opgave 5 oefening 2 stap 1 magali Leys

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 08 Nov 2008 08:02:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/08/t1226156585ur5u25qttm24lnw.htm/, Retrieved Sat, 08 Nov 2008 15:03:07 +0000

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/2008/Nov/08/t1226156585ur5u25qttm24lnw.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0,89 0,88 0,87 0,87 0,87 0,87 0,88 0,87 0,86 0,86 0,86 0,84 0,84 0,83 0,84 0,88 0,9 0,89 0,91 0,94 0,94 0,95 0,95 0,98 0,96 1 1,05 1,03 1,07 1,12 1,1 1,06 1,11 1,08 1,07 1,02 1 1,04 1,02 1,07 1,12 1,08 1,02 1,01 1,04 0,98 0,95 0,94 0,94 0,96 0,97 1,03 1,01 0,99 1 1 1,02 1,01 0,99 0,98 1,01 1,03 1,03 1 0,96 0,97 0,98 1,02 1,04 1,01 1,01 1 1,01 1,02 1,03 1,06 1,12 1,12 1,13 1,13 1,13 1,17 1,14 1,08 1,07 1,12 1,14 1,21 1,2 1,23 1,29 1,31 1,37 1,35 1,26 1,26

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.02208333333333 0.0119556166300968 85.4898049139816 Geometric Mean 1.01568926088609 Harmonic Mean 1.00951907862445 Quadratic Mean 1.02870468713491 Winsorized Mean ( 1 / 32 ) 1.02197916666667 0.0118762070408401 86.052656639638 Winsorized Mean ( 2 / 32 ) 1.02114583333333 0.0116461628644964 87.6808821252468 Winsorized Mean ( 3 / 32 ) 1.02052083333333 0.0114873784586536 88.8384444724687 Winsorized Mean ( 4 / 32 ) 1.02010416666667 0.0110575595238854 92.2540063621762 Winsorized Mean ( 5 / 32 ) 1.02010416666667 0.0110575595238854 92.2540063621761 Winsorized Mean ( 6 / 32 ) 1.01822916666667 0.0106468375088595 95.6367715595705 Winsorized Mean ( 7 / 32 ) 1.0175 0.0102373156432215 99.3912892266563 Winsorized Mean ( 8 / 32 ) 1.01666666666667 0.0100750110646697 100.909732023207 Winsorized Mean ( 9 / 32 ) 1.01385416666667 0.00956323574358736 106.015808231697 Winsorized Mean ( 10 / 32 ) 1.01072916666667 0.00905907124086548 111.570948035740 Winsorized Mean ( 11 / 32 ) 1.01072916666667 0.00905907124086548 111.570948035740 Winsorized Mean ( 12 / 32 ) 1.01072916666667 0.00867321546393944 116.534539107090 Winsorized Mean ( 13 / 32 ) 1.01072916666667 0.00867321546393944 116.534539107090 Winsorized Mean ( 14 / 32 ) 1.01072916666667 0.00867321546393944 116.534539107090 Winsorized Mean ( 15 / 32 ) 1.01072916666667 0.00820548168249817 123.177310702246 Winsorized Mean ( 16 / 32 ) 1.01072916666667 0.00820548168249817 123.177310702246 Winsorized Mean ( 17 / 32 ) 1.0125 0.00793614869696574 127.580774839453 Winsorized Mean ( 18 / 32 ) 1.014375 0.00766172490427397 132.395121552086 Winsorized Mean ( 19 / 32 ) 1.0203125 0.00686724542729995 148.576676165361 Winsorized Mean ( 20 / 32 ) 1.01822916666667 0.00655441927999371 155.350020065797 Winsorized Mean ( 21 / 32 ) 1.01604166666667 0.00623811003532845 162.876522041530 Winsorized Mean ( 22 / 32 ) 1.01145833333333 0.00561752264548303 180.054162157518 Winsorized Mean ( 23 / 32 ) 1.01385416666667 0.00530509890375807 191.109380816344 Winsorized Mean ( 24 / 32 ) 1.01385416666667 0.00530509890375807 191.109380816344 Winsorized Mean ( 25 / 32 ) 1.01125 0.00497196085431514 203.390579618571 Winsorized Mean ( 26 / 32 ) 1.01395833333333 0.0046298970439338 219.002350098010 Winsorized Mean ( 27 / 32 ) 1.01395833333333 0.0046298970439338 219.002350098010 Winsorized Mean ( 28 / 32 ) 1.01395833333333 0.0046298970439338 219.002350098010 Winsorized Mean ( 29 / 32 ) 1.01395833333333 0.00388282081927816 261.139614864287 Winsorized Mean ( 30 / 32 ) 1.01395833333333 0.00388282081927816 261.139614864287 Winsorized Mean ( 31 / 32 ) 1.01395833333333 0.00310446469192224 326.612937802654 Winsorized Mean ( 32 / 32 ) 1.010625 0.00270968252493995 