Central Tendency Minitutorial

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 23 Nov 2010 10:50:07 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290509419d2sb9vxxoefignc.htm/, Retrieved Tue, 23 Nov 2010 11:50:19 +0100

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/2010/Nov/23/t1290509419d2sb9vxxoefignc.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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55 20 80 52 75 30 90 68 24 60 65 60 80 65 90 65 76 70 38 60 10 5 93 70 61 72 40 75 100 29 70 25 70 82 40 50 70 91 10 25 56 30 74 60 80 80 60 64 40 80 71 65 90 68 76 25 79 40 61 27 70 40 13 15 38 47 65 62 50 80 87 40 80 20 60 48 70 91 10 50 70 45 20 10 90 80 74 71 40 29 60 31 67 82 40 30 70 63 35 35 70 60 80 70 71

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 56.8190476190476 2.26543468535795 25.0808588684029 Geometric Mean 49.9214664639798 Harmonic Mean 39.4823902597134 Quadratic Mean 61.3363870875387 Winsorized Mean ( 1 / 35 ) 56.8 2.24413766203276 25.3103902496561 Winsorized Mean ( 2 / 35 ) 56.7619047619048 2.23838163548279 25.3584571380125 Winsorized Mean ( 3 / 35 ) 56.7619047619048 2.23838163548279 25.3584571380125 Winsorized Mean ( 4 / 35 ) 56.7238095238095 2.23285060818654 25.4042116905793 Winsorized Mean ( 5 / 35 ) 56.8666666666667 2.20480937298089 25.7921012870983 Winsorized Mean ( 6 / 35 ) 56.9809523809524 2.18331086386591 26.0984147168389 Winsorized Mean ( 7 / 35 ) 57.3142857142857 2.1243104585073 26.9801833742131 Winsorized Mean ( 8 / 35 ) 57.0857142857143 2.09167696036962 27.2918406461898 Winsorized Mean ( 9 / 35 ) 56.6571428571429 2.03651773875448 27.8205987499987 Winsorized Mean ( 10 / 35 ) 57.0380952380952 1.97284327502842 28.9116200764977 Winsorized Mean ( 11 / 35 ) 56.9333333333333 1.93129550299852 29.4793485745391 Winsorized Mean ( 12 / 35 ) 56.9333333333333 1.93129550299852 29.4793485745391 Winsorized Mean ( 13 / 35 ) 56.9333333333333 1.93129550299852 29.4793485745391 Winsorized Mean ( 14 / 35 ) 57.2 1.88959944977397 30.2709656307543 Winsorized Mean ( 15 / 35 ) 57.4857142857143 1.84644566418570 31.1331740764038 Winsorized Mean ( 16 / 35 ) 57.4857142857143 1.84644566418570 31.1331740764038 Winsorized Mean ( 17 / 35 ) 57.647619047619 1.82262846828505 31.6288371715498 Winsorized Mean ( 18 / 35 ) 57.647619047619 1.82262846828505 31.6288371715498 Winsorized Mean ( 19 / 35 ) 57.647619047619 1.82262846828505 31.6288371715498 Winsorized Mean ( 20 / 35 ) 57.647619047619 1.77270622324059 32.5195558586331 Winsorized Mean ( 21 / 35 ) 57.847619047619 1.59180484522169 36.3408989621229 Winsorized Mean ( 22 / 35 ) 57.847619047619 1.59180484522169 36.3408989621229 Winsorized Mean ( 23 / 35 ) 58.2857142857143 1.47914156161212 39.4050953596278 Winsorized Mean ( 24 / 35 ) 58.2857142857143 1.47914156161212 39.4050953596278 Winsorized Mean ( 25 / 35 ) 58.5238095238095 1.39156901708879 42.0559877412643 Winsorized Mean ( 26 / 35 ) 58.5238095238095 1.39156901708879 42.0559877412643 Winsorized Mean ( 27 / 35 ) 58.0095238095238 1.33818909112546 43.3492726806911 Winsorized Mean ( 28 / 35 ) 57.7428571428571 1.31182481823660 44.0172013367432 Winsorized Mean ( 29 / 35 ) 57.7428571428571 1.31182481823660 44.0172013367432 Winsorized Mean ( 30 / 35 ) 57.7428571428571 1.31182481823660 44.0172013367432 Winsorized Mean ( 31 / 35 ) 57.447619047619 1.28359477992244 44.7552607304078 Winsorized Mean ( 32 / 35 ) 57.447619047619 1.28359477992244 44.7552607304078 Winsorized Mean ( 33 / 35 ) 59.0190476190476 1.08266231281331 54.5128863548286 Winsorized Mean ( 34 / 35 ) 59.6666666666667 1.00298699193105 59.4889735825887 Winsorized Mean ( 35 / 35 ) 60 0.962768444083559 62.3202810278154 Trimmed Mean ( 1 / 35 ) 56.9029126213592 