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Workshop8_q4b

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

Title produced by software: Central Tendency

Date of computation: Mon, 03 Dec 2007 11:24:58 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/03/t1196705602oq6eodomw60urdf.htm/, Retrieved Mon, 03 Dec 2007 19:13:24 +0100

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0.102859943244494 -0.704448721713728 -1.19519063840259 0.44691141803854 -0.122469346160724 -0.620894170508473 -0.0379463206461616 -0.812607925297044 -0.414127966779205 -0.0338608275242933 -0.0155426137374945 -2.30427479617714 0.47703432220834 -0.292263997642792 1.34785686440411 3.77455586414624 -0.112034324647126 -0.843319247014506 3.74396819713670 2.41218495263692 0.129138544811127 0.609686664979094 1.39374029362736 4.48518329911812 -3.35285565876433 4.42499955825501 3.44940240648027 -2.26985769386087 3.99778193114257 4.57247527263898 -1.25305993440814 -2.64647137378437 9.30963083756757 -4.80778100293253 -0.209769493797836 -6.79362955958386 -2.06361120145692 2.07893823001611 -2.66567420488195 5.35436331766857 3.42773241534232 -2.53000583454936 -4.67082562642099 -0.747544391686361 3.67782102794069 -8.23963319923666 -0.801720334949437 -0.906517420610001 0.817707549804723 -0.6557959936696 2.12754950254327 5.75414175899591 -2.77868745389412 -1.56734394787597 0.714114764980266 0.740316427493099 1.06258022339554 0.592187424080052 -3.4028437200746 0.653281980171059 2.48797421247258 2.52187383003347 0.256048391980144 -5.40255237539611 -3.39973024695381 1.50801148612538 -0.082947995610553 3.26238914245506 0.640420042156393 -1.00361795565095 0.495981100086695 -0.244143405650021 -0.318623059913733 -0.134199209650333 3.07757222063782 3.02404310528703 5.80457659652851 -2.21518447651957 2.79851632724939 2.25675689374799 0.628981035507024 3.83680645849256 -4.86510983423128 -2.95574620194742 -2.67743905011795 6.11161131226649 1.57364639021208 7.47553909025211 -2.93351777601697 6.90361698364063 5.64630827167207 1.72051651216142 4.50594251547807 -2.63433691013705 -8.07787467336885 -1.44961559902012

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Output produced by software:

