Central Tendency Residuals 1
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 3 seconds |
| R Server | 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 |
| Central Tendency - Ungrouped Data | |||
| Measure | Value | S.E. | Value/S.E. |
| Arithmetic Mean | 0.0571323668668234 | 0.0263765677099842 | 2.16602734271591 |
| Geometric Mean | NaN | ||
| Harmonic Mean | 0.0422079271300558 | ||
| Quadratic Mean | 0.210503642413163 | ||
| Winsorized Mean ( 1 / 20 ) | 0.0575660472841512 | 0.0259216254177813 | 2.2207730555609 |
| Winsorized Mean ( 2 / 20 ) | 0.0551955052965344 | 0.0252432942464049 | 2.18654129519547 |
| Winsorized Mean ( 3 / 20 ) | 0.0521906202283147 | 0.0237684429042363 | 2.19579466936863 |
| Winsorized Mean ( 4 / 20 ) | 0.0513906902021422 | 0.0231098955698935 | 2.22375259320045 |
| Winsorized Mean ( 5 / 20 ) | 0.0510330366327362 | 0.0224836058809415 | 2.26978879201912 |
| Winsorized Mean ( 6 / 20 ) | 0.058928748552861 | 0.0198976156892289 | 2.96159848864509 |
| Winsorized Mean ( 7 / 20 ) | 0.0589888361578334 | 0.0194588264208658 | 3.03146936418423 |
| Winsorized Mean ( 8 / 20 ) | 0.0577211466428962 | 0.0191823961394299 | 3.00906863894072 |
| Winsorized Mean ( 9 / 20 ) | 0.0588586376382354 | 0.0188175172655064 | 3.12786414954573 |
| Winsorized Mean ( 10 / 20 ) | 0.0596172785487949 | 0.0178842795668624 | 3.33350182353776 |
| Winsorized Mean ( 11 / 20 ) | 0.0545328593027975 | 0.0164417914887250 | 3.31672247152591 |
| Winsorized Mean ( 12 / 20 ) | 0.0591666943185246 | 0.0150445091918581 | 3.93277664056631 |
| Winsorized Mean ( 13 / 20 ) | 0.0578832256388644 | 0.0142260366874813 | 4.06882302572725 |
| Winsorized Mean ( 14 / 20 ) | 0.0558040400152388 | 0.0130957026802721 | 4.26124824132609 |
| Winsorized Mean ( 15 / 20 ) | 0.0610087387136793 | 0.0115167023274536 | 5.29741387586673 |
| Winsorized Mean ( 16 / 20 ) | 0.0577183604789213 | 0.0107479789548062 | 5.37015942454104 |
| Winsorized Mean ( 17 / 20 ) | 0.0683256578489768 | 0.0089000263209332 | 7.6770175036755 |
| Winsorized Mean ( 18 / 20 ) | 0.0725696362188142 | 0.007950369781443 | 9.12783156177205 |
| Winsorized Mean ( 19 / 20 ) | 0.0697803916489536 | 0.00651177851440125 | 10.7160265808534 |
| Winsorized Mean ( 20 / 20 ) | 0.0690722869720697 | 0.00631430377308732 | 10.9390186874550 |
| Trimmed Mean ( 1 / 20 ) | 0.0566430652437893 | 0.0246721225464986 | 2.29583268067173 |
| Trimmed Mean ( 2 / 20 ) | 0.0556541559148301 | 0.0231179506470843 | 2.40740006605427 |
| Trimmed Mean ( 3 / 20 ) | 0.0559089618138833 | 0.0216478310239458 | 2.58265882397361 |
| Trimmed Mean ( 4 / 20 ) | 0.0573390931929481 | 0.0205621958705188 | 2.78856857283217 |
| Trimmed Mean ( 5 / 20 ) | 0.0591236140901899 | 0.0194648339131405 | 3.03745792818074 |
| Trimmed Mean ( 6 / 20 ) | 0.0611462584545533 | 0.0182940636436707 | 3.34240984646997 |
| Trimmed Mean ( 7 / 20 ) | 0.0616283258244864 | 0.0176822318369368 | 3.48532506489083 |
| Trimmed Mean ( 8 / 20 ) | 0.062142512123185 | 0.0170205284981721 | 3.65103305281377 |
| Trimmed Mean ( 9 / 20 ) | 0.0629320416732366 | 0.0162305188686757 | 3.87738939108675 |
| Trimmed Mean ( 10 / 20 ) | 0.0636109423457368 | 0.0152882754508147 | 4.16076636965269 |
| Trimmed Mean ( 11 / 20 ) | 0.0642415208399908 | 0.0143058001148118 | 4.49059264944412 |
| Trimmed Mean ( 12 / 20 ) | 0.0657125301638079 | 0.0134020555160297 | 4.90316803159126 |
| Trimmed Mean ( 13 / 20 ) | 0.066675153082232 | 0.0126010837676920 | 5.29122370039161 |
| Trimmed Mean ( 14 / 20 ) | 0.06794321954041 | 0.0117237202500038 | 5.7953634248811 |
| Trimmed Mean ( 15 / 20 ) | 0.0696773880440058 | 0.0108277497757877 | 6.4350755685003 |
| Trimmed Mean ( 16 / 20 ) | 0.0709157665197668 | 0.0101022304260032 | 7.01981280660847 |
| Trimmed Mean ( 17 / 20 ) | 0.0728192385448887 | 0.00925450325854166 | 7.8685194127171 |
| Trimmed Mean ( 18 / 20 ) | 0.073480059235464 | 0.00876094769964665 | 8.38722724465387 |
| Trimmed Mean ( 19 / 20 ) | 0.0736180021167746 | 0.00835986516928026 | 8.8061231402746 |
| Trimmed Mean ( 20 / 20 ) | 0.0742239406116937 | 0.00827696113995301 | 8.9675352290122 |
| Median | 0.0776493711529287 | ||
| Midrange | 0.0713221139348115 | ||
| Midmean - Weighted Average at Xnp | 0.0646447675257745 | ||
| Midmean - Weighted Average at X(n+1)p | 0.0696773880440058 | ||
| Midmean - Empirical Distribution Function | 0.0646447675257745 | ||
| Midmean - Empirical Distribution Function - Averaging | 0.0696773880440058 | ||
| Midmean - Empirical Distribution Function - Interpolation | 0.0696773880440058 | ||
| Midmean - Closest Observation | 0.0646447675257745 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 0.0696773880440058 | ||
| Midmean - MS Excel (old versions) | 0.06794321954041 | ||
| Number of observations | 60 | ||
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t11973119715cb6felybleoz5c/11wti1197312787.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t11973119715cb6felybleoz5c/11wti1197312787.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t11973119715cb6felybleoz5c/2jm2f1197312787.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t11973119715cb6felybleoz5c/2jm2f1197312787.ps (open in new window) |
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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