WS 3 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 14:47:34 -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/t1256071739dn5m3rlf9n412ov.htm/, Retrieved Tue, 20 Oct 2009 22:49:01 +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/t1256071739dn5m3rlf9n412ov.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:

WS 3 y(t)= c + e(t) Question 3

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

-0,00027027 -0,007210884 -0,02375 -0,044935065 -0,066666667 -0,063870968 -0,085960265 0,037094017 -0,084294479 -0,045868263 -0,04 0,02 -0,00739726 -0,025751634 -0,019106145 -0,04097561 -0,051428571 -0,002346369 -0,068050314 0,055971223 -0,04741573 -0,047039106 -0,025977011 0,031976048 0,00125 0,007951807 -0,016649215 -0,030561798 -0,020697674 0,003870968 -0,053619632 0,059735099 -0,037291667 -0,030847458 0,009528796 0,075555556 0,054285714 0,02 0,038957346 0,014186047 -0,016082474 -0,02040404 -0,048181818 0,063209877 -0,026153846 -0,010150754 -0,01 0,03734104 0,004126984 -0,00688172 -0,026728972 -0,00688172 0,00989899 -0,023269231 -0,000408163 0,025649718 -0,01030303 0,010990991 0,039323671 0,109385475 0,082200957 0,005849057 0,057383178 0,04173913 0,029389671 0,036736402 0,037857143 0,129289617 0,059473684 0,064843049 0,121123596 0,117560976 0,10125 0,044390244 0,048248588 0,013975904 0,007654321 0,025464481

