Central Tendency - Uitvoer

*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, 21 Dec 2008 08:28:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229873427k8x1iqprvr48a9l.htm/, Retrieved Sun, 21 Dec 2008 16:30:29 +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/2008/Dec/21/t1229873427k8x1iqprvr48a9l.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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15916,4 16535,9 15796 14418,6 15044,5 14944,2 16754,8 14254 15454,9 15644,8 14568,3 12520,2 14803 15873,2 14755,3 12875,1 14291,1 14205,3 15859,4 15258,9 15498,6 15106,5 15023,6 12083 15761,3 16943 15070,3 13659,6 14768,9 14725,1 15998,1 15370,6 14956,9 15469,7 15101,8 11703,7 16283,6 16726,5 14968,9 14861 14583,3 15305,8 17903,9 16379,4 15420,3 17870,5 15912,8 13866,5 17823,2 17872 17420,4 16704,4 15991,2 16583,6 19123,5 17838,7 17209,4 18586,5 16258,1 15141,6 19202,1 17746,5 19090,1 18040,3 17515,5 17751,8 21072,4 17170 19439,5 19795,4 17574,9 16165,4 19464,6 19932,1 19961,2 17343,4 18924,2 18574,1 21350,6 18594,6 19823,1 20844,4 19640,2 17735,4 19813,6 22238,5 20682,2 17818,6 21872,1 22117 21865,9 23451,3 20953,7 22497,3

