Central Tendency of Xt (Paper)

*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: Sun, 28 Nov 2010 09:54:20 +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/28/t12909379926nfijm41jghu9ba.htm/, Retrieved Sun, 28 Nov 2010 10:53:12 +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/28/t12909379926nfijm41jghu9ba.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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1.579 2.146 2.462 3.695 4.831 5.134 6.250 5.760 6.249 2.917 1.741 2.359 1.511 2.059 2.635 2.867 4.403 5.720 4.502 5.749 5.627 2.846 1.762 2.429 1.169 2.154 2.249 2.687 4.359 5.382 4.459 6.398 4.596 3.024 1.887 2.070 1.351 2.218 2.461 3.028 4.784 4.975 4.607 6.249 4.809 3.157 1.910 2.228 1.594 2.467 2.222 3.607 4.685 4.962 5.770 5.480 5.000 3.228 1.993 2.288 1.580 2.111 2.192 3.601 4.665 4.876 5.813 5.589 5.331 3.075 2.002 2.306 1.507 1.992 2.487 3.490 4.647 5.594 5.611 5.788 6.204 3.013 1.931 2.549 1.504 2.090 2.702 2.939 4.500 6.208 6.415 5.657 5.964 3.163 1.997 2.422

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 3.60682291666667 0.163052684276387 22.1205982144571 Geometric Mean 3.25010801556357 Harmonic Mean 2.91740689930285 Quadratic Mean 3.94142847809226 Winsorized Mean ( 1 / 32 ) 3.60854166666667 0.162733039995837 22.17460981961 Winsorized Mean ( 2 / 32 ) 3.60864583333333 0.161738728273415 22.3115754145972 Winsorized Mean ( 3 / 32 ) 3.60870833333333 0.161720523844694 22.3144734356593 Winsorized Mean ( 4 / 32 ) 3.608875 0.161697743158474 22.3186479261066 Winsorized Mean ( 5 / 32 ) 3.61028125 0.160855480728851 22.4442538957422 Winsorized Mean ( 6 / 32 ) 3.61009375 0.160804700031499 22.4501755812662 Winsorized Mean ( 7 / 32 ) 3.59361458333333 0.157798526866047 22.7734355618155 Winsorized Mean ( 8 / 32 ) 3.59328125 0.154258535479335 23.2938893062509 Winsorized Mean ( 9 / 32 ) 3.59290625 0.153656918106686 23.3826520424247 Winsorized Mean ( 10 / 32 ) 3.60405208333333 0.151783026529643 23.7447635993045 Winsorized Mean ( 11 / 32 ) 3.60554166666667 0.151298735744439 23.8306133156119 Winsorized Mean ( 12 / 32 ) 3.60679166666667 0.150784493825514 23.9201762406711 Winsorized Mean ( 13 / 32 ) 3.611125 0.149243876604527 24.1961350921546 Winsorized Mean ( 14 / 32 ) 3.60208333333333 0.147871892655186 24.3594862326732 Winsorized Mean ( 15 / 32 ) 3.59802083333333 0.147117196523639 24.4568338600388 Winsorized Mean ( 16 / 32 ) 3.5961875 0.146635368953673 24.5246936374276 Winsorized Mean ( 17 / 32 ) 3.60327083333333 0.145057024085907 24.8403747149767 Winsorized Mean ( 18 / 32 ) 3.60439583333333 0.144690948230417 24.9109973872962 Winsorized Mean ( 19 / 32 ) 3.58678125 0.141168631433068 25.4077780140597 Winsorized Mean ( 20 / 32 ) 3.57073958333333 0.137827025178199 25.9073979048497 Winsorized Mean ( 21 / 32 ) 3.56723958333333 0.135441038625792 26.337952067757 Winsorized Mean ( 22 / 32 ) 3.52392708333333 0.129178557102508 27.2795049145577 Winsorized Mean ( 23 / 32 ) 3.50092708333333 0.124014820531972 28.2299088795664 Winsorized Mean ( 24 / 32 ) 3.50117708333333 0.122501983509534 28.5805746407433 Winsorized Mean ( 25 / 32 ) 3.49883333333333 0.121959022693585 28.6885976622161 Winsorized Mean ( 26 / 32 ) 3.47716666666667 0.118865904347606 29.2528516545686 Winsorized Mean ( 27 / 32 ) 3.47041666666667 0.116652838779524 29.7499546772781 Winsorized Mean ( 28 / 32 ) 3.475375 0.114618874790906 30.3211404434041 Winsorized Mean ( 29 / 32 ) 3.47326041666667 0.113103930862236 30.7085738770407 Winsorized Mean ( 30 / 32 ) 3.45888541666667 0.107569017899191 32.1550338956166 Winsorized