1.3068410489375 0.00740369108980822 176.512098233876 Trimmed Mean ( 7 / 20 ) 1.30671756982609 0.00705937090401804 185.103968553675 Trimmed Mean ( 8 / 20 ) 1.30658268086364 0.00665601406206104 196.301069781552 Trimmed Mean ( 9 / 20 ) 1.30664482485714 0.00625382510032321 208.935300219639 Trimmed Mean ( 10 / 20 ) 1.307031920475 0.00592975914297013 220.419057327905 Trimmed Mean ( 11 / 20 ) 1.30774425460526 0.00559778781002995 233.618046804505 Trimmed Mean ( 12 / 20 ) 1.30843139138889 0.00529324402358382 247.188942274195 Trimmed Mean ( 13 / 20 ) 1.30872763955882 0.00507655706436957 257.798272129016 Trimmed Mean ( 14 / 20 ) 1.30894540696875 0.00488348012669474 268.035370885122 Trimmed Mean ( 15 / 20 ) 1.30902869663333 0.00467793332371932 279.830558934208 Trimmed Mean ( 16 / 20 ) 1.30907380296429 0.00442613743464313 295.759863378448 Trimmed Mean ( 17 / 20 ) 1.30901410265385 0.00408532837458807 320.418331803214 Trimmed Mean ( 18 / 20 ) 1.30857039620833 0.00389910088287316 335.608242904471 Trimmed Mean ( 19 / 20 ) 1.30785013031818 0.00369367580500718 354.078213508951 Trimmed Mean ( 20 / 20 ) 1.30732684115 0.00351757540391782 371.655669326639 Median 1.302579603 Midrange 1.310388035 Midmean - Weighted Average at Xnp 1.307435978 Midmean - Weighted Average at X(n+1)p 1.30902869663333 Midmean - Empirical Distribution Function 1.307435978 Midmean - Empirical Distribution Function - Averaging 1.30902869663333 Midmean - Empirical Distribution Function - Interpolation 1.30902869663333 Midmean - Closest Observation 1.307435978 Midmean - True Basic - Statistics Graphics Toolkit 1.30902869663333 Midmean - MS Excel (old versions) 1.30894540696875 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/22/t12562262804nydrrk8tou5hcm/1qh3c1256226237.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t12562262804nydrrk8tou5hcm/1qh3c1256226237.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t12562262804nydrrk8tou5hcm/20le21256226237.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t12562262804nydrrk8tou5hcm/20le21256226237.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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