372.968047252103 Trimmed Mean ( 1 / 32 ) 1.02042553191489 0.0114464274867930 89.1479488331422 Trimmed Mean ( 2 / 32 ) 1.01880434782609 0.0109507894495196 93.0347855305335 Trimmed Mean ( 3 / 32 ) 1.01755555555556 0.0105235140206871 96.693514500503 Trimmed Mean ( 4 / 32 ) 1.01647727272727 0.0101014185414636 100.627181079064 Trimmed Mean ( 5 / 32 ) 1.01546511627907 0.0097669939966372 103.969052978705 Trimmed Mean ( 6 / 32 ) 1.01440476190476 0.00937879957882481 108.159338876913 Trimmed Mean ( 7 / 32 ) 1.01365853658537 0.00904089573536495 112.119259668074 Trimmed Mean ( 8 / 32 ) 1.013 0.0087482367120249 115.794763373010 Trimmed Mean ( 9 / 32 ) 1.01243589743590 0.00844402520639162 119.899677309057 Trimmed Mean ( 10 / 32 ) 1.01223684210526 0.00819841380510081 123.467400666636 Trimmed Mean ( 11 / 32 ) 1.01243243243243 0.00800964526573358 126.401656857859 Trimmed Mean ( 12 / 32 ) 1.01263888888889 0.00778725598983084 130.037960767087 Trimmed Mean ( 13 / 32 ) 1.01285714285714 0.00759520077614358 133.354887212266 Trimmed Mean ( 14 / 32 ) 1.01308823529412 0.00736677802560533 137.521211006066 Trimmed Mean ( 15 / 32 ) 1.01333333333333 0.00709355836788353 142.852610887260 Trimmed Mean ( 16 / 32 ) 1.01359375 0.00685148282054898 147.937866378359 Trimmed Mean ( 17 / 32 ) 1.01387096774194 0.00655834506084068 154.592501360697 Trimmed Mean ( 18 / 32 ) 1.014 0.00625358654155905 162.146952514581 Trimmed Mean ( 19 / 32 ) 1.01396551724138 0.00593338527393751 170.89156871293 Trimmed Mean ( 20 / 32 ) 1.01339285714286 0.00568820142364813 178.156992284024 Trimmed Mean ( 21 / 32 ) 1.01296296296296 0.00544735063172325 185.955160856336 Trimmed Mean ( 22 / 32 ) 1.01269230769231 0.0052113360064865 194.324892202656 Trimmed Mean ( 23 / 32 ) 1.0128 0.00503895032801111 200.994241671708 Trimmed Mean ( 24 / 32 ) 1.01270833333333 0.00488102767320286 207.478506809778 Trimmed Mean ( 25 / 32 ) 1.01260869565217 0.00467736643569723 216.491204949015 Trimmed Mean ( 26 / 32 ) 1.01272727272727 0.00448586735850506 225.759522471652 Trimmed Mean ( 27 / 32 ) 1.01261904761905 0.00431160716064513 234.858837990132 Trimmed Mean ( 28 / 32 ) 1.0125 0.00407855555124794 248.249652916999 Trimmed Mean ( 29 / 32 ) 1.01236842105263 0.00376088672026456 269.183439000635 Trimmed Mean ( 30 / 32 ) 1.01222222222222 0.00354363079679386 285.645508876952 Trimmed Mean ( 31 / 32 ) 1.01205882352941 0.00323691419492318 312.661616151808 Trimmed Mean ( 32 / 32 ) 1.011875 0.00305980378350449 330.699310019503 Median 1.01 Midrange 1.1 Midmean - Weighted Average at Xnp 1.01411764705882 Midmean - Weighted Average at X(n+1)p 1.01411764705882 Midmean - Empirical Distribution Function 1.01411764705882 Midmean - Empirical Distribution Function - Averaging 1.01411764705882 Midmean - Empirical Distribution Function - Interpolation 1.01411764705882 Midmean - Closest Observation 1.01411764705882 Midmean - True Basic - Statistics Graphics Toolkit 1.01411764705882 Midmean - MS Excel (old versions) 1.01411764705882 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226156585ur5u25qttm24lnw/1a8in1226156528.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226156585ur5u25qttm24lnw/1a8in1226156528.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226156585ur5u25qttm24lnw/2q5ke1226156528.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/08/t1226156585ur5u25qttm24lnw/2q5ke1226156528.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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We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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