Vicky Van der Steen - opgave 5 - oefening 2 - stap 1

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 04 Nov 2008 02:27:11 -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/04/t1225790925pqv1bt7csyebixb.htm/, Retrieved Tue, 04 Nov 2008 09:28:47 +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/04/t1225790925pqv1bt7csyebixb.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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IsPrivate?

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Dataseries X:

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2,13 1,87 2,23 3 2,12 1,6 1,17 1,02 1,22 1,8 2,13 2,21 2,38 1,99 1,82 2,47 1,94 1,39 1,11 0,97 1,38 2,39 1,88 2,11 2,11 2,17 2,54 3,13 2,25 1,39 1,36 1,33 1,6 1,95 2,23 2,53 2,36 1,95 2,16 2,76 2,09 1,49 1,17 1,3 1,26 2,17 2,03 2,18 2,61 2,58 3,86 3,81 2,41 1,47 1,33 1,38 1,57 2,6 2,18 2,36 2,24 2,41 2,51 2,98 1,87 1,9 1,47 1,45 2,71 2,9 2,11 2,18 2,24 2,05 2,42 2,77 1,99 1,47 1,09 0,93 1,32 2,03 2,04 2,78 2,8 3,03 3,11 2,75 2,78 1,76 1,29 1,28 1,43 1,71 1,89 1,84