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 0.00719604541025641 0.00542574335255658 1.32627825215243 Geometric Mean NaN Harmonic Mean -0.0142387497458589 Quadratic Mean 0.048151451390254 Winsorized Mean ( 1 / 26 ) 0.00711270906410256 0.00539133411987087 1.31928552487356 Winsorized Mean ( 2 / 26 ) 0.00743787688461538 0.00528183606194239 1.40819911814531 Winsorized Mean ( 3 / 26 ) 0.00717665173076923 0.00518917060004466 1.38300554826767 Winsorized Mean ( 4 / 26 ) 0.00690281706410256 0.00505897593645816 1.36446924255095 Winsorized Mean ( 5 / 26 ) 0.00633886148717949 0.00466672249189255 1.35831121267483 Winsorized Mean ( 6 / 26 ) 0.00599621994871795 0.00453386628699248 1.32254009473568 Winsorized Mean ( 7 / 26 ) 0.00532621638461538 0.00430402027684544 1.23749797677978 Winsorized Mean ( 8 / 26 ) 0.00523728469230769 0.00426153441833423 1.22896688802407 Winsorized Mean ( 9 / 26 ) 0.00487980538461538 0.00418499317526931 1.16602469352925 Winsorized Mean ( 10 / 26 ) 0.00499639871794872 0.00415526270707063 1.20242667435847 Winsorized Mean ( 11 / 26 ) 0.00483318861538462 0.00408465771961676 1.18325425216732 Winsorized Mean ( 12 / 26 ) 0.00522511169230769 0.00395396139768928 1.32148778573339 Winsorized Mean ( 13 / 26 ) 0.00510679519230769 0.00388283922738655 1.31522190161475 Winsorized Mean ( 14 / 26 ) 0.00450931952564102 0.00363595709747656 1.24020152184155 Winsorized Mean ( 15 / 26 ) 0.00500660125641026 0.00334206216167523 1.49805749091772 Winsorized Mean ( 16 / 26 ) 0.00452137992307692 0.00325182921791232 1.39041124858939 Winsorized Mean ( 17 / 26 ) 0.00483029324358974 0.00305959387882880 1.57873673267995 Winsorized Mean ( 18 / 26 ) 0.00487847808974359 0.00302951226084812 1.6103179884071 Winsorized Mean ( 19 / 26 ) 0.00465355511538462 0.00298484051613097 1.55906323645616 Winsorized Mean ( 20 / 26 ) 0.00457900998717949 0.00295806541546412 1.54797455230078 Winsorized Mean ( 21 / 26 ) 0.00505140525641026 0.00287755616334886 1.75544975307502 Winsorized Mean ( 22 / 26 ) 0.005086141 0.00284538905511092 1.78750283405506 Winsorized Mean ( 23 / 26 ) 0.0044407265 0.00254764648411682 1.74307013460678 Winsorized Mean ( 24 / 26 ) 0.00373526711538462 0.00242548077349258 1.54001101810673 Winsorized Mean ( 25 / 26 ) 0.00295255621794872 0.00220922071565884 1.33646955101460 Winsorized Mean ( 26 / 26 ) 0.00370978721794872 0.00209615202898705 1.76980828043348 Trimmed Mean ( 1 / 26 ) 0.00681529197368421 0.00518453877828203 1.31454161404547 Trimmed Mean ( 2 / 26 ) 0.00650179828378378 0.00494018591557245 1.31610396752252 Trimmed Mean ( 3 / 26 ) 0.00599475570833333 0.00472083545161487 1.26985059525485 Trimmed Mean ( 4 / 26 ) 0.00555576575714286 0.00450315481665903 1.23374966736426 Trimmed Mean ( 5 / 26 ) 0.00516947898529412 0.00429276202748721 1.20423143705455 Trimmed Mean ( 6 / 26 ) 0.00489307948484848 0.00416898396112816 1.17368632992399 Trimmed Mean ( 7 / 26 ) 0.004669004078125 0.00405791119508453 1.15059296610056 Trimmed Mean ( 8 / 26 ) 0.00455088758064516 0.00398232861410476 1.14277047969539 Trimmed Mean ( 9 / 26 ) 0.00443934805 0.00389974512917759 1.13836876589322 Trimmed Mean ( 10 / 26 ) 0.0043735325862069 0.00381548331731224 1.14625912957412 Trimmed Mean ( 11 / 26 ) 0.00428677623214286 0.00371762099220354 1.15309662849788 Trimmed Mean ( 12 / 26 ) 0.00421502511111111 0.00361133583174250 1.16716509000974 Trimmed Mean ( 13 / 26 ) 0.00408876428846154 0.00350628351919873 1.16612483447885 Trimmed Mean ( 14 / 26 ) 0.00396660058 0.00338902507580626 1.17042526723009 Trimmed Mean ( 15 / 26 ) 0.00390360641666667 0.00329383445984391 1.18512525879994 Trimmed Mean ( 16 / 26 ) 0.00377892004347826 0.00323242956769352 1.16906492913152 Trimmed Mean ( 17 / 26 ) 0.00369665886363636 0.00316962690501426 1.16627570828237 Trimmed Mean ( 18 / 26 ) 0.00357281645238095 0.00312462741339676 1.14343759421126 Trimmed Mean ( 19 / 26 ) 0.003431369775 0.00306718120481713 1.11873722022386 Trimmed Mean ( 20 / 26 ) 0.00329933313157895 0.00299658502239077 1.10103104264555 Trimmed Mean ( 21 / 26 ) 0.00316070147222222 0.00290343519495403 1.08860754933167 Trimmed Mean ( 22 / 26 ) 0.002954154 0.00279173292769723 1.05817930171306 Trimmed Mean ( 23 / 26 ) 0.00271793953125 0.00264001491095404 1.02951673491412 Trimmed Mean ( 24 / 26 ) 0.0025231897 0.00251625876433303 1.00275446061638 Trimmed Mean ( 25 / 26 ) 0.00238250214285714 0.00237392017341754 1.0036151044739 Trimmed Mean ( 26 / 26 ) 0.00231409565384615 0.00223853962314146 1.03375237584522 Median 0.002560484 Midrange 0.021664676 Midmean - Weighted Average at Xnp 0.00254865764102564 Midmean - Weighted Average at X(n+1)p 0.003431369775 Midmean - Empirical Distribution Function 0.003431369775 Midmean - Empirical Distribution Function - Averaging 0.003431369775 Midmean - Empirical Distribution Function - Interpolation 0.00329933313157895 Midmean - Closest Observation 0.003431369775 Midmean - True Basic - Statistics Graphics Toolkit 0.003431369775 Midmean - MS Excel (old versions) 0.003431369775 Number of observations 78

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071739dn5m3rlf9n412ov/14vy41256071652.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071739dn5m3rlf9n412ov/14vy41256071652.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071739dn5m3rlf9n412ov/2ls241256071652.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071739dn5m3rlf9n412ov/2ls241256071652.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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