WS3_Part 2 Central Tendency X(t)/Y(t)

*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, 18 Oct 2009 12:37:04 -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/18/t1255891228zyyn81b549fylot.htm/, Retrieved Sun, 18 Oct 2009 20:40:30 +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/18/t1255891228zyyn81b549fylot.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:

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-14,22222222 4,666666667 -1,375 -5,208333333 -9,055555556 -2,441860465 -2,95 -2,780487805 -5,9 -7,208333333 -6,642857143 -11,1875 -35,66666667 19,4 19,375 38,5 -3,5 -1,6 1400 -3,5 9,5 3,5 4,1 3,882352941 5,935483871 5,121212121 2,967741935 -1,228571429 -0,983333333 -1,350877193 -1,14893617 -0,547619048 -1,333333333 0,522727273 -2,08 16,66666667 9 7,578947368 -5,571428571 -4,111111111 -3,823529412 -0,290322581 1,952380952 -35 -10,16666667 -0,657894737 1,1 2,075757576 2,320754717 1,763157895 0,468085106 0,257575758 -1,636363636 -1,043478261 -0,483333333 -0,5 -0,625 -1,962962963 -2,366666667 -1,951219512 -2,225 -2,851851852 -0,423076923 1,290322581 2,181818182 3,633333333 6,5 11,46153846 13,4 8,307692308 3,4375 2,111111111 3,272727273 7,6 4,25 5,5 1 -1,307692308 4,363636364 2,25 1,8 1,483606557 1,24137931 0,98125 0,910179641 0,926380368 1,059171598

