WS3 Y(t) = c + e(t)

*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: Wed, 21 Oct 2009 16:34:23 -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/t1256164672ito6767gkf6gpoa.htm/, Retrieved Thu, 22 Oct 2009 00:37:52 +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/t1256164672ito6767gkf6gpoa.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:

IlseWS3P2

Dataseries X:

» Textbox « » Textfile « » CSV «

0.33 -0.08 -0.48 -0.38 -0.08 0.43 0.02 -0.08 0.33 0.33 0.53 0.63 -0.18 -0.08 0.43 0.43 0.43 -0.18 0.23 0.43 0.13 0.02 -0.08 -0.48 -0.68 -0.38 -0.28 -0.68 -0.58 -0.58 -0.58 -1.08 -1.08 -1.08 -1.18 -0.98 -0.18 0.53 0.73 1.13 1.23 2.03 1.73 2.73 3.43 3.53 3.03 3.13 2.43 0.83 0.33 -0.28 -0.48 -1.78 -1.68 -2.58 -3.38 -4.08 -3.08 -3.38

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.0106666666666667 0.19939893673204 -0.053494100026225 Geometric Mean NaN Harmonic Mean 1.70417898010697 Quadratic Mean 1.53164943769780 Winsorized Mean ( 1 / 20 ) -0.000666666666666667 0.195166865685222 -0.00341588037665118 Winsorized Mean ( 2 / 20 ) -0.0106666666666667 0.192292277927792 -0.0554711129412703 Winsorized Mean ( 3 / 20 ) -0.000666666666666682 0.186584657126337 -0.00357299832116034 Winsorized Mean ( 4 / 20 ) 0.0126666666666667 0.172223227018513 0.0735479579958459 Winsorized Mean ( 5 / 20 ) 0.0543333333333333 0.150001763956985 0.362217962642853 Winsorized Mean ( 6 / 20 ) 0.0243333333333333 0.137587643699141 0.176856966796687 Winsorized Mean ( 7 / 20 ) 0.0476666666666667 0.117659224168847 0.405124774563042 Winsorized Mean ( 8 / 20 ) -0.00566666666666669 0.100131373215749 -0.0565923195166511 Winsorized Mean ( 9 / 20 ) -0.0206666666666667 0.0970546082719276 -0.212938540834278 Winsorized Mean ( 10 / 20 ) -0.0706666666666667 0.0876423351338911 -0.806307437595191 Winsorized Mean ( 11 / 20 ) -0.0706666666666667 0.0809711068879457 -0.872739294084998 Winsorized Mean ( 12 / 20 ) -0.0306666666666667 0.0669019295181985 -0.458382394760749 Winsorized Mean ( 13 / 20 ) -0.0523333333333333 0.0633987322168538 -0.825463404446771 Winsorized Mean ( 14 / 20 ) -0.029 0.0596092265258127 -0.486501867079957 Winsorized Mean ( 15 / 20 ) -0.054 0.0557791245401295 -0.96810411502874 Winsorized Mean ( 16 / 20 ) -0.054 0.0557791245401295 -0.96810411502874 Winsorized Mean ( 17 / 20 ) -0.0256666666666667 0.0513860797318414 -0.499486763742406 Winsorized Mean ( 18 / 20 ) -0.0256666666666667 0.0513860797318414 -0.499486763742406 Winsorized Mean ( 19 / 20 ) -0.0256666666666667 0.0513860797318414 -0.499486763742406 Winsorized Mean ( 20 / 20 ) -0.0256666666666666 0.0415364292268729 -0.617931467495069 Trimmed Mean ( 1 / 20 ) -0.00155172413793104 0.183771044611266 -0.00844379015863695 Trimmed Mean ( 2 / 20 ) -0.00250000000000001 0.169472108190538 -0.0147516899783252 Trimmed Mean ( 3 / 20 ) 0.00203703703703703 0.153276440915089 0.0132899552264884 Trimmed Mean ( 4 / 20 ) 0.00307692307692307 0.135332822089307 0.022735970693736 Trimmed Mean ( 5 / 20 ) 0.000199999999999996 0.118601541787136 0.00168631871884897 Trimmed Mean ( 6 / 20 ) -0.0133333333333333 0.106067410208198 -0.125706221233850 Trimmed Mean ( 7 / 20 ) -0.0215217391304348 0.094343891144373 -0.228120113230229 Trimmed Mean ( 8 / 20 ) -0.035 0.0860413760538189 -0.40678103495355 Trimmed Mean ( 9 / 20 ) -0.0402380952380952 0.0810546682462572 -0.496431557968326 Trimmed Mean ( 10 / 20 ) -0.0435 0.0753721961250828 -0.577135896741157 Trimmed Mean ( 11 / 20 ) -0.0392105263157895 0.0706818866531306 -0.554746458710335 Trimmed Mean ( 12 / 20 ) -0.0344444444444444 0.0663485797798318 -0.519143658519042 Trimmed Mean ( 13 / 20 ) -0.035 0.0646425106949622 -0.541439365886629 Trimmed Mean ( 14 / 20 ) -0.0325 0.0631258982689202 -0.514844158914745 Trimmed Mean ( 15 / 20 ) -0.033 0.061930903284299 -0.532851908335823 Trimmed Mean ( 16 / 20 ) -0.03 0.0611075035010185 -0.490938072760573 Trimmed Mean ( 17 / 20 ) -0.0265384615384615 0.05959592734586 -0.445306629502513 Trimmed Mean ( 18 / 20 ) -0.0266666666666667 0.058584346065009 -0.455184165358364 Trimmed Mean ( 19 / 20 ) -0.0268181818181818 0.0566082702554533 -0.473750243509663 Trimmed Mean ( 20 / 20 ) -0.027 0.0529751679662522 -0.509672758700838 Median -0.08 Midrange -0.275 Midmean - Weighted Average at Xnp -0.0506451612903226 Midmean - Weighted Average at X(n+1)p -0.0506451612903226 Midmean - Empirical Distribution Function -0.0506451612903226 Midmean - Empirical Distribution Function - Averaging -0.0506451612903226 Midmean - Empirical Distribution Function - Interpolation -0.0506451612903226 Midmean - Closest Observation -0.0506451612903226 Midmean - True Basic - Statistics Graphics Toolkit -0.0506451612903226 Midmean - MS Excel (old versions) -0.0154545454545454 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/22/t1256164672ito6767gkf6gpoa/13tzv1256164458.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256164672ito6767gkf6gpoa/13tzv1256164458.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256164672ito6767gkf6gpoa/209ub1256164458.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/22/t1256164672ito6767gkf6gpoa/209ub1256164458.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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