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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, 19 May 2008 09:05:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/19/t1211209555icwpnwbd7ed6t9z.htm/, Retrieved Tue, 14 May 2024 18:25:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12885, Retrieved Tue, 14 May 2024 18:25:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

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] [Mean Plot Eigen R...] [2008-05-19 15:05:08] [88615a9036e6e98ff64037322024b7ad] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.16
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.43
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.68
8.92
8.92
8.92
8.92
8.92
8.92
8.92
8.92
8.92
8.92
8.92
8.92
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.3
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.9
9.9
9.9
9.9
9.9
9.9
9.9
9.9
9.9
9.9
9.9
9.9
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2

Tables (Output of Computation)





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

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12885&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12885&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.40750.07794228634059940.270000000000000
28.638333333333330.09731236802019040.25
38.880.09341987329938280.24
49.236666666666670.1479147993906900.380000000000001
59.550.1167748416242280.299999999999999
69.850.1167748416242290.300000000000001
710.150.1167748416242280.299999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.4075 & 0.0779422863405994 & 0.270000000000000 \tabularnewline
2 & 8.63833333333333 & 0.0973123680201904 & 0.25 \tabularnewline
3 & 8.88 & 0.0934198732993828 & 0.24 \tabularnewline
4 & 9.23666666666667 & 0.147914799390690 & 0.380000000000001 \tabularnewline
5 & 9.55 & 0.116774841624228 & 0.299999999999999 \tabularnewline
6 & 9.85 & 0.116774841624229 & 0.300000000000001 \tabularnewline
7 & 10.15 & 0.116774841624228 & 0.299999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12885&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]8.4075[/C][C]0.0779422863405994[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]2[/C][C]8.63833333333333[/C][C]0.0973123680201904[/C][C]0.25[/C][/ROW]
[ROW][C]3[/C][C]8.88[/C][C]0.0934198732993828[/C][C]0.24[/C][/ROW]
[ROW][C]4[/C][C]9.23666666666667[/C][C]0.147914799390690[/C][C]0.380000000000001[/C][/ROW]
[ROW][C]5[/C][C]9.55[/C][C]0.116774841624228[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]6[/C][C]9.85[/C][C]0.116774841624229[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]7[/C][C]10.15[/C][C]0.116774841624228[/C][C]0.299999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12885&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
18.40750.07794228634059940.270000000000000
28.638333333333330.09731236802019040.25
38.880.09341987329938280.24
49.236666666666670.1479147993906900.380000000000001
59.550.1167748416242280.299999999999999
69.850.1167748416242290.300000000000001
710.150.1167748416242280.299999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0863645367641452
beta0.0211932101104510
S.D.0.0124516485561579
T-STAT1.70204049808088
p-value0.149483049785013

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0863645367641452 \tabularnewline
beta & 0.0211932101104510 \tabularnewline
S.D. & 0.0124516485561579 \tabularnewline
T-STAT & 1.70204049808088 \tabularnewline
p-value & 0.149483049785013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12885&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0863645367641452[/C][/ROW]
[ROW][C]beta[/C][C]0.0211932101104510[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0124516485561579[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.70204049808088[/C][/ROW]
[ROW][C]p-value[/C][C]0.149483049785013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12885&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)
alpha-0.0863645367641452
beta0.0211932101104510
S.D.0.0124516485561579
T-STAT1.70204049808088
p-value0.149483049785013






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.69712328608441
beta2.01069505105049
S.D.0.975790765976838
T-STAT2.06058011733451
p-value0.094363532591579
Lambda-1.01069505105049

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.69712328608441 \tabularnewline
beta & 2.01069505105049 \tabularnewline
S.D. & 0.975790765976838 \tabularnewline
T-STAT & 2.06058011733451 \tabularnewline
p-value & 0.094363532591579 \tabularnewline
Lambda & -1.01069505105049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12885&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.69712328608441[/C][/ROW]
[ROW][C]beta[/C][C]2.01069505105049[/C][/ROW]
[ROW][C]S.D.[/C][C]0.975790765976838[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.06058011733451[/C][/ROW]
[ROW][C]p-value[/C][C]0.094363532591579[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.01069505105049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12885&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12885&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)
alpha-6.69712328608441
beta2.01069505105049
S.D.0.975790765976838
T-STAT2.06058011733451
p-value0.094363532591579
Lambda-1.01069505105049


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
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')