oef 5.2 Thomas Simons

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 19 May 2011 07:37:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305790446znweqcpacvx3ty7.htm/, Retrieved Thu, 19 May 2011 09:34:08 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

17,1 13,4 15,3 14 9,7 13,7 13,7 12,5 9,8 7 -1,9 -2,9 -6,8 -10,4 -17,2 -19,8 -16,8 -23,2 -21,7 -17,6 -13 -12,6 -4 -0,2 3,1 6,5 19,2 26,6 26,6 31,4 31,2 26,4 20,7 20,7 15 13,3 8,7 10,2 4,3 -0,1 -4,6 -3,9 -3,5 -3,4 -2,5 -1,1 0,3 -0,9 3,6 2,7 -0,2 -1 5,8 6,4 9,6 13,2 10,6 10,9 12,9 15,9 12,2 9,1 9 17,4 14,7 17 13,7 9,5 14,8 13,6 12,6 8,9 10,2 12,7 16 10,4 9,9 9,5 8,6 10 3,5 -4,2 -4,4 -1,5 -0,1 0,8 -2,4 -1,2 0,2 -1,9 -1,6 -4,2 -2,2 6,2 5,7 3,1 1,1 -0,9 0,1 -4 -4 -5,3 -8 -6,3 -3,6 -3,5 -5,1 -3,3