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 2.03677083333333 0.0623959651318059 32.6426689455133 Geometric Mean 1.94449089951667 Harmonic Mean 1.85086901555908 Quadratic Mean 2.12562809345066 Winsorized Mean ( 1 / 32 ) 2.03666666666667 0.0621611281103651 32.7643131419789 Winsorized Mean ( 2 / 32 ) 2.02354166666667 0.0584111597061416 34.6430660998142 Winsorized Mean ( 3 / 32 ) 2.02510416666667 0.05790342738842 34.9738220689794 Winsorized Mean ( 4 / 32 ) 2.02260416666667 0.0571242959939088 35.4070738461676 Winsorized Mean ( 5 / 32 ) 2.02416666666667 0.0563244958291626 35.9375905077988 Winsorized Mean ( 6 / 32 ) 2.02291666666667 0.0560982683901586 36.060233670627 Winsorized Mean ( 7 / 32 ) 2.02072916666667 0.0545049983205441 37.0741992281653 Winsorized Mean ( 8 / 32 ) 2.01572916666667 0.0526332362791873 38.2976482003586 Winsorized Mean ( 9 / 32 ) 2.01572916666667 0.052060134087618 38.7192465404366 Winsorized Mean ( 10 / 32 ) 2.01677083333333 0.0519058896177518 38.8543737172284 Winsorized Mean ( 11 / 32 ) 2.01677083333333 0.0515608341924786 39.1143949650747 Winsorized Mean ( 12 / 32 ) 2.01802083333333 0.0510060238512619 39.5643628136563 Winsorized Mean ( 13 / 32 ) 2.01802083333333 0.050604811285646 39.8780428592516 Winsorized Mean ( 14 / 32 ) 2.0121875 0.0497297969039654 40.4624113765393 Winsorized Mean ( 15 / 32 ) 2.00125 0.0468279442176263 42.7362343881566 Winsorized Mean ( 16 / 32 ) 2.00291666666667 0.0461231467242066 43.4254123779348 Winsorized Mean ( 17 / 32 ) 1.999375 0.0456447025471087 43.8030020665924 Winsorized Mean ( 18 / 32 ) 1.99375 0.0443884492838459 44.9159642241788 Winsorized Mean ( 19 / 32 ) 1.99177083333333 0.0441332200711929 45.130874885638 Winsorized Mean ( 20 / 32 ) 1.9959375 0.0424164757496651 47.055712779621 Winsorized Mean ( 21 / 32 ) 1.9915625 0.0407030668606683 48.92905261457 Winsorized Mean ( 22 / 32 ) 1.9846875 0.0386725890971638 51.3202644646711 Winsorized Mean ( 23 / 32 ) 1.98229166666667 0.0383901597768238 51.6354106935335 Winsorized Mean ( 24 / 32 ) 1.98229166666667 0.0383901597768238 51.6354106935335 Winsorized Mean ( 25 / 32 ) 1.98229166666667 0.0370530319232799 53.498770917616 Winsorized Mean ( 26 / 32 ) 2.00125 0.033762018652752 59.2751879140638 Winsorized Mean ( 27 / 32 ) 2.0040625 0.0319716081987035 62.6825678440933 Winsorized Mean ( 28 / 32 ) 2.0040625 0.0319716081987035 62.6825678440933 Winsorized Mean ( 29 / 32 ) 2.0040625 0.0238216040293407 84.1279410711229 Winsorized Mean ( 30 / 32 ) 2.0165625 0.0214817487429915 93.8732932838119 Winsorized Mean ( 31 / 32 ) 2.02947916666667 0.0198841875992940 102.064977838910 Winsorized Mean ( 32 / 32 ) 2.0328125 0.0187092851074662 108.652601546426 Trimmed Mean ( 1 / 32 ) 2.02914893617021 0.0595029475582403 34.1016541102291 Trimmed Mean ( 2 / 32 ) 2.02130434782609 0.056423340421087 35.8239043052238 Trimmed Mean ( 3 / 32 ) 2.02011111111111 0.0552161781383034 36.5854932235841 Trimmed Mean ( 4 / 32 ) 2.01829545454545 0.0540519172595028 37.3399419831055 Trimmed Mean ( 5 / 32 ) 2.01709302325581 0.0529811329191042 38.0719118697532 Trimmed Mean ( 6 / 32 ) 2.01547619047619 0.0519765395580200 38.7766520744685 Trimmed Mean ( 7 / 32 ) 2.01402439024390 0.0508730936529011 39.5891864565042 Trimmed Mean ( 8 / 32 ) 2.012875 0.0499595386129388 40.2901038697482 Trimmed Mean ( 9 / 32 ) 2.0124358974359 0.0492839793370547 40.8334701155681 Trimmed Mean ( 10 / 32 ) 2.01197368421053 0.0485986137037291 41.3998163913911 Trimmed Mean ( 11 / 32 ) 2.01135135135135 0.0478165708452819 42.0638978453599 Trimmed Mean ( 12 / 32 ) 2.01069444444444 0.0469526475363893 42.8238778843326 Trimmed Mean ( 13 / 32 ) 2.00985714285714 0.0460243399720299 43.6694397807461 Trimmed Mean ( 14 / 32 ) 2.00897058823529 0.0449881165198306 44.6555833772180 Trimmed Mean ( 15 / 32 ) 2.00863636363636 0.0439022469775753 45.7524728668751 Trimmed Mean ( 16 / 32 ) 2.009375 0.0430893284720777 46.6327759389914 Trimmed Mean ( 17 / 32 ) 2.01 0.0422189904162990 47.6089072756231 Trimmed Mean ( 18 / 32 ) 2.011 0.0412356463642010 48.7684849714363 Trimmed Mean ( 19 / 32 ) 2.01258620689655 0.0402416779016537 50.0124823774767 Trimmed Mean ( 20 / 32 ) 2.01446428571429 0.0390561697097056 51.5786443137481 Trimmed Mean ( 21 / 32 ) 2.01611111111111 0.0378994372278132 53.1963337342527 Trimmed Mean ( 22 / 32 ) 2.01826923076923 0.0367625797041534 54.900098061976 Trimmed Mean ( 23 / 32 ) 2.0212 0.0356955836747006 56.6232511679739 Trimmed Mean ( 24 / 32 ) 2.02458333333333 0.0343776460404334 58.8924364091745 Trimmed Mean ( 25 / 32 ) 2.02826086956522 0.0326706657531821 62.0820183123348 Trimmed Mean ( 26 / 32 ) 2.03227272727273 0.0307428529248361 66.1055345852735 Trimmed Mean ( 27 / 32 ) 2.035 0.0290504987053413 70.0504325464761 Trimmed Mean ( 28 / 32 ) 2.03775 0.0272464711900035 74.7895015758089 Trimmed Mean ( 29 / 32 ) 2.04078947368421 0.0247645572774391 82.4076703985094 Trimmed Mean ( 30 / 32 ) 2.04416666666667 0.0237158275459760 86.1941951088908 Trimmed Mean ( 31 / 32 ) 2.04676470588235 0.0229185980579166 89.3058423866095 Trimmed Mean ( 32 / 32 ) 2.0484375 0.0222481848435023 92.0721179911564 Median 2.07 Midrange 2.395 Midmean - Weighted Average at Xnp 2.01039215686275 Midmean - Weighted Average at X(n+1)p 2.01039215686275 Midmean - Empirical Distribution Function 2.01039215686275 Midmean - Empirical Distribution Function - Averaging 2.01039215686275 Midmean - Empirical Distribution Function - Interpolation 2.01039215686275 Midmean - Closest Observation 2.01039215686275 Midmean - True Basic - Statistics Graphics Toolkit 2.01039215686275 Midmean - MS Excel (old versions) 2.01039215686275 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225790925pqv1bt7csyebixb/1xs7u1225790828.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225790925pqv1bt7csyebixb/1xs7u1225790828.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225790925pqv1bt7csyebixb/2kn471225790828.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225790925pqv1bt7csyebixb/2kn471225790828.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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