E[t] bij 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: Tue, 20 Oct 2009 12:46:56 -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/t1256064503ljsfnci3wzc35ah.htm/, Retrieved Tue, 20 Oct 2009 20:48:24 +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/t1256064503ljsfnci3wzc35ah.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:

» Textbox « » Textfile « » CSV «

-402.63 -1216.13 -474.53 -466.63 -745.83 -628.33 -877.53 -709.33 -143.63 -292.23 -162.03 177.77 82.77 -810.53 377.07 -228.23 -2.63 -199.23 -370.83 -191.03 543.37 -449.43 338.77 -49.93 61.57 -814.63 74.17 120.87 174.37 -121.33 -151.43 35.17 789.57 -156.63 323.67 525.47 930.07 146.37 252.67 745.17 227.77 170.47 145.27 246.07 436.57 1032.27 855.07 1056.17 1631.47 -117.03 1318.77 805.37 -396.53 -347.83 -1048.53 -521.53 -213.53 -562.13 -509.23 -73.83 -169.23

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00114754098360971 74.0751030621394 1.54915880798313e-05 Geometric Mean NaN Harmonic Mean -164.059768941246 Quadratic Mean 573.783281057676 Winsorized Mean ( 1 / 20 ) -2.37754098360655 71.6328308589465 -0.0331906606942313 Winsorized Mean ( 2 / 20 ) -5.38081967213114 67.8977217248558 -0.0792488987176332 Winsorized Mean ( 3 / 20 ) -3.4627868852459 66.9494369488402 -0.0517224198299384 Winsorized Mean ( 4 / 20 ) -9.8955737704918 65.2252343506272 -0.151713886029091 Winsorized Mean ( 5 / 20 ) -10.7398360655738 62.7182081398003 -0.171239523323664 Winsorized Mean ( 6 / 20 ) -12.0381967213115 60.9157176095439 -0.197620535285714 Winsorized Mean ( 7 / 20 ) -4.55622950819671 58.7994004328768 -0.0774876865181293 Winsorized Mean ( 8 / 20 ) -1.69721311475409 56.0041364456552 -0.0303051385570604 Winsorized Mean ( 9 / 20 ) -25.4808196721311 48.7656660339216 -0.522515567703035 Winsorized Mean ( 10 / 20 ) -26.3988524590164 47.8579380298022 -0.551608647296447 Winsorized Mean ( 11 / 20 ) -36.1726229508197 43.8240824740699 -0.825405140477785 Winsorized Mean ( 12 / 20 ) -46.3234426229508 41.5149300202216 -1.11582610401576 Winsorized Mean ( 13 / 20 ) -50.8201639344262 39.5330567014242 -1.28551061250458 Winsorized Mean ( 14 / 20 ) -43.5447540983606 37.1955643865387 -1.17069749623479 Winsorized Mean ( 15 / 20 ) -59.5037704918033 34.1821049674966 -1.74078719108682 Winsorized Mean ( 16 / 20 ) -54.4939344262295 32.8227396046071 -1.66024942106236 Winsorized Mean ( 17 / 20 ) -53.1840983606557 31.0263054769764 -1.71416150079879 Winsorized Mean ( 18 / 20 ) -51.5316393442623 26.2825601854265 -1.96067806867751 Winsorized Mean ( 19 / 20 ) -32.6562295081967 23.1975089228895 -1.40774725496383 Winsorized Mean ( 20 / 20 ) -29.1152459016393 22.3368588077927 -1.30346196625829 Trimmed Mean ( 1 / 20 ) -7.03847457627118 68.2486794878123 -0.103129827992175 Trimmed Mean ( 2 / 20 ) -12.0264912280702 64.051255564424 -0.187763551582119 Trimmed Mean ( 3 / 20 ) -15.7118181818182 61.421146847592 -0.255804702260035 Trimmed Mean ( 4 / 20 ) -20.4111320754717 58.6086518487529 -0.348261415876707 Trimmed Mean ( 5 / 20 ) -23.5554901960784 55.7957834405979 -0.422173303134213 Trimmed Mean ( 6 / 20 ) -26.7463265306122 53.1508090046437 -0.503215793540893 Trimmed Mean ( 7 / 20 ) -29.9278723404255 50.3714518255482 -0.594143532810508 Trimmed Mean ( 8 / 20 ) -34.8411111111111 47.433409061272 -0.7345268198224 Trimmed Mean ( 9 / 20 ) -40.7183720930233 44.4414194044870 -0.916225733530737 Trimmed Mean ( 10 / 20 ) -43.2373170731707 42.7294566800668 -1.01188548679443 Trimmed Mean ( 11 / 20 ) -45.8710256410256 40.6880341507087 -1.12738367921928 Trimmed Mean ( 12 / 20 ) -47.3245945945946 39.1050296961494 -1.21019201269791 Trimmed Mean ( 13 / 20 ) -47.47 37.5843066212705 -1.26302715860494 Trimmed Mean ( 14 / 20 ) -46.9936363636364 36.0214800233364 -1.30460037547573 Trimmed Mean ( 15 / 20 ) -47.4783870967742 34.4906659871314 -1.37655756239930 Trimmed Mean ( 16 / 20 ) -45.7920689655172 33.187129313393 -1.37981410001128 Trimmed Mean ( 17 / 20 ) -44.5633333333333 31.6554451552526 -1.40776201739620 Trimmed Mean ( 18 / 20 ) -43.326 29.9242596566732 -1.44785536875724 Trimmed Mean ( 19 / 20 ) -42.1169565217391 29.029306647604 -1.45084266162504 Trimmed Mean ( 20 / 20 ) -43.5633333333333 28.6546732940249 -1.52028721061766 Median -73.83 Midrange 207.67 Midmean - Weighted Average at Xnp -57.4833333333334 Midmean - Weighted Average at X(n+1)p -47.4783870967742 Midmean - Empirical Distribution Function -47.4783870967742 Midmean - Empirical Distribution Function - Averaging -47.4783870967742 Midmean - Empirical Distribution Function - Interpolation -47.4783870967742 Midmean - Closest Observation -58.576875 Midmean - True Basic - Statistics Graphics Toolkit -47.4783870967742 Midmean - MS Excel (old versions) -47.4783870967742 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064503ljsfnci3wzc35ah/1zk3a1256064411.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064503ljsfnci3wzc35ah/1zk3a1256064411.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064503ljsfnci3wzc35ah/2hwoe1256064411.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256064503ljsfnci3wzc35ah/2hwoe1256064411.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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