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ct residuals: bel 20

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Wed, 30 Dec 2009 07:03:22 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/30/t126218184814kqsfxkpfewh7u.htm/, Retrieved Wed, 30 Dec 2009 15:04:11 +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/2009/Dec/30/t126218184814kqsfxkpfewh7u.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 «
3.03292826890205 12.0260515677640 59.7475455407064 -114.465065205481 -2.22693508199627 4.35951995596352 -147.147615338686 65.153572198053 -58.9442153086111 94.5064127441215 54.0497539166126 -31.9582830652207 -291.427228013426 103.210014980995 13.4184752845463 25.848767749962 81.7651411018169 0.0342656138418533 -13.8542282976155 63.9062793697858 -37.9084354029856 -239.488697273233 -197.314334937415 -18.3811532105201 -78.8708128245712 -37.8295732489139 153.835701431603 -46.2523335694268 -13.131794384233 -185.299119376881 -72.9117819276823 243.825225144514 56.6148178109725 51.4504706290238 -39.3475780548667 74.1339479106434 -2.27501727330446 16.1353440571070 29.3431180387506 1.19479122514349 142.274824521032 37.8895641544145 -61.2157143422046 44.3522168977665 -99.399814019555 69.8361993067019 -30.5517825502993 62.8935794195445 125.965949022935 71.5094060664719 52.3393013125101 19.3218862161034 19.4930838292207 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-2.5384380791427213.3406261203776-0.190278781238408
Geometric MeanNaN
Harmonic Mean3.48712742822243
Quadratic Mean139.940691898706
Winsorized Mean ( 1 / 37 )-0.45613138049444812.5530549477827-0.0363362848638702
Winsorized Mean ( 2 / 37 )0.58387262601171412.23732064948260.0477124562423229
Winsorized Mean ( 3 / 37 )1.7567305685848811.73479441492630.149702713696489
Winsorized Mean ( 4 / 37 )1.8151918499624611.68572146622050.155334170441215
Winsorized Mean ( 5 / 37 )1.3464052905176411.47198466292380.117364634810668
Winsorized Mean ( 6 / 37 )1.9332057483533711.18667081983490.172813322166023
Winsorized Mean ( 7 / 37 )2.6830254058370110.50802331394010.255331124197037
Winsorized Mean ( 8 / 37 )2.1500029119905210.05373287232630.213851207237520
Winsorized Mean ( 9 / 37 )4.311551221570179.608537704932970.448720851598121
Winsorized Mean ( 10 / 37 )5.253511150418739.38541559479820.55975263933229
Winsorized Mean ( 11 / 37 )4.953091427089639.151373037413630.541240249614989
Winsorized Mean ( 12 / 37 )8.324074734675478.528979385756720.97597547821215
Winsorized Mean ( 13 / 37 )10.94452754170297.810190615226051.40131375543721
Winsorized Mean ( 14 / 37 )10.19340975187817.647903593116181.33283711382726
Winsorized Mean ( 15 / 37 )11.24188185498487.493457099919091.50022635815265
Winsorized Mean ( 16 / 37 )10.72595008452487.132295265122161.50385670893016
Winsorized Mean ( 17 / 37 )11.41175552767036.719476754935221.69831014286772
Winsorized Mean ( 18 / 37 )11.65435973766376.60484067156991.76451792210964
Winsorized Mean ( 19 / 37 )11.4141349162686.537897528506211.74584181940764
Winsorized Mean ( 20 / 37 )10.45126399946536.370520522629041.64056672643010
Winsorized Mean ( 21 / 37 )10.28400353562806.279286060484441.63776636970646
Winsorized Mean ( 22 / 37 )9.93716408675386.209779992384841.60024414696494
Winsorized Mean ( 23 / 37 )9.162026082655556.101377945897791.50163228108424
Winsorized Mean ( 24 / 37 )8.760729636348986.016266995449731.45617367762684
Winsorized Mean ( 25 / 37 )10.00247705014535.828888142170581.71601801341491
Winsorized Mean ( 26 / 37 )10.10686728211855.621181713442271.79799689768956
Winsorized Mean ( 27 / 37 )10.16465179306475.166140702173411.96755225594
Winsorized Mean ( 28 / 37 )10.07559594895505.020250239538482.00699078097773
Winsorized Mean ( 29 / 37 )12.27743168144474.648426143920942.64120183935818
Winsorized Mean ( 30 / 37 )11.71211594934634.424103028944622.64734249467518
Winsorized Mean ( 31 / 37 )13.49714097457764.182567799202733.22699872962021
Winsorized Mean ( 32 / 37 )13.70040270251924.111559559225833.33216690775576
Winsorized Mean ( 33 / 37 )13.42277524960394.075558896802313.29348086716043
