Tijdreeks 2 - 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: Mon, 09 Aug 2010 20:31:29 +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/09/t1281386136f3kklz0265auitq.htm/, Retrieved Mon, 09 Aug 2010 22:35:38 +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/2010/Aug/09/t1281386136f3kklz0265auitq.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:

Van Puyenbroeck Cassandra

Dataseries X:

» Textbox « » Textfile « » CSV «

408 407 406 404 402 401 402 404 405 405 406 408 405 400 402 404 410 402 400 392 390 397 394 397 400 395 391 392 395 386 385 372 367 364 364 368 370 357 350 353 353 348 337 322 315 316 317 326 329 310 301 299 300 295 274 258 250 247 248 256 253 237 225 214 221 221 207 194 191 185 180 185 189 179 162 148 152 151 134 122 119 115 113 109

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 307.940476190476 10.5631091342142 29.1524467160005 Geometric Mean 289.004151610571 Harmonic Mean 266.162274776951 Quadratic Mean 322.627365030722 Winsorized Mean ( 1 / 28 ) 307.964285714286 10.5496591786733 29.1918706091333 Winsorized Mean ( 2 / 28 ) 308.011904761905 10.5391042191315 29.2256247170205 Winsorized Mean ( 3 / 28 ) 308.119047619048 10.5037818608241 29.3341057251234 Winsorized Mean ( 4 / 28 ) 308.214285714286 10.4675970726979 29.4446073510208 Winsorized Mean ( 5 / 28 ) 308.928571428571 10.3180737787818 29.9405274716929 Winsorized Mean ( 6 / 28 ) 309.857142857143 10.111358490678 30.6444621801127 Winsorized Mean ( 7 / 28 ) 310.107142857143 10.0634393042476 30.8152246445458 Winsorized Mean ( 8 / 28 ) 310.202380952381 10.0453329855778 30.8802487083049 Winsorized Mean ( 9 / 28 ) 311.166666666667 9.83355212374624 31.6433637358016 Winsorized Mean ( 10 / 28 ) 313.190476190476 9.47573638769377 33.0518350634173 Winsorized Mean ( 11 / 28 ) 313.321428571429 9.45343937317506 33.1436439377297 Winsorized Mean ( 12 / 28 ) 313.75 9.30033520577398 33.7353431955025 Winsorized Mean ( 13 / 28 ) 313.75 9.30033520577398 33.7353431955025 Winsorized Mean ( 14 / 28 ) 314.416666666667 9.18992576733366 34.2131889448211 Winsorized Mean ( 15 / 28 ) 314.773809523810 9.1314011757629 34.4715781800608 Winsorized Mean ( 16 / 28 ) 315.154761904762 9.016598674044 34.9527325433697 Winsorized Mean ( 17 / 28 ) 317.583333333333 8.57572673437987 37.0328186951375 Winsorized Mean ( 18 / 28 ) 319.083333333333 8.34538786763754 38.2346918314848 Winsorized Mean ( 19 / 28 ) 320.666666666667 8.10799760528677 39.5494278954372 Winsorized Mean ( 20 / 28 ) 319.952380952381 8.02457686353345 39.8715578894084 Winsorized Mean ( 21 / 28 ) 320.952380952381 7.8769019097184 40.7460172325359 Winsorized Mean ( 22 / 28 ) 323.571428571429 7.3623003829605 43.9497727259690 Winsorized Mean ( 23 / 28 ) 326.309523809524 6.98077386300907 46.744032998781 Winsorized Mean ( 24 / 28 ) 326.309523809524 6.90790529275695 47.2371160258472 Winsorized Mean ( 25 / 28 ) 326.309523809524 6.7567559567189 48.2938152420678 Winsorized Mean ( 26 / 28 ) 327.238095238095 6.63094890461988 49.3501156388196 Winsorized Mean ( 27 / 28 ) 327.880952380952 6.4634859650943 50.728191281246 Winsorized Mean ( 28 / 28 ) 328.214285714286 6.33511626235354 51.808723332309 Trimmed Mean ( 1 / 28 ) 309.121951219512 10.4679921117146 29.5302048301677 Trimmed Mean ( 2 / 28 ) 310.3375 10.3687081539431 29.9301991523392 Trimmed Mean ( 3 / 28 ) 311.589743589744 10.2552088873487 30.3835589320989 Trimmed Mean ( 4 / 28 ) 312.868421052632 10.1335700937010 30.8744517637578 Trimmed Mean ( 5 / 28 ) 314.189189189189 9.99903134286073 31.4219626297621 Trimmed Mean ( 6 / 28 ) 315.416666666667 9.88083834265482 31.9220551666185 Trimmed Mean ( 7 / 28 ) 316.528571428571 9.79023727665249 32.3310418822454 Trimmed Mean ( 8 / 28 ) 317.661764705882 9.68823971191834 32.7883882058677 Trimmed Mean ( 9 / 28 ) 318.848484848485 9.56477712772981 33.3356941401272 Trimmed Mean ( 10 / 28 ) 319.96875 9.4561689559993 33.8370381799282 Trimmed Mean ( 11 / 28 ) 320.887096774194 9.39120127935927 34.1689084525815 Trimmed Mean ( 12 / 28 ) 321.85 9.30857769178878 34.5756366500446 Trimmed Mean ( 13 / 28 ) 322.827586206897 9.22810804984934 34.9830739370425 Trimmed Mean ( 14 / 28 ) 323.875 9.12051571010005 35.5106016254477 Trimmed Mean ( 15 / 28 ) 324.925925925926 9.00057657334167 36.1005679223159 Trimmed Mean ( 16 / 28 ) 326.019230769231 8.85429612491778 36.8204571170538 Trimmed Mean ( 17 / 28 ) 327.16 8.68488529878554 37.6700426942597 Trimmed Mean ( 18 / 28 ) 328.145833333333 8.55224813789772 38.3695407385592 Trimmed Mean ( 19 / 28 ) 329.065217391304 8.42055239182625 39.078815982515 Trimmed Mean ( 20 / 28 ) 329.909090909091 8.29024351951833 39.794861288738 Trimmed Mean ( 21 / 28 ) 330.904761904762 8.12323845096608 40.7355716445093 Trimmed Mean ( 22 / 28 ) 331.9 7.92616569118401 41.8739669256675 Trimmed Mean ( 23 / 28 ) 332.736842105263 7.77489890166087 42.7962917992650 Trimmed Mean ( 24 / 28 ) 333.388888888889 7.65052937039433 43.5772314238831 Trimmed Mean ( 25 / 28 ) 334.117647058824 7.4793553901044 44.6719843665779 Trimmed Mean ( 26 / 28 ) 334.9375 7.26221683418873 46.1205590038563 Trimmed Mean ( 27 / 28 ) 335.766666666667 6.97510900229306 48.1378379257275 Trimmed Mean ( 28 / 28 ) 336.642857142857 6.59609758882936 51.0366701840448 Median 342.5 Midrange 259.5 Midmean - Weighted Average at Xnp 327.488888888889 Midmean - Weighted Average at X(n+1)p 332.441860465116 Midmean - Empirical Distribution Function 327.488888888889 Midmean - Empirical Distribution Function - Averaging 332.441860465116 Midmean - Empirical Distribution Function - Interpolation 332.441860465116 Midmean - Closest Observation 327.488888888889 Midmean - True Basic - Statistics Graphics Toolkit 332.441860465116 Midmean - MS Excel (old versions) 327.488888888889 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/09/t1281386136f3kklz0265auitq/12ig21281385886.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t1281386136f3kklz0265auitq/12ig21281385886.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t1281386136f3kklz0265auitq/2u9fn1281385886.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t1281386136f3kklz0265auitq/2u9fn1281385886.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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