Voorspelling part 3

*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: Mon, 19 Oct 2009 11:42:13 -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/19/t1255974216cepwi5rlrby2p6z.htm/, Retrieved Mon, 19 Oct 2009 19:43:38 +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/19/t1255974216cepwi5rlrby2p6z.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:

JSSWHWS3P3

Dataseries X:

» Textbox « » Textfile « » CSV «

1.3875 1.345679012 1.298701299 1.226666667 1.210526316 1.217948718 1.230769231 1.217948718 1.213333333 1.186666667 1.267605634 1.346666667 1.373333333 1.342105263 1.246753247 1.194805195 1.17721519 1.160493827 1.146341463 1.12195122 1.097560976 1.139240506 1.232876712 1.420289855 1.515151515 1.462686567 1.347826087 1.285714286 1.267605634 1.263888889 1.281690141 1.31884058 1.314285714 1.294117647 1.296875 1.253731343 1.227272727 1.203125 1.253968254 1.274193548 1.230769231 1.161764706 1.117647059 1.109375 1.114754098 1.120689655 1.131147541 1.138888889 1.191780822 1.202898551 1.295081967 1.293103448 1.258064516 1.169014085 1.090909091 1.037974684 1 0.972972973 0.973333333 1.0125

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 1.22144369383333 0.0144854508278751 84.322104182139 Geometric Mean 1.21631146684051 Harmonic Mean 1.21109970902727 Quadratic Mean 1.22650094417442 Winsorized Mean ( 1 / 20 ) 1.22057528403333 0.0142069229451624 85.9141200909343 Winsorized Mean ( 2 / 20 ) 1.2200509492 0.0135720623174284 89.8942931932525 Winsorized Mean ( 3 / 20 ) 1.21903645645 0.0130167750543996 93.6511886665791 Winsorized Mean ( 4 / 20 ) 1.21979032425 0.0123734879918837 98.5809599564903 Winsorized Mean ( 5 / 20 ) 1.222075921 0.0109380334750827 111.727206154922 Winsorized Mean ( 6 / 20 ) 1.2226251675 0.0107824329254307 113.390472814016 Winsorized Mean ( 7 / 20 ) 1.22388824388333 0.0104968551435609 116.595706727849 Winsorized Mean ( 8 / 20 ) 1.22412895708333 0.0102725812895401 119.164689242205 Winsorized Mean ( 9 / 20 ) 1.22107319878333 0.00954987321996663 127.862765364292 Winsorized Mean ( 10 / 20 ) 1.22082115378333 0.00932684120508299 130.893313924762 Winsorized Mean ( 11 / 20 ) 1.21819529795 0.00882017161862456 138.114693298901 Winsorized Mean ( 12 / 20 ) 1.21966930235 0.0084296603852265 144.687833982914 Winsorized Mean ( 13 / 20 ) 1.22095810393333 0.00807546009924435 151.193627227207 Winsorized Mean ( 14 / 20 ) 1.2208151399 0.00802640999797228 152.099773149941 Winsorized Mean ( 15 / 20 ) 1.2223368294 0.00768524786486289 159.049760124010 Winsorized Mean ( 16 / 20 ) 1.22414034993333 0.00676098738889254 181.059404421378 Winsorized Mean ( 17 / 20 ) 1.2233602579 0.00652912295355932 187.369768742537 Winsorized Mean ( 18 / 20 ) 1.2232860937 0.00584760508731322 209.194375378392 Winsorized Mean ( 19 / 20 ) 1.22379693751667 0.0051386892387583 238.153521385617 Winsorized Mean ( 20 / 20 ) 1.22694742985 0.00466560044911297 262.977390205642 Trimmed Mean ( 1 / 20 ) 1.22066374382759 0.0134127421936926 91.0077690452894 Trimmed Mean ( 2 / 20 ) 1.22075852217857 0.0124186571940174 98.3003639690342 Trimmed Mean ( 3 / 20 ) 1.22115161827778 0.0116201763285769 105.088906032747 Trimmed Mean ( 4 / 20 ) 1.22196514205769 0.0109021747801026 112.084530536777 Trimmed Mean ( 5 / 20 ) 1.2226175874 0.0102703011953997 119.043985579278 Trimmed Mean ( 6 / 20 ) 1.222753004 0.00999553503323152 122.329920302894 Trimmed Mean ( 7 / 20 ) 1.22278079454348 0.00969014914896885 126.188026184674 Trimmed Mean ( 8 / 20 ) 1.22256505765909 0.00937823986131192 130.361888343520 Trimmed Mean ( 9 / 20 ) 1.22228578990476 0.00903238711044713 135.322564783680 Trimmed Mean ( 10 / 20 ) 1.222487888425 0.0087783953864882 139.260973629266 Trimmed Mean ( 11 / 20 ) 1.22275105705263 0.00849322376427853 143.967837300528 Trimmed Mean ( 12 / 20 ) 1.22344132358333 0.0082363595618349 148.541514536645 Trimmed Mean ( 13 / 20 ) 1.22399603258824 0.00798585484770663 153.270508408970 Trimmed Mean ( 14 / 20 ) 1.224434195375 0.00772848934587472 158.431245820190 Trimmed Mean ( 15 / 20 ) 1.2249512033 0.00736018678964088 166.429363589530 Trimmed Mean ( 16 / 20 ) 1.22532468528571 0.00692952225836978 176.826719014534 Trimmed Mean ( 17 / 20 ) 1.22549550288462 0.00661596158646874 185.233164804199 Trimmed Mean ( 18 / 20 ) 1.2258095095 0.00620152181324492 197.662694160323 Trimmed Mean ( 19 / 20 ) 1.22619184522727 0.00582191456038955 210.616599145905 Trimmed Mean ( 20 / 20 ) 1.22656998855 0.0055113929563611 222.551721182270 Median 1.226969697 Midrange 1.244062244 Midmean - Weighted Average at Xnp 1.22218634209677 Midmean - Weighted Average at X(n+1)p 1.2249512033 Midmean - Empirical Distribution Function 1.22218634209677 Midmean - Empirical Distribution Function - Averaging 1.2249512033 Midmean - Empirical Distribution Function - Interpolation 1.2249512033 Midmean - Closest Observation 1.22218634209677 Midmean - True Basic - Statistics Graphics Toolkit 1.2249512033 Midmean - MS Excel (old versions) 1.224434195375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t1255974216cepwi5rlrby2p6z/1tzva1255974131.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255974216cepwi5rlrby2p6z/1tzva1255974131.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255974216cepwi5rlrby2p6z/2586s1255974131.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255974216cepwi5rlrby2p6z/2586s1255974131.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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