Summary of compuational 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 0.416125304150376 0.33218352380899 1.25269700128069 Geometric Mean NaN Harmonic Mean -0.665910360858699 Quadratic Mean 3.26435600851366 Winsorized Mean ( 1 / 32 ) 0.398705166426963 0.326849021398116 1.21984506706331 Winsorized Mean ( 2 / 32 ) 0.413545229076411 0.317350977250571 1.30311629306844 Winsorized Mean ( 3 / 32 ) 0.432266213851836 0.3026107493041 1.42845624237043 Winsorized Mean ( 4 / 32 ) 0.441866539911288 0.295736277648208 1.49412355976465 Winsorized Mean ( 5 / 32 ) 0.442225602086608 0.294674356409988 1.50072645436215 Winsorized Mean ( 6 / 32 ) 0.44404572016084 0.291810160098882 1.52169383002419 Winsorized Mean ( 7 / 32 ) 0.515215081269175 0.27223510136376 1.89253729107014 Winsorized Mean ( 8 / 32 ) 0.450317200276775 0.260661606625011 1.72759312776202 Winsorized Mean ( 9 / 32 ) 0.448474246935704 0.258946876324647 1.73191603351663 Winsorized Mean ( 10 / 32 ) 0.487677396983304 0.252419439595541 1.93201204219740 Winsorized Mean ( 11 / 32 ) 0.483328350480603 0.250909028051243 1.92630912579954 Winsorized Mean ( 12 / 32 ) 0.449279937356905 0.239564588677261 1.87540211947672 Winsorized Mean ( 13 / 32 ) 0.441191896780239 0.234268709171901 1.88327283801484 Winsorized Mean ( 14 / 32 ) 0.43382939170165 0.232649527354554 1.8647336043821 Winsorized Mean ( 15 / 32 ) 0.432050511090407 0.231508083308899 1.86624373937702 Winsorized Mean ( 16 / 32 ) 0.423048393498958 0.229572034656426 1.84276971771447 Winsorized Mean ( 17 / 32 ) 0.401074557250662 0.221031593587751 1.81455759667875 Winsorized Mean ( 18 / 32 ) 0.439336003607088 0.214635919187224 2.04688947344298 Winsorized Mean ( 19 / 32 ) 0.413423532348246 0.208970546702202 1.97838182879142 Winsorized Mean ( 20 / 32 ) 0.386310260582425 0.201964360081490 1.91276451165223 Winsorized Mean ( 21 / 32 ) 0.407757420519395 0.195869569614855 2.08178034659076 Winsorized Mean ( 22 / 32 ) 0.469802112831403 0.174003838697475 2.69995257776012 Winsorized Mean ( 23 / 32 ) 0.43172893145347 0.16134127545672 2.67587404544401 Winsorized Mean ( 24 / 32 ) 0.472392943216242 0.154269618001045 3.06212557817471 Winsorized Mean ( 25 / 32 ) 0.467726285968818 0.149796152562149 3.122418553272 Winsorized Mean ( 26 / 32 ) 0.477515454931635 0.138100574298000 3.45773692368020 Winsorized Mean ( 27 / 32 ) 0.468485401635575 0.130136435239213 3.59995569860522 Winsorized Mean ( 28 / 32 ) 0.472739914447172 0.126198343446007 3.74600728930671 Winsorized Mean ( 29 / 32 ) 0.373744065614051 0.110977882561922 3.3677346961951 Winsorized Mean ( 30 / 32 ) 0.33124952448851 0.104795666597244 3.1609086066658 Winsorized Mean ( 31 / 32 ) 0.327549235055881 0.100174711393797 3.26977967291817 Winsorized Mean ( 32 / 32 ) 0.303824060880752 0.0938596249507523 3.23700484676097 Trimmed Mean ( 1 / 32 ) 0.413596080426651 0.312248498909534 1.32457347872304 Trimmed Mean ( 2 / 32 ) 0.429134425469803 0.295357255361088 1.45293341429912 Trimmed Mean ( 3 / 32 ) 0.437448663546279 0.281835777717985 1.55214028214688 Trimmed Mean ( 4 / 32 ) 0.439333190707895 0.272844337399658 1.61019720949666 Trimmed Mean ( 5 / 32 ) 0.438626209534855 0.264916298592968 1.6557162087214 Trimmed Mean ( 6 / 32 ) 0.437803491237311 0.256090741423360 1.7095639178675 Trimmed Mean ( 7 / 32 ) 0.436585495349793 0.246631699541263 1.77019213735236 Trimmed Mean ( 8 / 32 ) 0.423106137763614 0.240343221019705 1.76042467920876 Trimmed Mean ( 9 / 32 ) 0.418919820453896 0.235551948358131 1.77846043462555 Trimmed Mean ( 10 / 32 ) 0.414771830772239 0.230297244293622 1.80102819746908 Trimmed Mean ( 11 / 32 ) 0.405313811371885 0.225369258565767 1.79844320361735 Trimmed Mean ( 12 / 32 ) 0.395857503601131 0.219840650864565 1.80065653028385 Trimmed Mean ( 13 / 32 ) 0.389752082600471 0.215356752686581 1.80979736060423 Trimmed Mean ( 14 / 32 ) 0.384165858436153 0.210936879711115 1.82123609186919 Trimmed Mean ( 15 / 32 ) 0.379006010824153 0.205925230889898 1.84050302717299 Trimmed Mean ( 16 / 32 ) 0.373701560797527 0.200099198102665 1.86758150128014 Trimmed Mean ( 17 / 32 ) 0.368926060858679 0.193408782234186 1.90749384075006 Trimmed Mean ( 18 / 32 ) 0.365900320021787 0.186840683810482 1.95835463968292 Trimmed Mean ( 19 / 32 ) 0.359147613485207 0.179964476827642 1.99565836445142 Trimmed Mean ( 20 / 32 ) 0.354250538099069 0.172576260835283 2.05271881766627 Trimmed Mean ( 21 / 32 ) 0.351400784989437 0.164781144540560 2.13253030842337 Trimmed Mean ( 22 / 32 ) 0.346446355492298 0.156236384719351 2.21744989884797 Trimmed Mean ( 23 / 32 ) 0.335680762124521 0.149903064196659 2.23931888199522 Trimmed Mean ( 24 / 32 ) 0.327328747400265 0.144466037635033 2.26578338243901 Trimmed Mean ( 25 / 32 ) 0.314714469503223 0.138853773834905 2.26651722031995 Trimmed Mean ( 26 / 32 ) 0.301360710975317 0.132513761069535 2.27418426994296 Trimmed Mean ( 27 / 32 ) 0.285874579638498 0.126799953286591 2.25453221573645 Trimmed Mean ( 28 / 32 ) 0.269642506572091 0.121059967309439 2.22734659991162 Trimmed Mean ( 29 / 32 ) 0.251317928417948 0.114203312383516 2.20061855626372 Trimmed Mean ( 30 / 32 ) 0.240060352583824 0.109263640946010 2.19707443853572 Trimmed Mean ( 31 / 32 ) 0.231477842286912 0.104174461727040 2.22202100639056 Trimmed Mean ( 32 / 32 ) 0.222180610728625 0.098299619228122 2.26023877277708 Median 0.115999244027811 Midrange 0.534998819165454 Midmean - Weighted Average at Xnp 0.291064577065155 Midmean - Weighted Average at X(n+1)p 0.327328747400265 Midmean - Empirical Distribution Function 0.291064577065155 Midmean - Empirical Distribution Function - Averaging 0.327328747400265 Midmean - Empirical Distribution Function - Interpolation 0.327328747400265 Midmean - Closest Observation 0.291064577065155 Midmean - True Basic - Statistics Graphics Toolkit 0.327328747400265 Midmean - MS Excel (old versions) 0.335680762124521 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/03/t1196705602oq6eodomw60urdf/1yfi81196706295.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/03/t1196705602oq6eodomw60urdf/1yfi81196706295.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/03/t1196705602oq6eodomw60urdf/2ccen1196706295.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/03/t1196705602oq6eodomw60urdf/2ccen1196706295.ps (open in new window)

Parameters:

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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

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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