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 16.6747939352644 16.1134160960530 1.03483915737451 Geometric Mean NaN Harmonic Mean -19.8663055081585 Quadratic Mean 150.357161735828 Winsorized Mean ( 1 / 29 ) 1.03303148319540 1.04530594341810 0.988257542875384 Winsorized Mean ( 2 / 29 ) 1.07160108733333 0.722996166357498 1.48216703932488 Winsorized Mean ( 3 / 29 ) 1.17538461216092 0.699073930404465 1.68134522121412 Winsorized Mean ( 4 / 29 ) 1.09779840526437 0.65338777868862 1.68016366554590 Winsorized Mean ( 5 / 29 ) 0.973915902045977 0.591600286098695 1.64623974147893 Winsorized Mean ( 6 / 29 ) 0.967623535356322 0.536090904554417 1.8049616718653 Winsorized Mean ( 7 / 29 ) 0.855296686045977 0.493941718413238 1.73157409905276 Winsorized Mean ( 8 / 29 ) 0.877628377356322 0.472943332820814 1.85567343157543 Winsorized Mean ( 9 / 29 ) 0.84000048808046 0.4532987144268 1.8530837642958 Winsorized Mean ( 10 / 29 ) 0.80039162945977 0.431227853028515 1.85607590937973 Winsorized Mean ( 11 / 29 ) 0.936459048885058 0.409519423940097 2.28672681719253 Winsorized Mean ( 12 / 29 ) 0.827305163505747 0.376725161324706 2.19604435391741 Winsorized Mean ( 13 / 29 ) 0.791295654068966 0.355366643828661 2.22670210558785 Winsorized Mean ( 14 / 29 ) 0.721217789770115 0.343801731970756 2.09777241561849 Winsorized Mean ( 15 / 29 ) 0.750737120977012 0.320182113381826 2.34471911328081 Winsorized Mean ( 16 / 29 ) 0.68519278883908 0.304760774913749 2.24829717352240 Winsorized Mean ( 17 / 29 ) 0.639924669850575 0.294016685570130 2.17649099951485 Winsorized Mean ( 18 / 29 ) 0.686474526954023 0.281280276420056 2.44053559563793 Winsorized Mean ( 19 / 29 ) 0.670137540310345 0.274367426223935 2.44248214714595 Winsorized Mean ( 20 / 29 ) 0.652670783528736 0.26298917440189 2.48174011349741 Winsorized Mean ( 21 / 29 ) 0.627562602287356 0.250064163917005 2.50960630446688 Winsorized Mean ( 22 / 29 ) 0.623441699850575 0.241669339982026 2.57973022104063 Winsorized Mean ( 23 / 29 ) 0.61002330183908 0.239002796718447 2.55236888528006 Winsorized Mean ( 24 / 29 ) 0.65142554983908 0.222137550401880 2.93253233710625 Winsorized Mean ( 25 / 29 ) 0.574235405586207 0.209027582850761 2.74717526631972 Winsorized Mean ( 26 / 29 ) 0.448124282965517 0.175998856339709 2.54617724390525 Winsorized Mean ( 27 / 29 ) 0.433652310896552 0.172393855800510 2.51547428348238 Winsorized Mean ( 28 / 29 ) 0.417355037057471 0.169038061096663 2.46900037985416 Winsorized Mean ( 29 / 29 ) 0.402333021724138 0.165160698027103 2.43600945339983 Trimmed Mean ( 1 / 29 ) 1.01616163574118 0.875526142398493 1.16062969057373 Trimmed Mean ( 2 / 29 ) 0.998478783590361 0.638065535754216 1.5648530247134 Trimmed Mean ( 3 / 29 ) 0.959209398246914 0.582737791848218 1.64603945662195 Trimmed Mean ( 4 / 29 ) 0.879853939974684 0.527300546152973 1.66860047157894 Trimmed Mean ( 5 / 29 ) 0.81829170464935 0.478837473762914 1.70891325237947 Trimmed Mean ( 6 / 29 ) 0.782186890853333 0.442329565938620 1.76833508561323 Trimmed Mean ( 7 / 29 ) 0.745353584753425 0.415613215613461 1.79338278176081 Trimmed Mean ( 8 / 29 ) 0.72610801169014 0.395303395142439 1.83683727641273 Trimmed Mean ( 9 / 29 ) 0.702227084492754 0.376254361665751 1.86636264197406 Trimmed Mean ( 10 / 29 ) 0.682349329746269 0.358083512234856 1.90555919619872 Trimmed Mean ( 11 / 29 ) 0.666549821938462 0.341248905553277 1.95326581592332 Trimmed Mean ( 12 / 29 ) 0.632665113793651 0.325466215645857 1.94387338341150 Trimmed Mean ( 13 / 29 ) 0.609531665262295 0.313380929287456 1.94501837316076 Trimmed Mean ( 14 / 29 ) 0.588914367966102 0.302995344747846 1.94364163732020 Trimmed Mean ( 15 / 29 ) 0.574490310701754 0.292615304314078 1.96329550174562 Trimmed Mean ( 16 / 29 ) 0.555904283436364 0.284384379763424 1.9547637739415 Trimmed Mean ( 17 / 29 ) 0.542640014603774 0.277138536652438 1.95800995833468 Trimmed Mean ( 18 / 29 ) 0.532877886568627 0.270097038565141 1.97291273314020 Trimmed Mean ( 19 / 29 ) 0.51772719755102 0.263537658683408 1.96452833396753 Trimmed Mean ( 20 / 29 ) 0.502878709510638 0.256451055084802 1.96091495644012 Trimmed Mean ( 21 / 29 ) 0.488398809022222 0.249562203746419 1.95702234429091 Trimmed Mean ( 22 / 29 ) 0.474991001697674 0.243204366897266 1.95305293139872 Trimmed Mean ( 23 / 29 ) 0.460672586243902 0.236487560716830 1.94797808750504 Trimmed Mean ( 24 / 29 ) 0.446187065333333 0.227988227620999 1.95706186231274 Trimmed Mean ( 25 / 29 ) 0.426079240837838 0.220378846524967 1.93339445938867 Trimmed Mean ( 26 / 29 ) 0.411348285028571 0.213254856344996 1.92890465464058 Trimmed Mean ( 27 / 29 ) 0.407619250272727 0.211598023710968 1.92638495919751 Trimmed Mean ( 28 / 29 ) 0.404913304903226 0.209438955121498 1.93332374423053 Trimmed Mean ( 29 / 29 ) 0.403580262172414 0.206469277400351 1.95467464822797 Median 0.522727273 Midrange 682.166666665 Midmean - Weighted Average at Xnp 0.416923024386364 Midmean - Weighted Average at X(n+1)p 0.488398809022222 Midmean - Empirical Distribution Function 0.488398809022222 Midmean - Empirical Distribution Function - Averaging 0.488398809022222 Midmean - Empirical Distribution Function - Interpolation 0.474991001697674 Midmean - Closest Observation 0.416923024386364 Midmean - True Basic - Statistics Graphics Toolkit 0.488398809022222 Midmean - MS Excel (old versions) 0.488398809022222 Number of observations 87

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t1255891228zyyn81b549fylot/1gcg91255891020.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255891228zyyn81b549fylot/1gcg91255891020.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255891228zyyn81b549fylot/26vxo1255891020.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255891228zyyn81b549fylot/26vxo1255891020.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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