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

Title produced by software: Central Tendency

Date of computation: Sun, 16 Aug 2009 07:57:23 -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/Aug/16/t1250431061b6s388r1br4frbj.htm/, Retrieved Sun, 16 Aug 2009 15:57:44 +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/Aug/16/t1250431061b6s388r1br4frbj.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

72,84 73,96 73,26 73,86 73,04 212,8 157,92 111,55 99,01 89,5 100,95 116,06 131,5 137,43 138,53 137,26 136,81 182,98 149,45 109,34 93,37 84,09 83,83 82,94 82,88 81,41 79,87 79,66 76,07 182,69 165,78 142,5 120,6 105,73 98,72 98,41 96,08 97,3 97,5 97,02 98,75 232,81 240,83 193,4 148,28 138,34 135,34 134,02 133,86 131,67 132,43 130,21 129,98 206,16 195,17 159,16 136,33 125,18 121,21 119,38 119,26 119,75 118,78 116,97 121,69 223,51 228,58 205,22 189,4 180,14 177,59 176,39 171,16 173,11 171,74 175,97 179,64 254,62 240,5 212,01 176,36 153,24 146,69 141,52 142,6 143,19 142,32 142,03 144,92 177,31 194,4 189,19 180,44 175,84 178,54 176,55

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	141.960208333333	4.57988290372405	30.9964711582257
Geometric Mean	134.897237679770
Harmonic Mean	127.909937951084
Quadratic Mean	148.813160890315
Winsorized Mean ( 1 / 32 )	141.818645833333	4.54447395682863	31.2068343180256
Winsorized Mean ( 2 / 32 )	141.816354166667	4.54217028059167	31.2221571200527
Winsorized Mean ( 3 / 32 )	141.594791666667	4.4859828520254	31.5638281146655
Winsorized Mean ( 4 / 32 )	141.422708333333	4.44827882513249	31.7926806958017
Winsorized Mean ( 5 / 32 )	141.268541666667	4.3775404678642	32.2712131855154
Winsorized Mean ( 6 / 32 )	140.823541666667	4.21637115317159	33.3992280448883
Winsorized Mean ( 7 / 32 )	140.78125	4.20372160263974	33.489670179775
Winsorized Mean ( 8 / 32 )	140.422083333333	4.09956319056502	34.2529378877508
Winsorized Mean ( 9 / 32 )	140.471770833333	4.06401562279747	34.5647713668579
Winsorized Mean ( 10 / 32 )	139.431145833333	3.89627791309757	35.7857290838077
Winsorized Mean ( 11 / 32 )	139.444895833333	3.86753604864972	36.0552284656837
Winsorized Mean ( 12 / 32 )	139.352395833333	3.84401856997767	36.251748865548
Winsorized Mean ( 13 / 32 )	139.543333333333	3.65676962244512	38.1602747071681
Winsorized Mean ( 14 / 32 )	140.077083333333	3.57285397776317	39.2059357043834
Winsorized Mean ( 15 / 32 )	139.530208333333	3.37905529586682	41.2926679548581
Winsorized Mean ( 16 / 32 )	139.638541666667	3.35142765788468	41.6653903712194
Winsorized Mean ( 17 / 32 )	139.2896875	3.29161949706307	42.3164608255239
Winsorized Mean ( 18 / 32 )	139.2709375	3.27919676219986	42.4710523947241
Winsorized Mean ( 19 / 32 )	139.352083333333	3.24218796235817	42.9808774047687
Winsorized Mean ( 20 / 32 )	139.1875	3.20379829402101	43.4445265358167
Winsorized Mean ( 21 / 32 )	138.98625	3.17619572473081	43.758717045619
Winsorized Mean ( 22 / 32 )	138.981666666667	3.16005546485116	43.9807681265534
Winsorized Mean ( 23 / 32 )	139.264375	3.07538711303325	45.2835268801799
Winsorized Mean ( 24 / 32 )	140.419375	2.91699345717838	48.1383921703507
Winsorized Mean ( 25 / 32 )	141.351666666667	2.80052697761317	50.4732387142142
Winsorized Mean ( 26 / 32 )	141.844583333333	2.71542424602341	52.2366195783428
Winsorized Mean ( 27 / 32 )	143.076458333333	2.56565193819508	55.7661217421357
Winsorized Mean ( 28 / 32 )	142.545625	2.42998910190187	58.6610141125466
Winsorized Mean ( 29 / 32 )	142.678541666667	2.31524248464411	61.6257444362674
Winsorized Mean ( 30 / 32 )	142.647291666667	2.27504735577841	62.7008010643627