Mean ( 31 / 32 ) 3.47277083333333 0.104623787673672 33.1929373859519 Winsorized Mean ( 32 / 32 ) 3.46910416666667 0.103658526023483 33.4666553707388 Trimmed Mean ( 1 / 32 ) 3.60288297872340 0.161721055546261 22.2783790679179 Trimmed Mean ( 2 / 32 ) 3.59697826086957 0.160531241501187 22.4067180147173 Trimmed Mean ( 3 / 32 ) 3.59075555555556 0.159715028925574 22.4822646917518 Trimmed Mean ( 4 / 32 ) 3.58422727272727 0.158738068794661 22.5795066044537 Trimmed Mean ( 5 / 32 ) 3.5773488372093 0.157576901311498 22.7022413020904 Trimmed Mean ( 6 / 32 ) 3.56982142857143 0.156423159619603 22.8215657914894 Trimmed Mean ( 7 / 32 ) 3.56196341463415 0.155055805288694 22.9721383730343 Trimmed Mean ( 8 / 32 ) 3.5565375 0.154081578696455 23.0821719902448 Trimmed Mean ( 9 / 32 ) 3.55088461538462 0.153575256148103 23.1214630823097 Trimmed Mean ( 10 / 32 ) 3.54498684210526 0.15300856012451 23.1685523948500 Trimmed Mean ( 11 / 32 ) 3.53732432432432 0.152567974069358 23.1852349479075 Trimmed Mean ( 12 / 32 ) 3.52905555555556 0.152026534687778 23.2134183864896 Trimmed Mean ( 13 / 32 ) 3.52017142857143 0.151364687841085 23.2562262624106 Trimmed Mean ( 14 / 32 ) 3.51029411764706 0.150708190758019 23.291992956662 Trimmed Mean ( 15 / 32 ) 3.50075757575758 0.150030074779285 23.3337054647721 Trimmed Mean ( 16 / 32 ) 3.49103125 0.149217088725897 23.3956531373750 Trimmed Mean ( 17 / 32 ) 3.48085483870968 0.148193386037087 23.4885977828900 Trimmed Mean ( 18 / 32 ) 3.46933333333333 0.147064055890078 23.5906273109078 Trimmed Mean ( 19 / 32 ) 3.45691379310345 0.145618062948232 23.7395946842968 Trimmed Mean ( 20 / 32 ) 3.44519642857143 0.144300208844254 23.8752005708453 Trimmed Mean ( 21 / 32 ) 3.43403703703704 0.143085986577410 23.9998138125092 Trimmed Mean ( 22 / 32 ) 3.42232692307692 0.141808513108383 24.1334377468669 Trimmed Mean ( 23 / 32 ) 3.41346 0.141115663111896 24.1890937173525 Trimmed Mean ( 24 / 32 ) 3.40585416666667 0.14088207428915 24.175213091173 Trimmed Mean ( 25 / 32 ) 3.39756521739130 0.140565055862532 24.1707670270058 Trimmed Mean ( 26 / 32 ) 3.38872727272727 0.139970022325215 24.2103788827988 Trimmed Mean ( 27 / 32 ) 3.38095238095238 0.139489516265364 24.2380393270593 Trimmed Mean ( 28 / 32 ) 3.373 0.138949884896752 24.2749391444718 Trimmed Mean ( 29 / 32 ) 3.36376315789474 0.138259005269078 24.3294326568328 Trimmed Mean ( 30 / 32 ) 3.35369444444444 0.137254489731663 24.4341329088836 Trimmed Mean ( 31 / 32 ) 3.34379411764706 0.136716517012053 24.45786500948 Trimmed Mean ( 32 / 32 ) 3.3313125 0.136086883993130 24.4793061774283 Median 3.0515 Midrange 3.792 Midmean - Weighted Average at Xnp 3.38108163265306 Midmean - Weighted Average at X(n+1)p 3.40585416666667 Midmean - Empirical Distribution Function 3.38108163265306 Midmean - Empirical Distribution Function - Averaging 3.40585416666667 Midmean - Empirical Distribution Function - Interpolation 3.40585416666667 Midmean - Closest Observation 3.38108163265306 Midmean - True Basic - Statistics Graphics Toolkit 3.40585416666667 Midmean - MS Excel (old versions) 3.41346 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t12909379926nfijm41jghu9ba/1hhg51290938056.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909379926nfijm41jghu9ba/1hhg51290938056.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909379926nfijm41jghu9ba/2sqxq1290938056.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t12909379926nfijm41jghu9ba/2sqxq1290938056.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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