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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 06 Dec 2008 07:32:39 -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/Dec/06/t12285740034rxllag4d8m96tc.htm/, Retrieved Sat, 18 May 2024 22:31:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29651, Retrieved Sat, 18 May 2024 22:31:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact254

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [Identification an...] [2008-12-04 19:58:38] [063e4b67ad7d3a8a83eccec794cd5aa7]
F    D    [Standard Deviation-Mean Plot] [Eigen tijdreeks SMP] [2008-12-06 14:17:16] [063e4b67ad7d3a8a83eccec794cd5aa7]
-    D        [Standard Deviation-Mean Plot] [Eigen tijdreeks t...] [2008-12-06 14:32:39] [6797a1f4a60918966297e9d9220cabc2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
8,8
8,7
8,7
8,6
8,6
8,5
8,5
8,3
8,2
8,1
7,8
7,5
7,4
7,3
7,7
7,7
7,6
7,3
7,2
7,5
8
8,1
8,4
8,6
8,7
8,6
8,4
8,4
8,5
8,9
8,8
8,7
8,6
8,6
8,6
8,8
8,8
8,8
8,8
8,7
8,7
8,9
8,9
9
8,9
9
9,1
9,3
9,4
9,4
9,2
9,2
9,4
9,9
10
9,9
9,6
9,5
9,6
9,5
9,6
9,6
9,5
9,5
9,5
9,5
9,4
9,5
9,5
9,5
9,5
9,5
9,4
9,3
9,2
9,3
9,4
9,5
9,6
9,5
9,3
9,1
9
9
8,9
9
9,2
9
8,7
8,3
8
7,7
7,9
7,9
7,8
7,7
7,5
7,3
7,2
7,1
7,1

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'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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29651&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29651&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.483333333333330.332574894732091.2
27.641666666666670.3629633924274241.2
38.616666666666670.1466804401246180.5
48.866666666666670.1230914909793330.4
59.533333333333330.2741377667369370.8
69.508333333333330.05149286505444350.199999999999999
79.341666666666670.1781640374554420.6
88.450.5680909018170181.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.48333333333333 & 0.33257489473209 & 1.2 \tabularnewline
2 & 7.64166666666667 & 0.362963392427424 & 1.2 \tabularnewline
3 & 8.61666666666667 & 0.146680440124618 & 0.5 \tabularnewline
4 & 8.86666666666667 & 0.123091490979333 & 0.4 \tabularnewline
5 & 9.53333333333333 & 0.274137766736937 & 0.8 \tabularnewline
6 & 9.50833333333333 & 0.0514928650544435 & 0.199999999999999 \tabularnewline
7 & 9.34166666666667 & 0.178164037455442 & 0.6 \tabularnewline
8 & 8.45 & 0.568090901817018 & 1.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29651&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]8.48333333333333[/C][C]0.33257489473209[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]7.64166666666667[/C][C]0.362963392427424[/C][C]1.2[/C][/ROW]
[ROW][C]3[/C][C]8.61666666666667[/C][C]0.146680440124618[/C][C]0.5[/C][/ROW]
[ROW][C]4[/C][C]8.86666666666667[/C][C]0.123091490979333[/C][C]0.4[/C][/ROW]
[ROW][C]5[/C][C]9.53333333333333[/C][C]0.274137766736937[/C][C]0.8[/C][/ROW]
[ROW][C]6[/C][C]9.50833333333333[/C][C]0.0514928650544435[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]7[/C][C]9.34166666666667[/C][C]0.178164037455442[/C][C]0.6[/C][/ROW]
[ROW][C]8[/C][C]8.45[/C][C]0.568090901817018[/C][C]1.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29651&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
18.483333333333330.332574894732091.2
27.641666666666670.3629633924274241.2
38.616666666666670.1466804401246180.5
48.866666666666670.1230914909793330.4
59.533333333333330.2741377667369370.8
69.508333333333330.05149286505444350.199999999999999
79.341666666666670.1781640374554420.6
88.450.5680909018170181.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.51414832628241
beta-0.143040210400075
S.D.0.0867246849991668
T-STAT-1.64935981492985
p-value0.150168119237613

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.51414832628241 \tabularnewline
beta & -0.143040210400075 \tabularnewline
S.D. & 0.0867246849991668 \tabularnewline
T-STAT & -1.64935981492985 \tabularnewline
p-value & 0.150168119237613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29651&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.51414832628241[/C][/ROW]
[ROW][C]beta[/C][C]-0.143040210400075[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0867246849991668[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.64935981492985[/C][/ROW]
[ROW][C]p-value[/C][C]0.150168119237613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29651&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)
alpha1.51414832628241
beta-0.143040210400075
S.D.0.0867246849991668
T-STAT-1.64935981492985
p-value0.150168119237613






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha11.0385932160751
beta-5.80949525241168
S.D.3.35423478691752
T-STAT-1.73198825409312
p-value0.133986180680650
Lambda6.80949525241168

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 11.0385932160751 \tabularnewline
beta & -5.80949525241168 \tabularnewline
S.D. & 3.35423478691752 \tabularnewline
T-STAT & -1.73198825409312 \tabularnewline
p-value & 0.133986180680650 \tabularnewline
Lambda & 6.80949525241168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29651&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.0385932160751[/C][/ROW]
[ROW][C]beta[/C][C]-5.80949525241168[/C][/ROW]
[ROW][C]S.D.[/C][C]3.35423478691752[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.73198825409312[/C][/ROW]
[ROW][C]p-value[/C][C]0.133986180680650[/C][/ROW]
[ROW][C]Lambda[/C][C]6.80949525241168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29651&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29651&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)
alpha11.0385932160751
beta-5.80949525241168
S.D.3.35423478691752
T-STAT-1.73198825409312
p-value0.133986180680650
Lambda6.80949525241168


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')