Yt-Xt CT

*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: Sat, 17 Oct 2009 03:38:10 -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/17/t1255772320u9grctnwsxyo3uv.htm/, Retrieved Sat, 17 Oct 2009 11:38:42 +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/17/t1255772320u9grctnwsxyo3uv.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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3.33 5.14 8.56 10.67 11.68 14.91 17.51 19.42 21.35 23.43 22.50 22.51 21.41 20.54 18.35 18.55 18.53 15.95 15.15 16.96 16.64 16.69 14.38 13.93 10.03 6.72 5.62 7.09 5.42 5.54 5.34 4.34 2.95 -2.93 -5.06 -7.73 -15.43 -21.24 -23.46 -21.71 -17.27 -17.77 -21.17 -21.37 -22.06 -24.96 -28.66 -27.52 -38.00 -40.73 -44.50 -42.33 -35.15 -32.69 -33.59 -39.36 -41.71 -42.42 -44.97 -51.41

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -5.401 2.98697209552333 -1.80818562319168 Geometric Mean NaN Harmonic Mean 29.8971181428719 Quadratic Mean 23.5705098940746 Winsorized Mean ( 1 / 20 ) -5.309 2.95828126826150 -1.79462313369545 Winsorized Mean ( 2 / 20 ) -5.29366666666667 2.95468639503958 -1.79161709870592 Winsorized Mean ( 3 / 20 ) -5.24416666666667 2.92322371862533 -1.79396692536854 Winsorized Mean ( 4 / 20 ) -5.24216666666667 2.92131387408844 -1.79445512964690 Winsorized Mean ( 5 / 20 ) -5.258 2.89995475125424 -1.81313173859899 Winsorized Mean ( 6 / 20 ) -5.272 2.86259469830775 -1.84168579754465 Winsorized Mean ( 7 / 20 ) -5.21366666666667 2.81469844614828 -1.85230026108168 Winsorized Mean ( 8 / 20 ) -5.035 2.77743138763037 -1.81282606023104 Winsorized Mean ( 9 / 20 ) -4.6345 2.68939735993113 -1.72324851249154 Winsorized Mean ( 10 / 20 ) -4.5145 2.61981921816672 -1.72321050578411 Winsorized Mean ( 11 / 20 ) -4.45033333333333 2.57467137902707 -1.72850538114695 Winsorized Mean ( 12 / 20 ) -3.69833333333333 2.42154743641691 -1.52726032854663 Winsorized Mean ( 13 / 20 ) -3.46216666666667 2.37723369942378 -1.45638464889079 Winsorized Mean ( 14 / 20 ) -3.02583333333333 2.25365635482229 -1.34263297368242 Winsorized Mean ( 15 / 20 ) -2.85083333333333 2.16407481166656 -1.31734509267630 Winsorized Mean ( 16 / 20 ) -2.5415 2.09543500095334 -1.21287465315971 Winsorized Mean ( 17 / 20 ) -2.5925 2.05871146998958 -1.25928282704575 Winsorized Mean ( 18 / 20 ) -2.6255 2.02388734061808 -1.29725600200562 Winsorized Mean ( 19 / 20 ) -3.29683333333333 1.92086660191541 -1.71632602183091 Winsorized Mean ( 20 / 20 ) -3.61016666666667 1.87316337908014 -1.92731008249773 Trimmed Mean ( 1 / 20 ) -5.1048275862069 2.94282818112997 -1.73466722214369 Trimmed Mean ( 2 / 20 ) -4.88607142857143 2.92083065794215 -1.67283625816701 Trimmed Mean ( 3 / 20 ) -4.65962962962963 2.89305212386539 -1.61062761060936 Trimmed Mean ( 4 / 20 ) -4.43480769230769 2.8701227039318 -1.54516309920563 Trimmed Mean ( 5 / 20 ) -4.1926 2.83867542853554 -1.47695645576604 Trimmed Mean ( 6 / 20 ) -3.92625 2.80257840415503 -1.40094207326333 Trimmed Mean ( 7 / 20 ) -3.63369565217391 2.76417113501355 -1.31456971174692 Trimmed Mean ( 8 / 20 ) -3.32590909090909 2.72443679456653 -1.22076940729259 Trimmed Mean ( 9 / 20 ) -3.02071428571429 2.67907865038822 -1.12751982300951 Trimmed Mean ( 10 / 20 ) -2.75175 2.63940773483468 -1.04256343712365 Trimmed Mean ( 11 / 20 ) -2.47342105263158 2.59981647443741 -0.95138294450835 Trimmed Mean ( 12 / 20 ) -2.17388888888889 2.55251025767190 -0.851667052994197 Trimmed Mean ( 13 / 20 ) -1.94970588235294 2.5244296044925 -0.772335215402016 Trimmed Mean ( 14 / 20 ) -1.7315625 2.48975315808223 -0.69547557129469 Trimmed Mean ( 15 / 20 ) -1.54666666666667 2.46726994797257 -0.626873710328133 Trimmed Mean ( 16 / 20 ) -1.36035714285714 2.44951984724525 -0.555356652605617 Trimmed Mean ( 17 / 20 ) -1.19 2.43125709807151 -0.489458725259422 Trimmed Mean ( 18 / 20 ) -0.98375 2.39929071739087 -0.410017007472021 Trimmed Mean ( 19 / 20 ) -0.735 2.34394335566060 -0.313574130631179 Trimmed Mean ( 20 / 20 ) -0.3305 2.27133214737172 -0.145509321647404 Median 4.74 Midrange -13.99 Midmean - Weighted Average at Xnp -2.30193548387097 Midmean - Weighted Average at X(n+1)p -1.54666666666667 Midmean - Empirical Distribution Function -2.30193548387097 Midmean - Empirical Distribution Function - Averaging -1.54666666666667 Midmean - Empirical Distribution Function - Interpolation -1.54666666666667 Midmean - Closest Observation -2.30193548387097 Midmean - True Basic - Statistics Graphics Toolkit -1.54666666666667 Midmean - MS Excel (old versions) -1.73156250000000 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/17/t1255772320u9grctnwsxyo3uv/10d331255772288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/17/t1255772320u9grctnwsxyo3uv/10d331255772288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/17/t1255772320u9grctnwsxyo3uv/2p33w1255772288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/17/t1255772320u9grctnwsxyo3uv/2p33w1255772288.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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