Winsorized Mean ( 34 / 37 )14.24278838769433.767910764239213.78002274440013
Winsorized Mean ( 35 / 37 )13.27017523531303.658778371041643.62694153336623
Winsorized Mean ( 36 / 37 )12.89442495008973.518504168475043.66474624802797
Winsorized Mean ( 37 / 37 )16.70864326124433.051532936238175.47549169888436
Trimmed Mean ( 1 / 37 )1.1668666977759811.96128511094740.0975536229554486
Trimmed Mean ( 2 / 37 )2.8505376014023211.28281225970670.252644246468782
Trimmed Mean ( 3 / 37 )4.0486319455373510.70378081912570.378243166031874
Trimmed Mean ( 4 / 37 )4.8719363236659210.26689106827240.474528880385375
Trimmed Mean ( 5 / 37 )5.711784434015139.785402332135280.583704608164921
Trimmed Mean ( 6 / 37 )6.690687635890339.297300177440630.719637691393992
Trimmed Mean ( 7 / 37 )6.690687635890338.812980531223990.75918556862636
Trimmed Mean ( 8 / 37 )8.418443766554068.422781412434740.999485010275314
Trimmed Mean ( 9 / 37 )9.353654700501048.074407469344441.15843233525351
Trimmed Mean ( 10 / 37 )10.03701671046607.767911199741981.29211269958897
Trimmed Mean ( 11 / 37 )10.63361122413497.459187212482451.42557237420455
Trimmed Mean ( 12 / 37 )11.29248029150377.145903853594021.5802731918684
Trimmed Mean ( 13 / 37 )11.61551266092336.898543517741611.68376304810582
Trimmed Mean ( 14 / 37 )11.61551266092336.73403570079841.72489621038779
Trimmed Mean ( 15 / 37 )11.83049602283176.569279001762181.80088195670457
Trimmed Mean ( 16 / 37 )11.88563203349086.402336713240711.85645219329219
Trimmed Mean ( 17 / 37 )11.99011636493176.262868344066731.91447683492993
Trimmed Mean ( 18 / 37 )12.04046777899926.16012282136661.95458242118751
Trimmed Mean ( 19 / 37 )12.07308421171476.055210873442681.99383381752494
Trimmed Mean ( 20 / 37 )12.12730465040615.940443556292422.04148133645007
Trimmed Mean ( 21 / 37 )12.26211661580785.827915073340392.10403145232855
Trimmed Mean ( 22 / 37 )12.41817244516105.706582938002452.17611354817318
Trimmed Mean ( 23 / 37 )12.61075421284165.571074401681782.26361260029748
Trimmed Mean ( 24 / 37 )12.87494249610645.423739919662542.37381266189243
Trimmed Mean ( 25 / 37 )13.18688076621095.258133642937772.50790140793061
Trimmed Mean ( 26 / 37 )13.42652063908095.088261649371672.63872449262489
Trimmed Mean ( 27 / 37 )13.67515864354984.915170676251082.78223474713195
Trimmed Mean ( 28 / 37 )13.67515864354984.779569405897862.86116959127636
Trimmed Mean ( 29 / 37 )14.22642676143474.635354663889013.0691128927552
Trimmed Mean ( 30 / 37 )14.37270022585594.52208098736943.17833764277998
Trimmed Mean ( 31 / 37 )14.37270022585594.417104613996653.25387363032167
Trimmed Mean ( 32 / 37 )14.65561049025574.326784616252323.38718281358544
Trimmed Mean ( 33 / 37 )14.72924109056044.221523224775413.48908209342945
Trimmed Mean ( 34 / 37 )14.83143820708354.089489671979563.62672103287258
Trimmed Mean ( 35 / 37 )14.87831061020553.981058549214483.73727500519711
Trimmed Mean ( 36 / 37 )15.00908205827373.857779272489393.89060156067159
Trimmed Mean ( 37 / 37 )15.18530348395573.722213535032524.07964329317368
Median12.026051567764
Midrange-204.477548421212
Midmean - Weighted Average at Xnp12.5955374066374
Midmean - Weighted Average at X(n+1)p13.6751586435498
Midmean - Empirical Distribution Function13.6751586435498
Midmean - Empirical Distribution Function - Averaging13.6751586435498
Midmean - Empirical Distribution Function - Interpolation13.9375601657073
Midmean - Closest Observation12.5955374066374
Midmean - True Basic - Statistics Graphics Toolkit13.6751586435498
Midmean - MS Excel (old versions)13.6751586435498
Number of observations111
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/30/t126218184814kqsfxkpfewh7u/1t5oi1262181799.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/30/t126218184814kqsfxkpfewh7u/1t5oi1262181799.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/30/t126218184814kqsfxkpfewh7u/2qbke1262181799.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/30/t126218184814kqsfxkpfewh7u/2qbke1262181799.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')
 





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