Winsorized Mean ( 31 / 32 )	140.94875	2.04499075755000	68.9239056360644
Winsorized Mean ( 32 / 32 )	138.865416666667	1.75527295146294	79.1132892185962
Trimmed Mean ( 1 / 32 )	141.497021276596	4.45887929548646	31.7337635535071
Trimmed Mean ( 2 / 32 )	141.161413043478	4.36127165609187	32.3670305761171
Trimmed Mean ( 3 / 32 )	140.812111111111	4.25104059668545	33.1241511127659
Trimmed Mean ( 4 / 32 )	140.5275	4.14909813899749	33.8694085539164
Trimmed Mean ( 5 / 32 )	140.277674418605	4.04503234097318	34.6789994724383
Trimmed Mean ( 6 / 32 )	140.051190476190	3.94587886210403	35.4930283900080
Trimmed Mean ( 7 / 32 )	139.900487804878	3.87264150682225	36.1253391408479
Trimmed Mean ( 8 / 32 )	139.7495	3.79054345866464	36.8679324017648
Trimmed Mean ( 9 / 32 )	139.646025641026	3.7172918483719	37.5666026067305
Trimmed Mean ( 10 / 32 )	139.530131578947	3.63870791359665	38.3460653869933
Trimmed Mean ( 11 / 32 )	139.542972972973	3.57836227780985	38.9963234964518
Trimmed Mean ( 12 / 32 )	139.554861111111	3.51215261088832	39.7348511219203
Trimmed Mean ( 13 / 32 )	139.578	3.43776182424677	40.6014166006345
Trimmed Mean ( 14 / 32 )	139.581764705882	3.38137418712853	41.2795972824337
Trimmed Mean ( 15 / 32 )	139.530303030303	3.32733325932854	41.9345740734309
Trimmed Mean ( 16 / 32 )	139.5303125	3.29288758226003	42.3732389929435
Trimmed Mean ( 17 / 32 )	139.519838709677	3.25415253156249	42.8744004334323
Trimmed Mean ( 18 / 32 )	139.5415	3.21510029036710	43.4019120392873
Trimmed Mean ( 19 / 32 )	139.566379310345	3.16785682443979	44.0570351013341
Trimmed Mean ( 20 / 32 )	139.585714285714	3.11453410930051	44.81752627749
Trimmed Mean ( 21 / 32 )	139.621111111111	3.05376257667156	45.721010591233
Trimmed Mean ( 22 / 32 )	139.676923076923	2.98167082360486	46.8451855822411
Trimmed Mean ( 23 / 32 )	139.7376	2.89313091558157	48.2997845854169
Trimmed Mean ( 24 / 32 )	139.77875	2.79685216966394	49.977167730247
Trimmed Mean ( 25 / 32 )	139.723043478261	2.70510790536499	51.6515600731309
Trimmed Mean ( 26 / 32 )	139.580909090909	2.60925792829740	53.4944849940491
Trimmed Mean ( 27 / 32 )	139.381904761905	2.50082497974917	55.7343700141242
Trimmed Mean ( 28 / 32 )	139.0535	2.38749228888539	58.2424917757192
Trimmed Mean ( 29 / 32 )	138.738421052632	2.26935921694241	61.1355046908612
Trimmed Mean ( 30 / 32 )	138.376111111111	2.13599522463119	64.7829683865531
Trimmed Mean ( 31 / 32 )	137.974117647059	1.95834878596613	70.4543126514569
Trimmed Mean ( 32 / 32 )	137.68625	1.79084132496703	76.8835563935485
Median	137.345
Midrange	163.73
Midmean - Weighted Average at Xnp	138.986326530612
Midmean - Weighted Average at X(n+1)p	139.77875
Midmean - Empirical Distribution Function	138.986326530612
Midmean - Empirical Distribution Function - Averaging	139.77875
Midmean - Empirical Distribution Function - Interpolation	139.77875
Midmean - Closest Observation	138.986326530612
Midmean - True Basic - Statistics Graphics Toolkit	139.77875
Midmean - MS Excel (old versions)	139.7376
Number of observations	96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431061b6s388r1br4frbj/1641h1250431041.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431061b6s388r1br4frbj/1641h1250431041.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431061b6s388r1br4frbj/2hjbr1250431041.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250431061b6s388r1br4frbj/2hjbr1250431041.ps (open in new window)

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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')

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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