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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 computationWed, 21 Dec 2011 04:59:33 -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/21/t13244618125egkck09v5o3ut7.htm/, Retrieved Tue, 07 May 2024 13:09:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158416, Retrieved Tue, 07 May 2024 13:09:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46

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] [] [2011-12-21 09:59:33] [bbaf0bbad09b34135f8973992e5d67ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.581
2.592
2.600
2.602
2.608
2.619
2.637
2.646
2.659
2.671
2.684
2.686
2.691
2.705
2.723
2.725
2.734
2.735
2.740
2.744
2.737
2.743
2.747
2.748
2.749
2.754
2.766
2.784
2.794
2.804
2.818
2.833
2.836
2.866
2.893
2.897
2.897
2.913
2.921
2.922
2.924
2.924
2.945
2.948
2.952
2.968
2.987
2.997
3.002
3.012
3.027
3.032
3.036
3.039
3.048
3.050
3.089
3.093
3.094
3.098
3.104
3.106
3.116
3.119
3.124
3.131
3.147
3.156

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158416&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158416&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12.632083333333330.03687930765799880.105
22.7310.01751882104792140.0570000000000004
32.816166666666670.05060332963053880.148
42.94150.03048546598567320.1
53.051666666666670.03370819520891650.0960000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.63208333333333 & 0.0368793076579988 & 0.105 \tabularnewline
2 & 2.731 & 0.0175188210479214 & 0.0570000000000004 \tabularnewline
3 & 2.81616666666667 & 0.0506033296305388 & 0.148 \tabularnewline
4 & 2.9415 & 0.0304854659856732 & 0.1 \tabularnewline
5 & 3.05166666666667 & 0.0337081952089165 & 0.0960000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158416&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]2.63208333333333[/C][C]0.0368793076579988[/C][C]0.105[/C][/ROW]
[ROW][C]2[/C][C]2.731[/C][C]0.0175188210479214[/C][C]0.0570000000000004[/C][/ROW]
[ROW][C]3[/C][C]2.81616666666667[/C][C]0.0506033296305388[/C][C]0.148[/C][/ROW]
[ROW][C]4[/C][C]2.9415[/C][C]0.0304854659856732[/C][C]0.1[/C][/ROW]
[ROW][C]5[/C][C]3.05166666666667[/C][C]0.0337081952089165[/C][C]0.0960000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158416&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
12.632083333333330.03687930765799880.105
22.7310.01751882104792140.0570000000000004
32.816166666666670.05060332963053880.148
42.94150.03048546598567320.1
53.051666666666670.03370819520891650.0960000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0241248462241228
beta0.0034271422829864
S.D.0.0413178927565682
T-STAT0.082945718049515
p-value0.939119201961413

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0241248462241228 \tabularnewline
beta & 0.0034271422829864 \tabularnewline
S.D. & 0.0413178927565682 \tabularnewline
T-STAT & 0.082945718049515 \tabularnewline
p-value & 0.939119201961413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158416&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0241248462241228[/C][/ROW]
[ROW][C]beta[/C][C]0.0034271422829864[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0413178927565682[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.082945718049515[/C][/ROW]
[ROW][C]p-value[/C][C]0.939119201961413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158416&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)
alpha0.0241248462241228
beta0.0034271422829864
S.D.0.0413178927565682
T-STAT0.082945718049515
p-value0.939119201961413






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.27291064026303
beta0.798802383642536
S.D.3.78304508719678
T-STAT0.211153281346283
p-value0.846297751012621
Lambda0.201197616357464

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.27291064026303 \tabularnewline
beta & 0.798802383642536 \tabularnewline
S.D. & 3.78304508719678 \tabularnewline
T-STAT & 0.211153281346283 \tabularnewline
p-value & 0.846297751012621 \tabularnewline
Lambda & 0.201197616357464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158416&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.27291064026303[/C][/ROW]
[ROW][C]beta[/C][C]0.798802383642536[/C][/ROW]
[ROW][C]S.D.[/C][C]3.78304508719678[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.211153281346283[/C][/ROW]
[ROW][C]p-value[/C][C]0.846297751012621[/C][/ROW]
[ROW][C]Lambda[/C][C]0.201197616357464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158416&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158416&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-4.27291064026303
beta0.798802383642536
S.D.3.78304508719678
T-STAT0.211153281346283
p-value0.846297751012621
Lambda0.201197616357464


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')