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4.49537037037037 1.05032868667415 4.27996533599868 Geometric Mean NaN Harmonic Mean -6.43992816210507 Quadratic Mean 11.7579642039863 Winsorized Mean ( 1 / 36 ) 4.50740740740741 1.0465495761834 4.30692201304518 Winsorized Mean ( 2 / 36 ) 4.45740740740741 1.01970224488853 4.37128331309565 Winsorized Mean ( 3 / 36 ) 4.51851851851852 1.0066309644011 4.4887537521825 Winsorized Mean ( 4 / 36 ) 4.52592592592593 1.00209400899132 4.51646840048628 Winsorized Mean ( 5 / 36 ) 4.28055555555556 0.94991706687734 4.50624133918029 Winsorized Mean ( 6 / 36 ) 4.49166666666667 0.908977117119114 4.94145186063916 Winsorized Mean ( 7 / 36 ) 4.42037037037037 0.88866244447498 4.97418383982898 Winsorized Mean ( 8 / 36 ) 4.45 0.840611518988824 5.29376519293113 Winsorized Mean ( 9 / 36 ) 4.625 0.805811494773458 5.73955575218029 Winsorized Mean ( 10 / 36 ) 4.72685185185185 0.788739992765737 5.99291514974031 Winsorized Mean ( 11 / 36 ) 4.67592592592593 0.767423517306993 6.09301880965867 Winsorized Mean ( 12 / 36 ) 4.77592592592593 0.751496568894711 6.3552198687351 Winsorized Mean ( 13 / 36 ) 4.72777777777778 0.738663993444734 6.40044434239978 Winsorized Mean ( 14 / 36 ) 4.7537037037037 0.725561128414405 6.55176182617741 Winsorized Mean ( 15 / 36 ) 4.7537037037037 0.718586293742124 6.61535537916848 Winsorized Mean ( 16 / 36 ) 4.76851851851852 0.71314931505695 6.68656397452716 Winsorized Mean ( 17 / 36 ) 4.65833333333333 0.699095896633296 6.66336815273401 Winsorized Mean ( 18 / 36 ) 4.64166666666667 0.688974040478124 6.7370704757548 Winsorized Mean ( 19 / 36 ) 4.64166666666667 0.688974040478124 6.7370704757548 Winsorized Mean ( 20 / 36 ) 4.64166666666667 0.688974040478124 6.7370704757548 Winsorized Mean ( 21 / 36 ) 4.64166666666667 0.684316119495858 6.78292755997948 Winsorized Mean ( 22 / 36 ) 4.66203703703704 0.672274850448721 6.93471878938396 Winsorized Mean ( 23 / 36 ) 4.66203703703704 0.667252750676907 6.98691317841334 Winsorized Mean ( 24 / 36 ) 4.63981481481481 0.664570874764573 6.98167041469955 Winsorized Mean ( 25 / 36 ) 4.59351851851852 0.65361877486227 7.02782523266175 Winsorized Mean ( 26 / 36 ) 4.56944444444444 0.645176015724175 7.08247723579044 Winsorized Mean ( 27 / 36 ) 4.64444444444444 0.630942271888444 7.3611242285976 Winsorized Mean ( 28 / 36 ) 4.72222222222222 0.616412388052769 7.66081654708401 Winsorized Mean ( 29 / 36 ) 4.66851851851852 0.604030033460683 7.72895097909465 Winsorized Mean ( 30 / 36 ) 4.36296296296296 0.557041511069577 7.83238390005375 Winsorized Mean ( 31 / 36 ) 4.36296296296296 0.538231326222433 8.10611116522024 Winsorized Mean ( 32 / 36 ) 4.3037037037037 0.531848149388695 8.09197833752054 Winsorized Mean ( 33 / 36 ) 4.33425925925926 0.515394981456707 8.40958762735514 Winsorized Mean ( 34 / 36 ) 4.36574074074074 0.512015817494151 8.52657396817748 Winsorized Mean ( 35 / 36 ) 4.39814814814815 0.494789362726636 8.88893027916217 Winsorized Mean ( 36 / 36 ) 4.39814814814815 0.487750577259488 9.01720746874338 Trimmed Mean ( 1 / 36 ) 4.50283018867925 1.00571454132335 4.47724478832163 Trimmed Mean ( 2 / 36 ) 4.49807692307692 0.959321997293256 4.68880827893901 Trimmed Mean ( 3 / 36 ) 4.51960784313725 0.923143447639003 4.89588899178826 Trimmed Mean ( 4 / 36 ) 4.52 0.887766463057314 5.09142909547845 Trimmed Mean ( 5 / 36 ) 4.51836734693878 0.849003260768317 5.32196701205813 Trimmed Mean ( 6 / 36 ) 4.571875 0.820207642629907 5.574045842027 Trimmed Mean ( 7 / 36 ) 4.58723404255319 0.797967324476637 5.74864897577331 Trimmed Mean ( 8 / 36 ) 4.61521739130435 0.777235128678761 5.93799382067285 Trimmed Mean ( 9 / 36 ) 4.64 0.763436935873671 6.07777772068366 Trimmed Mean ( 10 / 36 ) 4.64204545454545 0.75408106239985 6.15589713892592 Trimmed Mean ( 11 / 36 ) 4.63139534883721 0.746157070469056 6.20699787234581 Trimmed Mean ( 12 / 36 ) 4.62619047619048 0.740313463883178 6.24896169242235 Trimmed Mean ( 13 / 36 ) 4.60975609756098 0.735745007402148 6.26542627022048 Trimmed Mean ( 14 / 36 ) 4.5975 0.7320509921196 6.28030021062914 Trimmed Mean ( 15 / 36 ) 4.58205128205128 0.729253500481495 6.2832077995182 Trimmed Mean ( 16 / 36 ) 4.56578947368421 0.726557740021044 6.28413850983401 Trimmed Mean ( 17 / 36 ) 4.5472972972973 0.723716862897027 6.28325458535613 Trimmed Mean ( 18 / 36 ) 4.5375 0.721824537644392 6.28615371653576 Trimmed Mean ( 19 / 36 ) 4.52857142857143 0.720401150203025 6.28618017516376 Trimmed Mean ( 20 / 36 ) 4.51911764705882 0.718164721937497 6.29259208788054 Trimmed Mean ( 21 / 36 ) 4.50909090909091 0.714964022674574 6.30673819393467 Trimmed Mean ( 22 / 36 ) 4.4984375 0.711228300459497 6.32488540893794 Trimmed Mean ( 23 / 36 ) 4.48548387096774 0.707805117581702 6.33717355180041 Trimmed Mean ( 24 / 36 ) 4.47166666666667 0.703755429344208 6.35400663385798 Trimmed Mean ( 25 / 36 ) 4.45862068965517 0.698611683864631 6.38211583435113 Trimmed Mean ( 26 / 36 ) 4.44821428571429 0.693312166490739 6.41588955265176 Trimmed Mean ( 27 / 36 ) 4.43888888888889 0.687404992058818 6.45745803444656 Trimmed Mean ( 28 / 36 ) 4.42307692307692 0.681552965536199 6.48970387737533 Trimmed Mean ( 29 / 36 ) 4.4 0.675730896805791 6.51146783549337 Trimmed Mean ( 30 / 36 ) 4.37916666666667 0.669629663272025 6.53968440595754 Trimmed Mean ( 31 / 36 ) 4.3804347826087 0.668762066144015 6.55006467078142 Trimmed Mean ( 32 / 36 ) 4.38181818181818 0.66934754706811 6.54640209112816 Trimmed Mean ( 33 / 36 ) 4.38809523809524 0.669557053478191 6.55372864089792 Trimmed Mean ( 34 / 36 ) 4.3925 0.670986524951632 6.54633116561713 Trimmed Mean ( 35 / 36 ) 4.39473684210526 0.671455684608376 6.54508844417406 Trimmed Mean ( 36 / 36 ) 4.39444444444444 0.673287886778936 6.52684316877855 Median 3.95 Midrange 4.1 Midmean - Weighted Average at Xnp 4.29818181818182 Midmean - Weighted Average at X(n+1)p 4.43888888888889 Midmean - Empirical Distribution Function 4.29818181818182 Midmean - Empirical Distribution Function - Averaging 4.43888888888889 Midmean - Empirical Distribution Function - Interpolation 4.43888888888889 Midmean - Closest Observation 4.29818181818182 Midmean - True Basic - Statistics Graphics Toolkit 4.43888888888889 Midmean - MS Excel (old versions) 4.44821428571428 Number of observations 108

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305790446znweqcpacvx3ty7/17wjf1305790659.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305790446znweqcpacvx3ty7/17wjf1305790659.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305790446znweqcpacvx3ty7/251lg1305790659.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305790446znweqcpacvx3ty7/251lg1305790659.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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