workshop 3

*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, 20 Oct 2009 14:26:18 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070418dbbad9zesjbtf59.htm/, Retrieved Tue, 20 Oct 2009 22:27:00 +0200

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/2009/Oct/20/t1256070418dbbad9zesjbtf59.htm/}, year = {2009}, } @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 = {2009}, 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:

» Textbox « » Textfile « » CSV «

-0,034795 -0,035595 -0,040445 -0,047915 -0,536795 -0,060695 -0,061025 -0,042875 -0,046685 -0,045665 -0,051215 -0,049475 -0,053005 -0,057995 -0,053865 -0,055525 -0,041365 -0,025545 -0,030895 -0,033265 -0,039005 -0,039655 -0,032505 -0,027425 -0,012485 0,000175 0,012955 0,019425 0,043625 0,032645 0,030855 0,029595 0,027335 0,028035 0,023185 0,032365 0,022555 0,007305 0,001645 -0,004275 0,001975 -0,005315 -0,003835 -0,000175 0,011705 0,021845 0,029025 0,025405 0,029075 0,020085 0,022735 0,013335 0,014395 -0,000645 0,017965 0,015675 0,008005 0,011775 0,009735 0,009625 0,016385 0,013375 0,019755 0,025035 0,013705 0,017065 0,018225 0,007095 0,005515 0,002945 0,004375 0,003265 -0,006185 -0,001595 0,010615 0,009745 0,011765 0,006025 0,004805 0,008065 0,019275 0,026545 0,039365 0,051045 0,077655

