Workshop 3 part 2. Yt-Xt

*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 14:31:10 -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/t1256070799ft4w8ai6bh9b95e.htm/, Retrieved Tue, 20 Oct 2009 22:33:21 +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/t1256070799ft4w8ai6bh9b95e.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:

De berekening om de extremen weg te werken

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,2 0,4 0,4 0,3 0,2 0 -0,2 -0,2 -0,5 -0,5 0,1 0,3 0,2 0,1 0 0,1 0,3 0,3 0 -0,3 -0,6 -0,6 0,2 0,4 0,4 0,1 -0,1 0 0,2 0,2 0 -0,2 -0,5 -0,6 0,1 0,2 0,2 0 -0,1 0 0,2 0,2 0,1 0 -0,3 -0,4 0,1 0,1 0,1 0 -0,1 0 0,2 0,2 0 -0,1 -0,3 -0,4 0,2 0,3 0,2 0 -0,1 0 0,2 0,2 0,1 -0,3 -0,5 -0,4 0,4 0,4 0,2 -0,2 -0,3 -0,2 0,2 0,3 0,2 -0,1 -0,4 -0,3 0,3

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00602409638554217 0.029609536430608 0.203451222536363 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 0.268193420581814 Winsorized Mean ( 1 / 27 ) 0.00602409638554217 0.029609536430608 0.203451222536363 Winsorized Mean ( 2 / 27 ) 0.00602409638554217 0.029609536430608 0.203451222536363 Winsorized Mean ( 3 / 27 ) 0.00963855421686747 0.0287671275602443 0.335054453965984 Winsorized Mean ( 4 / 27 ) 0.00963855421686747 0.0287671275602443 0.335054453965984 Winsorized Mean ( 5 / 27 ) 0.00963855421686747 0.0287671275602443 0.335054453965984 Winsorized Mean ( 6 / 27 ) 0.00240963855421687 0.0276929505662032 0.0870127055784954 Winsorized Mean ( 7 / 27 ) 0.0108433734939759 0.0259416855589767 0.417990321767034 Winsorized Mean ( 8 / 27 ) 0.0108433734939759 0.0259416855589767 0.417990321767034 Winsorized Mean ( 9 / 27 ) 0.0108433734939759 0.0259416855589767 0.417990321767034 Winsorized Mean ( 10 / 27 ) 0.0108433734939759 0.0259416855589767 0.417990321767035 Winsorized Mean ( 11 / 27 ) 0.0240963855421687 0.0235412094798144 1.02358315798644 Winsorized Mean ( 12 / 27 ) 0.0240963855421687 0.0235412094798144 1.02358315798644 Winsorized Mean ( 13 / 27 ) 0.00843373493975904 0.0215614954907210 0.391147958331022 Winsorized Mean ( 14 / 27 ) 0.00843373493975904 0.0215614954907210 0.391147958331022 Winsorized Mean ( 15 / 27 ) 0.00843373493975904 0.0215614954907210 0.391147958331022 Winsorized Mean ( 16 / 27 ) 0.00843373493975904 0.0215614954907210 0.391147958331022 Winsorized Mean ( 17 / 27 ) 0.0289156626506024 0.0181845859688485 1.59011938463361 Winsorized Mean ( 18 / 27 ) 0.0289156626506024 0.0181845859688485 1.59011938463361 Winsorized Mean ( 19 / 27 ) 0.0289156626506024 0.0181845859688485 1.59011938463361 Winsorized Mean ( 20 / 27 ) 0.0289156626506024 0.0181845859688485 1.59011938463361 Winsorized Mean ( 21 / 27 ) 0.0289156626506024 0.0181845859688485 1.59011938463361 Winsorized Mean ( 22 / 27 ) 0.055421686746988 0.0143681713953220 3.8572540111146 Winsorized Mean ( 23 / 27 ) 0.055421686746988 0.0143681713953220 3.8572540111146 Winsorized Mean ( 24 / 27 ) 0.055421686746988 0.0143681713953220 3.8572540111146 Winsorized Mean ( 25 / 27 ) 0.0554216867469879 0.0143681713953220 3.8572540111146 Winsorized Mean ( 26 / 27 ) 0.0554216867469879 0.0143681713953220 3.8572540111146 Winsorized Mean ( 27 / 27 ) 0.055421686746988 