Tijdreeks B - Stap 9

*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Thu, 19 Aug 2010 20:09:56 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/19/t1282248571dh9wc674mbg0u76.htm/, Retrieved Thu, 19 Aug 2010 22:09:33 +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/2010/Aug/19/t1282248571dh9wc674mbg0u76.htm/}, year = {2010}, } @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 = {2010}, 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:

Gregory Goris

Dataseries X:

» Textbox « » Textfile « » CSV «

225 224 223 221 219 218 219 221 222 222 223 225 226 229 235 229 231 229 226 232 234 230 232 231 237 241 256 255 264 259 253 258 265 258 257 255 255 255 275 276 278 268 253 257 255 253 245 248 246 243 260 262 262 251 236 238 239 243 233 238 232 224 238 236 231 209 179 179 165 174 163 166 164 152 163 167 157 138 111 110 91 100 88 89

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 219.988095238095 5.02796237417804 43.7529318771122 Geometric Mean 213.571225832828 Harmonic Mean 204.852325865385 Quadratic Mean 224.706554675839 Winsorized Mean ( 1 / 28 ) 219.976190476190 5.02095369011255 43.811635010571 Winsorized Mean ( 2 / 28 ) 220 5.00289646454903 43.9745258689521 Winsorized Mean ( 3 / 28 ) 220.071428571429 4.8738470315024 45.1535362412862 Winsorized Mean ( 4 / 28 ) 220.404761904762 4.71941094395811 46.7017525114928 Winsorized Mean ( 5 / 28 ) 220.404761904762 4.69595103507426 46.9350639004856 Winsorized Mean ( 6 / 28 ) 222.190476190476 4.17253664055507 53.2506950402522 Winsorized Mean ( 7 / 28 ) 223.357142857143 3.90174956921177 57.2453815641135 Winsorized Mean ( 8 / 28 ) 223.642857142857 3.77621427876616 59.2240907515264 Winsorized Mean ( 9 / 28 ) 224.178571428571 3.63013779036255 61.7548380735659 Winsorized Mean ( 10 / 28 ) 224.059523809524 3.61652797325259 61.9543179166984 Winsorized Mean ( 11 / 28 ) 224.190476190476 3.58998240432470 62.4489066911313 Winsorized Mean ( 12 / 28 ) 224.190476190476 3.54511438034505 63.2392786628948 Winsorized Mean ( 13 / 28 ) 224.345238095238 3.51406868579991 63.8420185131271 Winsorized Mean ( 14 / 28 ) 224.345238095238 3.46225835913309 64.7973706247073 Winsorized Mean ( 15 / 28 ) 225.416666666667 3.19648259125649 70.5202234741591 Winsorized Mean ( 16 / 28 ) 226.369047619048 3.01396537965906 75.106717929406 Winsorized Mean ( 17 / 28 ) 226.369047619048 3.01396537965906 75.106717929406 Winsorized Mean ( 18 / 28 ) 232.797619047619 1.88995743788379 123.176117293036 Winsorized Mean ( 19 / 28 ) 234.833333333333 1.60480429504561 146.33144618214 Winsorized Mean ( 20 / 28 ) 234.595238095238 1.50368824126316 156.013215810059 Winsorized Mean ( 21 / 28 ) 234.595238095238 1.50368824126316 156.013215810059 Winsorized Mean ( 22 / 28 ) 235.119047619048 1.43998358124612 163.278978094724 Winsorized Mean ( 23 / 28 ) 234.571428571429 1.35911171615704 172.591719858535 Winsorized Mean ( 24 / 28 ) 234 1.20204931152270 194.667554614362 Winsorized Mean ( 25 / 28 ) 233.404761904762 1.11990787359033 208.414252108511 Winsorized Mean ( 26 / 28 ) 233.404761904762 1.04050484343322 224.318765431813 Winsorized Mean ( 27 / 28 ) 232.761904761905 0.95579565693397 243.526849147406 Winsorized Mean ( 28 / 28 ) 233.095238095238 