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.00696511764705882 0.0070920963632882 -0.982095742961605 Geometric Mean NaN Harmonic Mean 0.0538468793439283 Quadratic Mean 0.0653722468118948 Winsorized Mean ( 1 / 28 ) -0.00168088235294118 0.00324448295049947 -0.518074028615997 Winsorized Mean ( 2 / 28 ) -0.00184770588235294 0.0032111750704382 -0.57539867550753 Winsorized Mean ( 3 / 28 ) -0.00190276470588235 0.00316638494121918 -0.600926527003289 Winsorized Mean ( 4 / 28 ) -0.00210276470588235 0.00309649421977862 -0.679079163930326 Winsorized Mean ( 5 / 28 ) -0.00202158823529412 0.00307446793262019 -0.657540842708104 Winsorized Mean ( 6 / 28 ) -0.00206747058823529 0.00304838734932707 -0.678217808734735 Winsorized Mean ( 7 / 28 ) -0.00202382352941176 0.00300619724706892 -0.673217145476738 Winsorized Mean ( 8 / 28 ) -0.001909 0.00296852009833683 -0.64308137952967 Winsorized Mean ( 9 / 28 ) -0.00174911764705882 0.00293664879457731 -0.595616898516659 Winsorized Mean ( 10 / 28 ) -0.00172088235294118 0.00289533924367589 -0.59436294268452 Winsorized Mean ( 11 / 28 ) -0.00167947058823529 0.00286004047642257 -0.587219167728714 Winsorized Mean ( 12 / 28 ) -0.00139711764705882 0.00277551150101602 -0.503373034681134 Winsorized Mean ( 13 / 28 ) -0.00134052941176471 0.00271401517341177 -0.493928488277218 Winsorized Mean ( 14 / 28 ) -0.00124994117647059 0.00268039166116479 -0.466327811185406 Winsorized Mean ( 15 / 28 ) -0.001437 0.00261881026293951 -0.548722456275631 Winsorized Mean ( 16 / 28 ) -0.00139935294117647 0.00258815720457701 -0.540675403604461 Winsorized Mean ( 17 / 28 ) -0.000753352941176471 0.00246779701283478 -0.305273463440613 Winsorized Mean ( 18 / 28 ) -0.00073429411764706 0.00242258629068294 -0.303103390154189 Winsorized Mean ( 19 / 28 ) -0.000785705882352942 0.00232260942904625 -0.338285840282489 Winsorized Mean ( 20 / 28 ) -0.000684529411764706 0.00228461024574317 -0.299626342410117 Winsorized Mean ( 21 / 28 ) -0.000368294117647059 0.00221024031538910 -0.166630802579593 Winsorized Mean ( 22 / 28 ) 0.000491 0.00205972575885254 0.238381249489025 Winsorized Mean ( 23 / 28 ) 0.000715588235294117 0.00194720785774371 0.367494529383879 Winsorized Mean ( 24 / 28 ) 0.00432970588235294 0.00136873310933886 3.16329447487707 Winsorized Mean ( 25 / 28 ) 0.00591794117647059 0.00107584636506302 5.50073074432327 Winsorized Mean ( 26 / 28 ) 0.00597605882352941 0.00101486692458108 5.88851471930293 Winsorized Mean ( 27 / 28 ) 0.00608088235294118 0.000943989764195172 6.44168250926494 Winsorized Mean ( 28 / 28 ) 0.00580417647058824 0.000874833769112077 6.63460496784349 Trimmed Mean ( 1 / 28 ) -0.00160114457831325 0.00318076587930327 -0.503383348246924 Trimmed Mean ( 2 / 28 ) -0.00151746913580247 0.0031070104946581 -0.488401676921099 Trimmed Mean ( 3 / 28 ) -0.00133981012658228 0.00304175358051168 -0.440472934811799 Trimmed Mean ( 4 / 28 ) -0.00113266233766234 0.00298499493591994 -0.379452013144962 Trimmed Mean ( 5 / 28 ) -0.0008578 0.00294200203673351 -0.291570158446392 Trimmed Mean ( 6 / 28 ) -0.000586780821917808 0.00289722670457791 -0.202531897483423 Trimmed Mean ( 7 / 28 ) -0.000291338028169014 0.00285025341977147 -0.102214780674616 Trimmed Mean ( 8 / 28 ) 1.35507246376812e-05 0.00280372338961908 0.00483311752074166 Trimmed Mean ( 9 / 28 ) 0.000318432835820896 0.00275582789851840 0.115548883147635 Trimmed Mean ( 10 / 28 ) 0.000618846153846154 0.00270446871730834 0.228823557797359 Trimmed Mean ( 11 / 28 ) 0.00093452380952381 0.00265006791040878 0.35264145716917 Trimmed Mean ( 12 / 28 ) 0.00126565573770492 0.00259023500282941 0.48862583368783 Trimmed Mean ( 13 / 28 ) 0.00158533898305085 0.00253339064206472 0.625777547579 Trimmed Mean ( 14 / 28 ) 0.0019209649122807 0.00247443701173432 0.776324029737297 Trimmed Mean ( 15 / 28 ) 0.002271 0.00240707627673495 0.943468232373786 Trimmed Mean ( 16 / 28 ) 0.00266745283018868 0.0023333196560366 1.14320077117922 Trimmed Mean ( 17 / 28 ) 0.00309107843137255 0.00224536654203991 1.37664758670730 Trimmed Mean ( 18 / 28 ) 0.00348336734693878 0.00215997756718122 1.61268681668976 Trimmed Mean ( 19 / 28 ) 0.00390712765957447 0.00205862734002177 1.8979285777547 Trimmed Mean ( 20 / 28 ) 0.00437366666666667 0.00194743487332917 2.24586029888118 Trimmed Mean ( 21 / 28 ) 0.00487360465116279 0.00180772709542641 2.69598473325599 Trimmed Mean ( 22 / 28 ) 0.00539109756097561 0.00163790287831313 3.29146351249341 Trimmed Mean ( 23 / 28 ) 0.00587653846153846 0.00145114336876666 4.04959192042684 Trimmed Mean ( 24 / 28 ) 0.00639202702702703 0.00121650047395505 5.25443858336155 Trimmed Mean ( 25 / 28 ) 0.00660071428571429 0.00111498247984986 5.92001614823858 Trimmed Mean ( 26 / 28 ) 0.0066710606060606 0.00106877699676996 6.24177038448787 Trimmed Mean ( 27 / 28 ) 0.00674435483870968 0.00102025686576816 6.61044788327084 Trimmed Mean ( 28 / 28 ) 0.00681637931034483 0.000971722319919146 7.01473988053706 Median 0.007305 Midrange -0.22957 Midmean - Weighted Average at Xnp 0.00452714285714286 Midmean - Weighted Average at X(n+1)p 0.00487360465116279 Midmean - Empirical Distribution Function 0.00487360465116279 Midmean - Empirical Distribution Function - Averaging 0.00487360465116279 Midmean - Empirical Distribution Function - Interpolation 0.00487360465116279 Midmean - Closest Observation 0.00402409090909091 Midmean - True Basic - Statistics Graphics Toolkit 0.00487360465116279 Midmean - MS Excel (old versions) 0.00487360465116279 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070418dbbad9zesjbtf59/1ccd91256070377.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070418dbbad9zesjbtf59/1ccd91256070377.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070418dbbad9zesjbtf59/2lj1q1256070377.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256070418dbbad9zesjbtf59/2lj1q1256070377.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 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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