0.0143681713953220 3.8572540111146 Trimmed Mean ( 1 / 27 ) 0.00864197530864198 0.0289847517843540 0.298155919116994 Trimmed Mean ( 2 / 27 ) 0.0113924050632911 0.0282559901518547 0.403185483929799 Trimmed Mean ( 3 / 27 ) 0.0142857142857143 0.0274026135999149 0.521326706068602 Trimmed Mean ( 4 / 27 ) 0.016 0.0267817337239631 0.597422114823131 Trimmed Mean ( 5 / 27 ) 0.0178082191780822 0.0260504184018133 0.6836058793145 Trimmed Mean ( 6 / 27 ) 0.0197183098591549 0.0251850070622142 0.78293842882176 Trimmed Mean ( 7 / 27 ) 0.0197183098591549 0.0244413217265725 0.806761192366994 Trimmed Mean ( 8 / 27 ) 0.0253731343283582 0.0239990279071647 1.05725675333638 Trimmed Mean ( 9 / 27 ) 0.0276923076923077 0.0234631147011493 1.18024857505177 Trimmed Mean ( 10 / 27 ) 0.0301587301587302 0.0228123672492173 1.3220342207039 Trimmed Mean ( 11 / 27 ) 0.0327868852459016 0.0220185355939421 1.48905839382535 Trimmed Mean ( 12 / 27 ) 0.0338983050847458 0.0215704531840234 1.57151566522734 Trimmed Mean ( 13 / 27 ) 0.0350877192982456 0.0210160500889666 1.66956774225936 Trimmed Mean ( 14 / 27 ) 0.0350877192982456 0.0206772389202812 1.69692478930685 Trimmed Mean ( 15 / 27 ) 0.0415094339622642 0.0202369781572196 2.05116760218746 Trimmed Mean ( 16 / 27 ) 0.0450980392156863 0.0196665786950899 2.29313089556069 Trimmed Mean ( 17 / 27 ) 0.0489795918367347 0.0189257520316239 2.58798655688252 Trimmed Mean ( 18 / 27 ) 0.0510638297872340 0.0187175165244493 2.72813061073210 Trimmed Mean ( 19 / 27 ) 0.0533333333333333 0.0184226474588735 2.89498745782298 Trimmed Mean ( 20 / 27 ) 0.0558139534883721 0.0180138760288717 3.09838667696593 Trimmed Mean ( 21 / 27 ) 0.0585365853658537 0.0174522378731691 3.35410196624968 Trimmed Mean ( 22 / 27 ) 0.0615384615384615 0.0166796378466725 3.68943631175651 Trimmed Mean ( 23 / 27 ) 0.0621621621621622 0.0165995727681876 3.74480494349187 Trimmed Mean ( 24 / 27 ) 0.0628571428571429 0.0164422668527093 3.82290005509706 Trimmed Mean ( 25 / 27 ) 0.0636363636363636 0.0161773912909565 3.93366040864312 Trimmed Mean ( 26 / 27 ) 0.064516129032258 0.0157592008262893 4.09387060571201 Trimmed Mean ( 27 / 27 ) 0.0655172413793104 0.0151152078744495 4.33452466704474 Median 0.1 Midrange -0.1 Midmean - Weighted Average at Xnp 0.060377358490566 Midmean - Weighted Average at X(n+1)p 0.060377358490566 Midmean - Empirical Distribution Function 0.060377358490566 Midmean - Empirical Distribution Function - Averaging 0.060377358490566 Midmean - Empirical Distribution Function - Interpolation 0.060377358490566 Midmean - Closest Observation 0.060377358490566 Midmean - True Basic - Statistics Graphics Toolkit 0.060377358490566 Midmean - MS Excel (old versions) 0.060377358490566 Number of observations 83

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070799ft4w8ai6bh9b95e/14k7f1256070667.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070799ft4w8ai6bh9b95e/14k7f1256070667.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070799ft4w8ai6bh9b95e/2y3oh1256070667.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070799ft4w8ai6bh9b95e/2y3oh1256070667.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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