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 17018.2095744681 259.487017804779 65.5840500940646 Geometric Mean 16838.4721471480 Harmonic Mean 16662.7006226408 Quadratic Mean 17201.2055907304 Winsorized Mean ( 1 / 31 ) 17012.0957446808 256.102394779050 66.4269295855584 Winsorized Mean ( 2 / 31 ) 17015.8914893617 253.005433935999 67.2550435958862 Winsorized Mean ( 3 / 31 ) 17023.3404255319 250.057701185206 68.077649057981 Winsorized Mean ( 4 / 31 ) 17046.3021276596 242.306816480045 70.3500725868493 Winsorized Mean ( 5 / 31 ) 17056.9776595745 240.624407446664 70.8863154846637 Winsorized Mean ( 6 / 31 ) 17045.7117021277 230.812538832902 73.8508912397865 Winsorized Mean ( 7 / 31 ) 17028.6212765957 226.264638204145 75.2597551776158 Winsorized Mean ( 8 / 31 ) 17021.6765957447 223.925004340819 76.0150776634007 Winsorized Mean ( 9 / 31 ) 17023.4191489362 220.385243817943 77.243915490998 Winsorized Mean ( 10 / 31 ) 17022.0893617021 215.210033116141 79.095240659695 Winsorized Mean ( 11 / 31 ) 16939.4723404255 200.406119213399 84.525724099212 Winsorized Mean ( 12 / 31 ) 16953.8595744681 197.561388513396 85.8156530587378 Winsorized Mean ( 13 / 31 ) 16942.9617021277 194.63445633432 87.0501658402408 Winsorized Mean ( 14 / 31 ) 16943.5723404255 194.165078811296 87.2637471380346 Winsorized Mean ( 15 / 31 ) 16946.1095744681 193.051380810230 87.7803075188886 Winsorized Mean ( 16 / 31 ) 16929.5648936170 187.729671770403 90.1805491585912 Winsorized Mean ( 17 / 31 ) 16912.8542553192 181.08629545196 93.3966549655655 Winsorized Mean ( 18 / 31 ) 16910.4797872340 180.075261113288 93.9078454346674 Winsorized Mean ( 19 / 31 ) 16864.9202127660 172.672784479976 97.669822511733 Winsorized Mean ( 20 / 31 ) 16859.8351063830 168.883077574068 99.831406133564 Winsorized Mean ( 21 / 31 ) 16857.0425531915 167.264809777792 100.780568103869 Winsorized Mean ( 22 / 31 ) 16824.2531914894 161.049416881533 104.46640240781 Winsorized Mean ( 23 / 31 ) 16751.3138297872 149.115379627820 112.337935037936 Winsorized Mean ( 24 / 31 ) 16750.4457446808 148.697952073862 112.647454191975 Winsorized Mean ( 25 / 31 ) 16756.4829787234 147.154358068975 113.870110261153 Winsorized Mean ( 26 / 31 ) 16641.2808510638 124.507129006182 133.657253073738 Winsorized Mean ( 27 / 31 ) 16615.5734042553 118.236814077094 140.52791877005 Winsorized Mean ( 28 / 31 ) 16625.3734042553 114.841927460530 144.767453593718 Winsorized Mean ( 29 / 31 ) 16640.2436170213 112.997057322432 147.262627995162 Winsorized Mean ( 30 / 31 ) 16641.1372340426 110.533651276340 150.552678228631 Winsorized Mean ( 31 / 31 ) 16640.9063829787 109.376214801200 152.143739964168 Trimmed Mean ( 1 / 31 ) 17006.0510869565 248.979594753598 68.302991270375 Trimmed Mean ( 2 / 31 ) 16999.7377777778 240.835382091918 70.5865460054768 Trimmed Mean ( 3 / 31 ) 16999.7377777778 233.403117376896 72.8342361868578 Trimmed Mean ( 4 / 31 ) 16979.3674418605 226.14592925192 75.0814639822499 Trimmed Mean ( 5 / 31 ) 16960.6416666667 220.460433496032 76.9328146448188 Trimmed Mean ( 6 / 31 ) 16960.6416666667 214.353740089254 79.1245427283169 Trimmed Mean ( 7 / 31 ) 16917.57 209.811327755272 80.6323003671801 Trimmed Mean ( 8 / 31 ) 16898.4512820513 205.577281819624 82.1999937564999 Trimmed Mean ( 9 / 31 ) 16879.4 201.117395122979 83.9280957754976 Trimmed Mean ( 10 / 31 ) 16859.0729729730 196.577265434765 85.7630862637456 Trimmed Mean ( 11 / 31 ) 16837.7902777778 192.204738950725 87.6034085824203 Trimmed Mean ( 12 / 31 ) 16837.7902777778 189.803039332462 88.7119107101568 Trimmed Mean ( 13 / 31 ) 16810.5764705882 187.354801082502 89.7258910551519 Trimmed Mean ( 14 / 31 ) 16796.0727272727 184.864692943735 90.8560334578583 Trimmed Mean ( 15 / 31 ) 16780.5984375 181.880287866895 92.2617763271878 Trimmed Mean ( 16 / 31 ) 16763.8693548387 178.396298432713 93.9698273008826 Trimmed Mean ( 17 / 31 ) 16747.645 175.032742270719 95.6829264212568 Trimmed Mean ( 18 / 31 ) 16731.8948275862 171.999754839905 97.2785969559087 Trimmed Mean ( 19 / 31 ) 16715.2410714286 168.364132007392 99.2802972470092 Trimmed Mean ( 20 / 31 ) 16701.5277777778 165.153330603656 101.127405161807 Trimmed Mean ( 21 / 31 ) 16687.2192307692 161.734092049914 103.176881381442 Trimmed Mean ( 22 / 31 ) 16672.016 157.644491890288 105.757047392451 Trimmed Mean ( 23 / 31 ) 16658.4645833333 153.620943629819 108.438759649044 Trimmed Mean ( 24 / 31 ) 16658.4645833333 150.787431111905 110.476479773506 Trimmed Mean ( 25 / 31 ) 16641.2931818182 147.081402056286 113.143422276120 Trimmed Mean ( 26 / 31 ) 16630.9809523810 142.444707908464 116.753940504888 Trimmed Mean ( 27 / 31 ) 16630.05 141.129625540239 117.835287497864 Trimmed Mean ( 28 / 31 ) 16631.3763157895 140.348611758996 118.500468991803 Trimmed Mean ( 29 / 31 ) 16631.9361111111 139.631877196467 119.112744489637 Trimmed Mean ( 30 / 31 ) 16631.1441176471 138.634070978985 119.964334886826 Trimmed Mean ( 31 / 31 ) 16631.1441176471 137.380450419436 121.059030355997 Median 16559.75 Midrange 17577.5 Midmean - Weighted Average at Xnp 16617.2702127660 Midmean - Weighted Average at X(n+1)p 16658.4645833333 Midmean - Empirical Distribution Function 16658.4645833333 Midmean - Empirical Distribution Function - Averaging 16658.4645833333 Midmean - Empirical Distribution Function - Interpolation 16650.2152173913 Midmean - Closest Observation 16658.4645833333 Midmean - True Basic - Statistics Graphics Toolkit 16658.4645833333 Midmean - MS Excel (old versions) 16658.4645833333 Number of observations 94

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229873427k8x1iqprvr48a9l/14z481229873335.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229873427k8x1iqprvr48a9l/14z481229873335.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229873427k8x1iqprvr48a9l/224f11229873335.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229873427k8x1iqprvr48a9l/224f11229873335.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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