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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, 19 Oct 2008 14:26:46 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/19/t1224448122i1py7vhh2negk9p.htm/, Retrieved Sun, 19 Oct 2008 20:28:42 +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/Oct/19/t1224448122i1py7vhh2negk9p.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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Dataseries X:

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93.9 97.5 98.1 89.6 98.4 102 99.2 101.8 108.3 106.7 108.2 94.2 95.1 98.1 93.2 94 97.2 95 90.5 91.6 90.5 79.9 74.9 74.3 75.9 77.7 86.9 90.7 91 89.5 92.5 94.1 98.5 96.8 91.2 97.1 104.9 110.9 104.8 94.1 95.8 99.3 101.1 104 99 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179 190.6 190 181.6 174.8 180.5 196.8 193.8 197 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 158.5 7.79527597222808 20.3328272872804 Geometric Mean 142.589383443550 Harmonic Mean 130.339104146971 Quadratic Mean 177.147344690146 Winsorized Mean ( 1 / 34 ) 158.443269230769 7.7750404647066 20.3784494691692 Winsorized Mean ( 2 / 34 ) 158.002884615385 7.63582713060635 20.6923077111147 Winsorized Mean ( 3 / 34 ) 157.463461538462 7.46679593644809 21.0884913527402 Winsorized Mean ( 4 / 34 ) 156.971153846154 7.30796286742173 21.4794679028704 Winsorized Mean ( 5 / 34 ) 156.639423076923 7.10913162498025 22.0335522451883 Winsorized Mean ( 6 / 34 ) 155.549038461538 6.80594222026508 22.8548867191940 Winsorized Mean ( 7 / 34 ) 154.418269230769 6.55928580939978 23.5419333320527 Winsorized Mean ( 8 / 34 ) 153.8875 6.42945542805778 23.9347642614402 Winsorized Mean ( 9 / 34 ) 153.515384615385 6.35499350408406 24.1566548442146 Winsorized Mean ( 10 / 34 ) 151.842307692308 6.02989854170682 25.181569248979 Winsorized Mean ( 11 / 34 ) 150.234615384615 5.73752808021927 26.1845542686867 Winsorized Mean ( 12 / 34 ) 149.542307692308 5.616273114563 26.6266088991549 Winsorized Mean ( 13 / 34 ) 148.429807692308 5.42649484500375 27.3527962214815 Winsorized Mean ( 14 / 34 ) 148.079807692308 5.34226360220635 27.7185512955877 Winsorized Mean ( 15 / 34 ) 147.964423076923 5.29956120717116 27.9201272129291 Winsorized Mean ( 16 / 34 ) 147.718269230769 5.23615189951128 28.2112268829628 Winsorized Mean ( 17 / 34 ) 147.146153846154 5.14850774929783 28.5803500764318 Winsorized Mean ( 18 / 34 ) 147.111538461538 5.13927465359379 28.6249613763426 Winsorized Mean ( 19 / 34 ) 146.727884615385 5.08423783279494 28.8593668197312 Winsorized Mean ( 20 / 34 ) 146.074038461538 4.98724755289246 29.289510278434 Winsorized Mean ( 21 / 34 ) 145.9125 4.92598801186292 29.6209612464766 Winsorized Mean ( 22 / 34 ) 144.706730769231 4.75631635861771 30.4241181323115 Winsorized Mean ( 23 / 34 ) 144.198076923077 4.65227846175164 30.9951517538322 Winsorized Mean ( 24 / 34 ) 143.667307692308 4.5293127612748 31.7194495643246 Winsorized Mean ( 25 / 34 ) 143.114423076923 4.44155882196629 32.2216655938749 Winsorized Mean ( 26 / 34 ) 142.439423076923 4.35026297314643 32.7427155452859 Winsorized Mean ( 27 / 34 ) 142.05 4.28390944517139 33.158964216695 Winsorized Mean ( 28 / 34 ) 142.157692307692 4.26094134648141 33.3629779778788 Winsorized Mean ( 29 / 34 ) 142.101923076923 4.25400131913984 33.4042968998552 Winsorized Mean ( 30 / 34 ) 141.380769230769 4.14548376161997 34.1047697592525 Winsorized Mean ( 31 / 34 ) 140.486538461538 4.02985151641899 34.8614676965512 Winsorized Mean ( 32 / 34 ) 140.609615384615 4.01059917582447 35.0595033859772 Winsorized Mean ( 33 / 34 ) 140.482692307692 3.98119375796237 35.2865750446653 Winsorized Mean ( 34 / 34 ) 137.769230769231 3.65181778139594 37.7262062392848 