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: Tue, 03 Aug 2010 17:22:02 +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/03/t1280856193zs9giiuyvsq82q6.htm/, Retrieved Tue, 03 Aug 2010 19:23:14 +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/03/t1280856193zs9giiuyvsq82q6.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:

Lisa Bruggeman

Dataseries X:

» Textbox « » Textfile « » CSV «

108 115 119 121 123 123 124 124 125 126 126 127 128 129 129 130 131 132 132 132 132 132 132 134 134 135 136 136 136 136 137 137 137 137 138 138 138 139 139 139 139 139 139 140 140 142 142 142 143 144 144 145 145 145 146 146 146 147 147 148 148 149 150 150 151 151 151 152 153 154 155 156 156 156 157 158 158 159 159 160 160 161 162 162

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 140.75 1.30764939130466 107.635885380233 Geometric Mean 140.23748223639 Harmonic Mean 139.716111865038 Quadratic Mean 141.253276405321 Winsorized Mean ( 1 / 28 ) 140.833333333333 1.28496238186768 109.601133325501 Winsorized Mean ( 2 / 28 ) 140.904761904762 1.25877517073947 111.9379895474 Winsorized Mean ( 3 / 28 ) 140.940476190476 1.23760071658812 113.882025358735 Winsorized Mean ( 4 / 28 ) 141.035714285714 1.21986879233072 115.615478625571 Winsorized Mean ( 5 / 28 ) 140.97619047619 1.20894735112177 116.610694705092 Winsorized Mean ( 6 / 28 ) 141.047619047619 1.19641661879667 117.891725032607 Winsorized Mean ( 7 / 28 ) 140.964285714286 1.18164466573334 119.294987572937 Winsorized Mean ( 8 / 28 ) 141.059523809524 1.16550034199134 121.029156944316 Winsorized Mean ( 9 / 28 ) 141.059523809524 1.1295020443453 124.886470560828 Winsorized Mean ( 10 / 28 ) 140.940476190476 1.10964467268592 127.014061041113 Winsorized Mean ( 11 / 28 ) 141.071428571429 1.08882416883992 129.5630943991 Winsorized Mean ( 12 / 28 ) 141.214285714286 1.06704016184548 132.342053058294 Winsorized Mean ( 13 / 28 ) 141.214285714286 1.01876701891693 138.612934156834 Winsorized Mean ( 14 / 28 ) 141.047619047619 0.99206616943605 142.17561629765 Winsorized Mean ( 15 / 28 ) 141.047619047619 0.938576081512504 150.278301169067 Winsorized Mean ( 16 / 28 ) 141.047619047619 0.883147626898456 159.71012631599 Winsorized Mean ( 17 / 28 ) 141.047619047619 0.826085190399344 170.742219672809 Winsorized Mean ( 18 / 28 ) 141.047619047619 0.826085190399344 170.742219672809 Winsorized Mean ( 19 / 28 ) 141.047619047619 0.826085190399344 170.742219672809 Winsorized Mean ( 20 / 28 ) 140.809523809524 0.792151002094543 177.755911988 Winsorized Mean ( 21 / 28 ) 140.809523809524 0.792151002094543 177.755911988 Winsorized Mean ( 22 / 28 ) 140.547619047619 0.756195440255047 185.861500302376 Winsorized Mean ( 23 / 28 ) 140.821428571429 0.647197212942055 217.586580651788 Winsorized Mean ( 24 / 28 ) 140.821428571429 0.647197212942055 217.586580651788 Winsorized Mean ( 25 / 28 ) 140.821428571429 0.57064364478226 246.776477507537 Winsorized Mean ( 26 / 28 ) 141.130952380952 0.533657683009208 264.459703053722 Winsorized Mean ( 27 / 28 ) 140.809523809524 0.491895356193459 286.259103763818 Winsorized Mean ( 28 / 28 ) 140.809523809524 0.491895356193459 286.259103763818 Trimmed Mean ( 1 / 28 ) 140.890243902439 1.25107675365237 112.615188069898 Trimmed Mean ( 2 / 28 ) 140.95 1.21174369600594 116.319977949619 Trimmed Mean ( 3 / 28 ) 140.974358974359 1.18233957028652 119.233393279898 Trimmed Mean ( 4 / 28 ) 140.986842105263 1.15735533688144 121.818112046004 Trimmed Mean ( 5 / 28 ) 140.972972972973 1.13426210676012 124.286064158173 Trimmed Mean ( 6 / 28 ) 140.972222222222 1.110303893008 126.96724123006 Trimmed Mean ( 7 / 28 ) 140.957142857143 1.0852742379449 129.881589306001 Trimmed Mean ( 8 / 28 ) 140.955882352941 1.05914509554612 133.08458203289 Trimmed Mean ( 9 / 28 ) 140.939393939394 1.03163906245753 136.616961365978 Trimmed Mean ( 10 / 28 ) 140.921875 1.00650283659285 140.011403720471 Trimmed Mean ( 11 / 28 ) 140.91935483871 0.980318855923468 143.748489572775 Trimmed Mean ( 12 / 28 ) 140.9 0.952753962465835 147.887078459726 Trimmed Mean ( 13 / 28 ) 140.862068965517 0.923396330914085 152.547789339899 Trimmed Mean ( 14 / 28 ) 140.821428571429 0.89700335998775 156.990971107791 Trimmed Mean ( 15 / 28 ) 140.796296296296 0.869701037667185 161.890454533614 Trimmed Mean ( 16 / 28 ) 140.769230769231 0.846256678243447 166.343420841797 Trimmed Mean ( 17 / 28 ) 140.74 0.82749190759962 170.080213120461 Trimmed Mean ( 18 / 28 ) 140.708333333333 0.814299471227636 172.796788288714 Trimmed Mean ( 19 / 28 ) 140.673913043478 0.796765410062804 176.556250141921 Trimmed Mean ( 20 / 28 ) 140.636363636364 0.773566265087146 181.802606943466 Trimmed Mean ( 21 / 28 ) 140.619047619048 0.750495292091991 187.368327424246 Trimmed Mean ( 22 / 28 ) 140.6 0.719508379167545 195.411205860689 Trimmed Mean ( 23 / 28 ) 140.605263157895 0.686736228984205 204.744204868692 Trimmed Mean ( 24 / 28 ) 140.583333333333 0.669488077350363 209.986313557249 Trimmed Mean ( 25 / 28 ) 140.558823529412 0.644725171133704 218.013550304309 Trimmed Mean ( 26 / 28 ) 140.53125 0.630195142268416 222.996403136577 Trimmed Mean ( 27 / 28 ) 140.466666666667 0.617248870863589 227.568932560607 Trimmed Mean ( 28 / 28 ) 140.428571428571 0.609511408604009 230.395312452315 Median 139 Midrange 135 Midmean - Weighted Average at Xnp 140.085106382979 Midmean - Weighted Average at X(n+1)p 140.085106382979 Midmean - Empirical Distribution Function 140.085106382979 Midmean - Empirical Distribution Function - Averaging 140.085106382979 Midmean - Empirical Distribution Function - Interpolation 140.085106382979 Midmean - Closest Observation 140.085106382979 Midmean - True Basic - Statistics Graphics Toolkit 140.085106382979 Midmean - MS Excel (old versions) 140.085106382979 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280856193zs9giiuyvsq82q6/1kko81280856118.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280856193zs9giiuyvsq82q6/1kko81280856118.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280856193zs9giiuyvsq82q6/2vbnb1280856118.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/03/t1280856193zs9giiuyvsq82q6/2vbnb1280856118.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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