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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 computationSun, 06 Jan 2008 13:31:59 -0700
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/Jan/06/t1199651489a32cyvzw94adk1y.htm/, Retrieved Sun, 05 May 2024 07:17:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7887, Retrieved Sun, 05 May 2024 07:17:45 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsInducing time series Q1 EA
Estimated Impact154

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [WS2 - Robustness ...] [2007-10-20 13:06:37] [5343e105a400b9e32bf6f011133bbaf4]
- RM D    [Standard Deviation-Mean Plot] [CVWS7EAQ1] [2008-01-06 20:31:59] [b523c8d839cc24a05ea912c062a47207] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13,5
16,2
17,6
15,8
17,6
15,2
15,9
12,0
13,3
14,8
16,1
16,9
17,6
13,9
10,0
7,6
7,1
8,1
8,1
7,7
4,0
1,4
0,3
-1,0
-1,9
-1,5
-0,2
3,4
3,0
4,1
3,4
3,2
6,1
5,8
6,2
5,8
5,9
6,7
5,9
3,8
1,7
1,4
1,8
3,0
3,6
4,8
4,3
4,2
2,9
4,9
7,2
8,7
9,1
8,9
9,0
11,6
9,6
9,1
9,2
10,8
11,0
8,5
6,5
7,2
7,8
8,7
7,8
7,5
7,7
7,5
8,3
7,9
10,4
11,5
14,0
11,9
11,9
10,3
11,3
9,9
8,9
9,2
8,8
6,7
7,1
6,6
7,2
5,0
5,3
6,3

Tables (Output of Computation)





Summary of compuational 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 compuational 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=7887&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7887&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7887&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 compuational 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
115.40833333333331.743798535764195.6
27.066666666666675.4057769323589618.6
33.116666666666672.883127510607928.1
43.9251.739971264130535.3
58.416666666666672.406367814904048.7
68.033333333333331.103163495121964.5
710.41.899282161047367.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.4083333333333 & 1.74379853576419 & 5.6 \tabularnewline
2 & 7.06666666666667 & 5.40577693235896 & 18.6 \tabularnewline
3 & 3.11666666666667 & 2.88312751060792 & 8.1 \tabularnewline
4 & 3.925 & 1.73997126413053 & 5.3 \tabularnewline
5 & 8.41666666666667 & 2.40636781490404 & 8.7 \tabularnewline
6 & 8.03333333333333 & 1.10316349512196 & 4.5 \tabularnewline
7 & 10.4 & 1.89928216104736 & 7.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7887&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]15.4083333333333[/C][C]1.74379853576419[/C][C]5.6[/C][/ROW]
[ROW][C]2[/C][C]7.06666666666667[/C][C]5.40577693235896[/C][C]18.6[/C][/ROW]
[ROW][C]3[/C][C]3.11666666666667[/C][C]2.88312751060792[/C][C]8.1[/C][/ROW]
[ROW][C]4[/C][C]3.925[/C][C]1.73997126413053[/C][C]5.3[/C][/ROW]
[ROW][C]5[/C][C]8.41666666666667[/C][C]2.40636781490404[/C][C]8.7[/C][/ROW]
[ROW][C]6[/C][C]8.03333333333333[/C][C]1.10316349512196[/C][C]4.5[/C][/ROW]
[ROW][C]7[/C][C]10.4[/C][C]1.89928216104736[/C][C]7.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7887&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7887&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
115.40833333333331.743798535764195.6
27.066666666666675.4057769323589618.6
33.116666666666672.883127510607928.1
43.9251.739971264130535.3
58.416666666666672.406367814904048.7
68.033333333333331.103163495121964.5
710.41.899282161047367.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.13250586981141
beta-0.0841996459150489
S.D.0.148907789631661
T-STAT-0.565448228889337
p-value0.5961987171189

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.13250586981141 \tabularnewline
beta & -0.0841996459150489 \tabularnewline
S.D. & 0.148907789631661 \tabularnewline
T-STAT & -0.565448228889337 \tabularnewline
p-value & 0.5961987171189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7887&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.13250586981141[/C][/ROW]
[ROW][C]beta[/C][C]-0.0841996459150489[/C][/ROW]
[ROW][C]S.D.[/C][C]0.148907789631661[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.565448228889337[/C][/ROW]
[ROW][C]p-value[/C][C]0.5961987171189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7887&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7887&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)
alpha3.13250586981141
beta-0.0841996459150489
S.D.0.148907789631661
T-STAT-0.565448228889337
p-value0.5961987171189






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.20718604539951
beta-0.216453634283791
S.D.0.393839032457819
T-STAT-0.549599243459885
p-value0.606239896727253
Lambda1.21645363428379

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.20718604539951 \tabularnewline
beta & -0.216453634283791 \tabularnewline
S.D. & 0.393839032457819 \tabularnewline
T-STAT & -0.549599243459885 \tabularnewline
p-value & 0.606239896727253 \tabularnewline
Lambda & 1.21645363428379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7887&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.20718604539951[/C][/ROW]
[ROW][C]beta[/C][C]-0.216453634283791[/C][/ROW]
[ROW][C]S.D.[/C][C]0.393839032457819[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.549599243459885[/C][/ROW]
[ROW][C]p-value[/C][C]0.606239896727253[/C][/ROW]
[ROW][C]Lambda[/C][C]1.21645363428379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7887&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7887&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)
alpha1.20718604539951
beta-0.216453634283791
S.D.0.393839032457819
T-STAT-0.549599243459885
p-value0.606239896727253
Lambda1.21645363428379


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')