0.915321714150602 254.659355821735 Trimmed Mean ( 1 / 28 ) 220.890243902439 4.83703113998559 45.6664920092073 Trimmed Mean ( 2 / 28 ) 221.85 4.61999301331052 48.0195531380318 Trimmed Mean ( 3 / 28 ) 222.846153846154 4.37335486115835 50.955424592993 Trimmed Mean ( 4 / 28 ) 223.868421052632 4.13929997070287 54.0836427988132 Trimmed Mean ( 5 / 28 ) 224.851351351351 3.91820679354989 57.3862900042691 Trimmed Mean ( 6 / 28 ) 225.888888888889 3.65686673499459 61.7711569107051 Trimmed Mean ( 7 / 28 ) 226.628571428571 3.50374962877004 64.6817254200117 Trimmed Mean ( 8 / 28 ) 227.205882352941 3.39301293793347 66.962869434657 Trimmed Mean ( 9 / 28 ) 227.772727272727 3.28965287875866 69.23913727903 Trimmed Mean ( 10 / 28 ) 228.296875 3.19804935644526 71.3862888138037 Trimmed Mean ( 11 / 28 ) 228.870967741935 3.08829042391535 74.1092761126306 Trimmed Mean ( 12 / 28 ) 229.466666666667 2.95889606329303 77.5514454574276 Trimmed Mean ( 13 / 28 ) 230.103448275862 2.80735461970551 81.9645108817781 Trimmed Mean ( 14 / 28 ) 230.767857142857 2.62344463152815 87.9636849848191 Trimmed Mean ( 15 / 28 ) 231.481481481481 2.39871569712335 96.5022581705222 Trimmed Mean ( 16 / 28 ) 232.134615384615 2.17867576502459 106.548491111524 Trimmed Mean ( 17 / 28 ) 232.74 1.94029452845254 119.950861370320 Trimmed Mean ( 18 / 28 ) 233.395833333333 1.60609973793763 145.318393260579 Trimmed Mean ( 19 / 28 ) 233.456521739130 1.51600368428393 153.994692862110 Trimmed Mean ( 20 / 28 ) 233.318181818182 1.46371646334470 159.401214416235 Trimmed Mean ( 21 / 28 ) 233.190476190476 1.41759234438686 164.497556094899 Trimmed Mean ( 22 / 28 ) 233.05 1.35540229622625 171.941570889222 Trimmed Mean ( 23 / 28 ) 232.842105263158 1.28484232295800 181.222318959031 Trimmed Mean ( 24 / 28 ) 232.666666666667 1.21171529999995 192.014301269181 Trimmed Mean ( 25 / 28 ) 232.529411764706 1.15642458242052 201.076157753407 Trimmed Mean ( 26 / 28 ) 232.4375 1.10345635501335 210.644942089429 Trimmed Mean ( 27 / 28 ) 232.333333333333 1.05081613966810 221.097987138564 Trimmed Mean ( 28 / 28 ) 232.285714285714 1.00245352827034 231.717189610282 Median 232 Midrange 183 Midmean - Weighted Average at Xnp 233.318181818182 Midmean - Weighted Average at X(n+1)p 233.318181818182 Midmean - Empirical Distribution Function 233.318181818182 Midmean - Empirical Distribution Function - Averaging 233.318181818182 Midmean - Empirical Distribution Function - Interpolation 233.318181818182 Midmean - Closest Observation 233.318181818182 Midmean - True Basic - Statistics Graphics Toolkit 233.318181818182 Midmean - MS Excel (old versions) 233.318181818182 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282248571dh9wc674mbg0u76/1t8dk1282248593.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282248571dh9wc674mbg0u76/1t8dk1282248593.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282248571dh9wc674mbg0u76/2mhun1282248593.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282248571dh9wc674mbg0u76/2mhun1282248593.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

Parameters (R input):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

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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