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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 05 Dec 2011 17:01:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/05/t13231229022yat5lxqaelcy6y.htm/, Retrieved Fri, 03 May 2024 04:22:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151300, Retrieved Fri, 03 May 2024 04:22:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact66

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2011-12-05 22:01:38] [d06e8713ea83045a022ab0926c74dd0b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14097.80
14776.80
16833.30
15385.50
15172.60
16858.90
14143.50
14731.80
16471.60
15214.00
17637.40
17972.40
16896.20
16698.00
19691.60
15930.70
17444.60
17699.40
15189.80
15672.70
17180.80
17664.90
17862.90
16162.30
17463.60
16772.10
19106.90
16721.30
18161.30
18509.90
17802.70
16409.90
17967.70
20286.60
19537.30
18021.90
20194.30
19049.60
20244.70
21473.30
19673.60
21053.20
20159.50
18203.60
21289.50
20432.30
17180.40
15816.80
15076.60
14531.60
15761.30
14345.50
13916.80
15496.80
14285.60
13597.30
16263.10
16773.30
15986.90
16842.60
15911.90
15782.90
18622.80
17422.50
16989.80
18990.50
16849.30
16511.30
18704.50
19111.10
19420.70
18985.10

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151300&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151300&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115273.351165.404268912722735.5
215226.71166.940715432172715.4
316823.851251.229767069182758.4
417304.1251645.207527689643760.9
516501.6251255.90183898532509.6
617217.725759.7152202196131700.6
717515.9751113.349880241312385.6
817720.95920.4863551405852100
918953.3751148.572764709892318.9
1020240.475989.981603785312423.7
1119772.4751191.803941860132849.6
1218679.752602.995690225655472.7
1314928.75635.8479404176231415.8
1414324.125830.8307223295651899.5
1516466.475411.081973779764855.699999999999
1616935.0251349.122320560052839.9
1717335.2251121.640059243612479.2
1819055.35296.995774380714716.200000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15273.35 & 1165.40426891272 & 2735.5 \tabularnewline
2 & 15226.7 & 1166.94071543217 & 2715.4 \tabularnewline
3 & 16823.85 & 1251.22976706918 & 2758.4 \tabularnewline
4 & 17304.125 & 1645.20752768964 & 3760.9 \tabularnewline
5 & 16501.625 & 1255.9018389853 & 2509.6 \tabularnewline
6 & 17217.725 & 759.715220219613 & 1700.6 \tabularnewline
7 & 17515.975 & 1113.34988024131 & 2385.6 \tabularnewline
8 & 17720.95 & 920.486355140585 & 2100 \tabularnewline
9 & 18953.375 & 1148.57276470989 & 2318.9 \tabularnewline
10 & 20240.475 & 989.98160378531 & 2423.7 \tabularnewline
11 & 19772.475 & 1191.80394186013 & 2849.6 \tabularnewline
12 & 18679.75 & 2602.99569022565 & 5472.7 \tabularnewline
13 & 14928.75 & 635.847940417623 & 1415.8 \tabularnewline
14 & 14324.125 & 830.830722329565 & 1899.5 \tabularnewline
15 & 16466.475 & 411.081973779764 & 855.699999999999 \tabularnewline
16 & 16935.025 & 1349.12232056005 & 2839.9 \tabularnewline
17 & 17335.225 & 1121.64005924361 & 2479.2 \tabularnewline
18 & 19055.35 & 296.995774380714 & 716.200000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151300&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]15273.35[/C][C]1165.40426891272[/C][C]2735.5[/C][/ROW]
[ROW][C]2[/C][C]15226.7[/C][C]1166.94071543217[/C][C]2715.4[/C][/ROW]
[ROW][C]3[/C][C]16823.85[/C][C]1251.22976706918[/C][C]2758.4[/C][/ROW]
[ROW][C]4[/C][C]17304.125[/C][C]1645.20752768964[/C][C]3760.9[/C][/ROW]
[ROW][C]5[/C][C]16501.625[/C][C]1255.9018389853[/C][C]2509.6[/C][/ROW]
[ROW][C]6[/C][C]17217.725[/C][C]759.715220219613[/C][C]1700.6[/C][/ROW]
[ROW][C]7[/C][C]17515.975[/C][C]1113.34988024131[/C][C]2385.6[/C][/ROW]
[ROW][C]8[/C][C]17720.95[/C][C]920.486355140585[/C][C]2100[/C][/ROW]
[ROW][C]9[/C][C]18953.375[/C][C]1148.57276470989[/C][C]2318.9[/C][/ROW]
[ROW][C]10[/C][C]20240.475[/C][C]989.98160378531[/C][C]2423.7[/C][/ROW]
[ROW][C]11[/C][C]19772.475[/C][C]1191.80394186013[/C][C]2849.6[/C][/ROW]
[ROW][C]12[/C][C]18679.75[/C][C]2602.99569022565[/C][C]5472.7[/C][/ROW]
[ROW][C]13[/C][C]14928.75[/C][C]635.847940417623[/C][C]1415.8[/C][/ROW]
[ROW][C]14[/C][C]14324.125[/C][C]830.830722329565[/C][C]1899.5[/C][/ROW]
[ROW][C]15[/C][C]16466.475[/C][C]411.081973779764[/C][C]855.699999999999[/C][/ROW]
[ROW][C]16[/C][C]16935.025[/C][C]1349.12232056005[/C][C]2839.9[/C][/ROW]
[ROW][C]17[/C][C]17335.225[/C][C]1121.64005924361[/C][C]2479.2[/C][/ROW]
[ROW][C]18[/C][C]19055.35[/C][C]296.995774380714[/C][C]716.200000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151300&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115273.351165.404268912722735.5
215226.71166.940715432172715.4
316823.851251.229767069182758.4
417304.1251645.207527689643760.9
516501.6251255.90183898532509.6
617217.725759.7152202196131700.6
717515.9751113.349880241312385.6
817720.95920.4863551405852100
918953.3751148.572764709892318.9
1020240.475989.981603785312423.7
1119772.4751191.803941860132849.6
1218679.752602.995690225655472.7
1314928.75635.8479404176231415.8
1414324.125830.8307223295651899.5
1516466.475411.081973779764855.699999999999
1616935.0251349.122320560052839.9
1717335.2251121.640059243612479.2
1819055.35296.995774380714716.200000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180.624599086341
beta0.0535197749979915
S.D.0.0738278792191321
T-STAT0.724926349829675
p-value0.478965741385236

