investigating associations
| Summary of compuational 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 | 551.890410958904 | 5.43214548616753 | 101.597133648987 |
| Geometric Mean | 549.919974939706 | ||
| Harmonic Mean | 547.905173014011 | ||
| Quadratic Mean | 553.811896259331 | ||
| Winsorized Mean ( 1 / 24 ) | 551.890410958904 | 5.42608284628349 | 101.710649577883 |
| Winsorized Mean ( 2 / 24 ) | 551.972602739726 | 5.38261946589102 | 102.547208889186 |
| Winsorized Mean ( 3 / 24 ) | 552.13698630137 | 5.26075455218458 | 104.953953054527 |
| Winsorized Mean ( 4 / 24 ) | 552.13698630137 | 5.23901020766782 | 105.389561084126 |
| Winsorized Mean ( 5 / 24 ) | 552.13698630137 | 5.23901020766782 | 105.389561084126 |
| Winsorized Mean ( 6 / 24 ) | 551.890410958904 | 5.06902738967335 | 108.875010634825 |
| Winsorized Mean ( 7 / 24 ) | 551.890410958904 | 5.03290397197378 | 109.656455603397 |
| Winsorized Mean ( 8 / 24 ) | 554.301369863014 | 4.53427186646554 | 122.247052269297 |
| Winsorized Mean ( 9 / 24 ) | 554.54794520548 | 4.49297782456958 | 123.425480128784 |
| Winsorized Mean ( 10 / 24 ) | 552.904109589041 | 4.13702536092924 | 133.647744780769 |
| Winsorized Mean ( 11 / 24 ) | 553.205479452055 | 3.99385748422543 | 138.514076087355 |
| Winsorized Mean ( 12 / 24 ) | 553.534246575342 | 3.94164444816837 | 140.432312922735 |
| Winsorized Mean ( 13 / 24 ) | 553.356164383562 | 3.91579801224272 | 141.313766096590 |
| Winsorized Mean ( 14 / 24 ) | 553.54794520548 | 3.88578572571865 | 142.454572711444 |
| Winsorized Mean ( 15 / 24 ) | 553.54794520548 | 3.82434130458584 | 144.743343001763 |
| Winsorized Mean ( 16 / 24 ) | 553.328767123288 | 3.72836502796883 | 148.410566822835 |
| Winsorized Mean ( 17 / 24 ) | 553.328767123288 | 3.66007371124345 | 151.179678546775 |
| Winsorized Mean ( 18 / 24 ) | 554.068493150685 | 3.47716670114487 | 159.344817425134 |
| Winsorized Mean ( 19 / 24 ) | 553.808219178082 | 3.44104829509785 | 160.941716501638 |
| Winsorized Mean ( 20 / 24 ) | 553.260273972603 | 3.21117646054426 | 172.292080728205 |
| Winsorized Mean ( 21 / 24 ) | 552.109589041096 | 3.06180387011557 | 180.321670643214 |
| Winsorized Mean ( 22 / 24 ) | 553.315068493151 | 2.88318200518298 | 191.911252046690 |
| Winsorized Mean ( 23 / 24 ) | 553.315068493151 | 2.71109372585749 | 204.092932389544 |
| Winsorized Mean ( 24 / 24 ) | 552.328767123288 | 2.50076508799052 | 220.863914717839 |
| Trimmed Mean ( 1 / 24 ) | 552.169014084507 | 5.30282131033028 | 104.127403465178 |
| Trimmed Mean ( 2 / 24 ) | 552.463768115942 | 5.1563607459556 | 107.142187161608 |
| Trimmed Mean ( 3 / 24 ) | 552.731343283582 | 5.00956038001978 | 110.335299178767 |
| Trimmed Mean ( 4 / 24 ) | 552.953846153846 | 4.88976711973148 | 113.083881627518 |
| Trimmed Mean ( 5 / 24 ) | 553.190476190476 | 4.75324866096906 | 116.381556204488 |
| Trimmed Mean ( 6 / 24 ) | 553.44262295082 | 4.58755292640299 | 120.640051859797 |
| Trimmed Mean ( 7 / 24 ) | 553.762711864407 | 4.43541476524058 | 124.850265685214 |
| Trimmed Mean ( 8 / 24 ) | 554.105263157895 | 4.25809594587647 | 130.129820981251 |
| Trimmed Mean ( 9 / 24 ) | 554.072727272727 | 4.16825057130949 | 132.926924088122 |
| Trimmed Mean ( 10 / 24 ) | 554 | 4.0651444167671 | 136.280521231908 |
| Trimmed Mean ( 11 / 24 ) | 554.156862745098 | 4.01432460063098 | 138.044856327262 |
| Trimmed Mean ( 12 / 24 ) | 554.285714285714 | 3.97697454487859 | 139.373714372777 |
| Trimmed Mean ( 13 / 24 ) | 554.382978723404 | 3.93583517338011 | 140.855232575021 |
| Trimmed Mean ( 14 / 24 ) | 554.511111111111 | 3.88348253351335 | 142.787074829316 |
| Trimmed Mean ( 15 / 24 ) | 554.627906976744 | 3.8175475327492 | 145.283824816539 |
| Trimmed Mean ( 16 / 24 ) | 554.756097560976 | 3.74031766092669 | 148.317909827886 |
| Trimmed Mean ( 17 / 24 ) | 554.923076923077 | 3.65524868315984 | 151.815409846031 |
| Trimmed Mean ( 18 / 24 ) | 555.108108108108 | 3.55264647448185 | 156.251997516603 |
| Trimmed Mean ( 19 / 24 ) | 555.228571428571 | 3.45562158347978 | 160.674008428163 |
| Trimmed Mean ( 20 / 24 ) | 555.393939393939 | 3.32487735987638 | 167.041932462312 |
| Trimmed Mean ( 21 / 24 ) | 555.645161290323 | 3.20099056815424 | 173.585379106793 |
| Trimmed Mean ( 22 / 24 ) | 556.068965517241 | 3.05690328934379 | 181.905972444621 |
| Trimmed Mean ( 23 / 24 ) | 556.407407407407 | 2.90360776630861 | 191.626229225435 |
| Trimmed Mean ( 24 / 24 ) | 556.8 | 2.72702524129621 | 204.178528151555 |
| Median | 561 | ||
| Midrange | 542 | ||
| Midmean - Weighted Average at Xnp | 554.166666666667 | ||
| Midmean - Weighted Average at X(n+1)p | 555.108108108108 | ||
| Midmean - Empirical Distribution Function | 555.108108108108 | ||
| Midmean - Empirical Distribution Function - Averaging | 555.108108108108 | ||
| Midmean - Empirical Distribution Function - Interpolation | 555.108108108108 | ||
| Midmean - Closest Observation | 554 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 555.108108108108 | ||
| Midmean - MS Excel (old versions) | 555.108108108108 | ||
| Number of observations | 73 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/23/t119581007123t1ozrbkq6h6w7/1j00u1195810567.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/23/t119581007123t1ozrbkq6h6w7/1j00u1195810567.ps (open in new window) |
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/23/t119581007123t1ozrbkq6h6w7/2ijgy1195810567.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/23/t119581007123t1ozrbkq6h6w7/2ijgy1195810567.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')
Copyright
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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.