Trimmed Mean ( 1 / 34 ) 156.824509803922 7.49345737227923 20.9281913558442 Trimmed Mean ( 2 / 34 ) 155.141 7.16926691306071 21.6397299586335 Trimmed Mean ( 3 / 34 ) 153.622448979592 6.88280674419335 22.3197388346251 Trimmed Mean ( 4 / 34 ) 152.235416666667 6.6281702079224 22.9679401540874 Trimmed Mean ( 5 / 34 ) 150.925531914894 6.39099667999032 23.6153356779904 Trimmed Mean ( 6 / 34 ) 149.633695652174 6.17635498579804 24.2268613116058 Trimmed Mean ( 7 / 34 ) 148.494444444444 6.00848866045358 24.7141091272750 Trimmed Mean ( 8 / 34 ) 147.494318181818 5.87263244230295 25.1155371344811 Trimmed Mean ( 9 / 34 ) 146.527906976744 5.74278126566632 25.5151467900707 Trimmed Mean ( 10 / 34 ) 145.566666666667 5.6065932555058 25.9634790741627 Trimmed Mean ( 11 / 34 ) 144.770731707317 5.51014981120293 26.273465634814 Trimmed Mean ( 12 / 34 ) 144.125 5.44859129976719 26.4517913109317 Trimmed Mean ( 13 / 34 ) 143.523076923077 5.39511808129769 26.6023977159283 Trimmed Mean ( 14 / 34 ) 143.006578947368 5.36049432635642 26.6778715246904 Trimmed Mean ( 15 / 34 ) 143.006578947368 5.32958080827216 26.8326129374762 Trimmed Mean ( 16 / 34 ) 141.970833333333 5.29612624456374 26.8065425137969 Trimmed Mean ( 17 / 34 ) 141.437142857143 5.26241730638464 26.8768390309039 Trimmed Mean ( 18 / 34 ) 140.923529411765 5.23179779375389 26.9359663670507 Trimmed Mean ( 19 / 34 ) 140.381818181818 5.19267051544857 27.0346092177757 Trimmed Mean ( 20 / 34 ) 139.8390625 5.15027190354971 27.1517824920310 Trimmed Mean ( 21 / 34 ) 139.316129032258 5.1100171186271 27.2633390061300 Trimmed Mean ( 22 / 34 ) 138.771666666667 5.0659046919972 27.393264402682 Trimmed Mean ( 23 / 34 ) 138.287931034483 5.03414420233333 27.4699979731185 Trimmed Mean ( 24 / 34 ) 137.810714285714 5.00565827798087 27.5309872613404 Trimmed Mean ( 25 / 34 ) 137.340740740741 4.98330652728921 27.5601631143189 Trimmed Mean ( 26 / 34 ) 136.878846153846 4.96265718530934 27.5817653814655 Trimmed Mean ( 27 / 34 ) 136.434 4.94437764392186 27.5937660562232 Trimmed Mean ( 28 / 34 ) 135.983333333333 4.92411324534226 27.615801375397 Trimmed Mean ( 29 / 34 ) 135.484782608696 4.89284893486738 27.6903669850105 Trimmed Mean ( 30 / 34 ) 135.484782608696 4.84485784219221 27.9646559345468 Trimmed Mean ( 31 / 34 ) 134.414285714286 4.79540596481121 28.0298032534931 Trimmed Mean ( 32 / 34 ) 133.905 4.74548901859872 28.2173237521347 Trimmed Mean ( 33 / 34 ) 133.331578947368 4.67168935615835 28.5403349372122 Trimmed Mean ( 34 / 34 ) 132.705555555556 4.56827560194311 29.049375983163 Median 129.65 Midrange 243.95 Midmean - Weighted Average at Xnp 136.128301886792 Midmean - Weighted Average at X(n+1)p 136.878846153846 Midmean - Empirical Distribution Function 136.128301886792 Midmean - Empirical Distribution Function - Averaging 136.878846153846 Midmean - Empirical Distribution Function - Interpolation 136.878846153846 Midmean - Closest Observation 136.128301886792 Midmean - True Basic - Statistics Graphics Toolkit 136.878846153846 Midmean - MS Excel (old versions) 137.340740740741 Number of observations 104

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/19/t1224448122i1py7vhh2negk9p/14o6z1224447999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/19/t1224448122i1py7vhh2negk9p/14o6z1224447999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/19/t1224448122i1py7vhh2negk9p/27s7h1224447999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/19/t1224448122i1py7vhh2negk9p/27s7h1224447999.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 do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

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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