2.21388736631356 25.7027134655503 Trimmed Mean ( 2 / 35 ) 57.009900990099 2.17976722571879 26.1541233932901 Trimmed Mean ( 3 / 35 ) 57.1414141414141 2.14458853098335 26.6444650411393 Trimmed Mean ( 4 / 35 ) 57.2783505154639 2.10473928624599 27.2139883974065 Trimmed Mean ( 5 / 35 ) 57.4315789473684 2.06130307189821 27.8617830295478 Trimmed Mean ( 6 / 35 ) 57.5591397849462 2.01985599109836 28.4966552262207 Trimmed Mean ( 7 / 35 ) 57.6703296703297 1.97796499714427 29.1563954638188 Trimmed Mean ( 8 / 35 ) 57.7303370786517 1.9433212441207 29.707047794238 Trimmed Mean ( 9 / 35 ) 57.8275862068966 1.91004651921722 30.2754857670144 Trimmed Mean ( 10 / 35 ) 57.9882352941176 1.88161487631191 30.8183337749638 Trimmed Mean ( 11 / 35 ) 58.1084337349398 1.85999946664643 31.2411023642437 Trimmed Mean ( 12 / 35 ) 58.2469135802469 1.84127328329194 31.6340404810033 Trimmed Mean ( 13 / 35 ) 58.3924050632911 1.81901115922282 32.1011802303838 Trimmed Mean ( 14 / 35 ) 58.5454545454545 1.79260894794183 32.6593564160623 Trimmed Mean ( 15 / 35 ) 58.68 1.76799983694101 33.1900483099185 Trimmed Mean ( 16 / 35 ) 58.7945205479452 1.74539608621040 33.6854889342622 Trimmed Mean ( 17 / 35 ) 58.9154929577465 1.71825873196359 34.2879054602093 Trimmed Mean ( 18 / 35 ) 59.0289855072464 1.68944002366477 34.9399710438962 Trimmed Mean ( 19 / 35 ) 59.1492537313433 1.65476351867367 35.7448378960835 Trimmed Mean ( 20 / 35 ) 59.2769230769231 1.61297439239826 36.7500707737751 Trimmed Mean ( 21 / 35 ) 59.4126984126984 1.57043781187286 37.8319332122069 Trimmed Mean ( 22 / 35 ) 59.5409836065574 1.54717683499291 38.4836317736299 Trimmed Mean ( 23 / 35 ) 59.6779661016949 1.51814289446754 39.3098477878303 Trimmed Mean ( 24 / 35 ) 59.7894736842105 1.49994503702670 39.8611097128795 Trimmed Mean ( 25 / 35 ) 59.9090909090909 1.47647608667634 40.5757271991792 Trimmed Mean ( 26 / 35 ) 60.0188679245283 1.46053317650749 41.0938066248169 Trimmed Mean ( 27 / 35 ) 60.0188679245283 1.43923171439491 41.7020187397426 Trimmed Mean ( 28 / 35 ) 60.3061224489796 1.41877716391408 42.5057041957235 Trimmed Mean ( 29 / 35 ) 60.5106382978723 1.39474112745146 43.3848526489217 Trimmed Mean ( 30 / 35 ) 60.7333333333333 1.36196530607409 44.5924232155363 Trimmed Mean ( 31 / 35 ) 60.9767441860465 1.31752325281101 46.2813419466786 Trimmed Mean ( 32 / 35 ) 61.2682926829268 1.26154395834391 48.5661179522881 Trimmed Mean ( 33 / 35 ) 61.5897435897436 1.18396731722474 52.0198004570871 Trimmed Mean ( 34 / 35 ) 61.8108108108108 1.13954171142123 54.2418151010205 Trimmed Mean ( 35 / 35 ) 62 1.10080184678368 56.3225799276697 Median 62 Midrange 52.5 Midmean - Weighted Average at Xnp 59.377358490566 Midmean - Weighted Average at X(n+1)p 59.9090909090909 Midmean - Empirical Distribution Function 59.9090909090909 Midmean - Empirical Distribution Function - Averaging 59.9090909090909 Midmean - Empirical Distribution Function - Interpolation 59.9090909090909 Midmean - Closest Observation 59.9090909090909 Midmean - True Basic - Statistics Graphics Toolkit 59.9090909090909 Midmean - MS Excel (old versions) 59.9090909090909 Number of observations 105

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290509419d2sb9vxxoefignc/1sea01290509403.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290509419d2sb9vxxoefignc/1sea01290509403.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290509419d2sb9vxxoefignc/23oal1290509403.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290509419d2sb9vxxoefignc/23oal1290509403.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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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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