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 180.624599086341 \tabularnewline
beta & 0.0535197749979915 \tabularnewline
S.D. & 0.0738278792191321 \tabularnewline
T-STAT & 0.724926349829675 \tabularnewline
p-value & 0.478965741385236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151300&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]180.624599086341[/C][/ROW]
[ROW][C]beta[/C][C]0.0535197749979915[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0738278792191321[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.724926349829675[/C][/ROW]
[ROW][C]p-value[/C][C]0.478965741385236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151300&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180.624599086341
beta0.0535197749979915
S.D.0.0738278792191321
T-STAT0.724926349829675
p-value0.478965741385236






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.38159534667201
beta0.463864718406083
S.D.1.25155759038091
T-STAT0.37062994301757
p-value0.715774248830717
Lambda0.536135281593917

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.38159534667201 \tabularnewline
beta & 0.463864718406083 \tabularnewline
S.D. & 1.25155759038091 \tabularnewline
T-STAT & 0.37062994301757 \tabularnewline
p-value & 0.715774248830717 \tabularnewline
Lambda & 0.536135281593917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151300&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.38159534667201[/C][/ROW]
[ROW][C]beta[/C][C]0.463864718406083[/C][/ROW]
[ROW][C]S.D.[/C][C]1.25155759038091[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.37062994301757[/C][/ROW]
[ROW][C]p-value[/C][C]0.715774248830717[/C][/ROW]
[ROW][C]Lambda[/C][C]0.536135281593917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151300&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151300&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.38159534667201
beta0.463864718406083
S.D.1.25155759038091
T-STAT0.37062994301757
p-value0.715774248830717
Lambda0.536135281593917


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')