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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 computationThu, 13 Dec 2012 09:56:50 -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/2012/Dec/13/t1355410671r3az43quz2ba11s.htm/, Retrieved Tue, 30 Apr 2024 00:12:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199264, Retrieved Tue, 30 Apr 2024 00:12:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
-   PD  [Variance Reduction Matrix] [] [2010-12-15 16:39:48] [8d263c682820d5327cb5f02a8c3630cf]
-    D    [Variance Reduction Matrix] [] [2010-12-17 08:24:47] [4dfa50539945b119a90a7606969443b9]
- R         [Variance Reduction Matrix] [] [2010-12-17 11:46:46] [c6813a60da787bb62b5d86150b8926dd]
- RM D        [Standard Deviation-Mean Plot] [] [2010-12-17 12:01:15] [c6813a60da787bb62b5d86150b8926dd]
-    D          [Standard Deviation-Mean Plot] [] [2010-12-27 21:00:10] [c6813a60da787bb62b5d86150b8926dd]
- R P               [Standard Deviation-Mean Plot] [Deel 4: ARIMA Sta...] [2012-12-13 14:56:50] [f988ca26b10d35edf58465884f70a009] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
6
8
4
8
10
9
12
9
11
11
11
11
11
9
8
6
7
8
6
5
2
3
3
7
8
7
7
6
6
7
5
5
5
4
4
4
1
-1
3
4
3
2
1
4
3
5
6
6
6
6
6
5
6
5
6
5
7
4
5
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
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' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199264&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199264&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.752.454124543035118
26.583333333333332.998737107921319
35.916666666666671.311372170551514
42.916666666666671.928651593652157
55.583333333333330.7929614610987593
63.583333333333331.781640374554426
74.916666666666671.083624669450833
83.166666666666672.124888588879787
9-2.752.094364733365147
100.08333333333333332.108783937953277

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.75 & 2.45412454303511 & 8 \tabularnewline
2 & 6.58333333333333 & 2.99873710792131 & 9 \tabularnewline
3 & 5.91666666666667 & 1.31137217055151 & 4 \tabularnewline
4 & 2.91666666666667 & 1.92865159365215 & 7 \tabularnewline
5 & 5.58333333333333 & 0.792961461098759 & 3 \tabularnewline
6 & 3.58333333333333 & 1.78164037455442 & 6 \tabularnewline
7 & 4.91666666666667 & 1.08362466945083 & 3 \tabularnewline
8 & 3.16666666666667 & 2.12488858887978 & 7 \tabularnewline
9 & -2.75 & 2.09436473336514 & 7 \tabularnewline
10 & 0.0833333333333333 & 2.10878393795327 & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199264&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]8.75[/C][C]2.45412454303511[/C][C]8[/C][/ROW]
[ROW][C]2[/C][C]6.58333333333333[/C][C]2.99873710792131[/C][C]9[/C][/ROW]
[ROW][C]3[/C][C]5.91666666666667[/C][C]1.31137217055151[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]2.91666666666667[/C][C]1.92865159365215[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]5.58333333333333[/C][C]0.792961461098759[/C][C]3[/C][/ROW]
[ROW][C]6[/C][C]3.58333333333333[/C][C]1.78164037455442[/C][C]6[/C][/ROW]
[ROW][C]7[/C][C]4.91666666666667[/C][C]1.08362466945083[/C][C]3[/C][/ROW]
[ROW][C]8[/C][C]3.16666666666667[/C][C]2.12488858887978[/C][C]7[/C][/ROW]
[ROW][C]9[/C][C]-2.75[/C][C]2.09436473336514[/C][C]7[/C][/ROW]
[ROW][C]10[/C][C]0.0833333333333333[/C][C]2.10878393795327[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199264&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
18.752.454124543035118
26.583333333333332.998737107921319
35.916666666666671.311372170551514
42.916666666666671.928651593652157
55.583333333333330.7929614610987593
63.583333333333331.781640374554426
74.916666666666671.083624669450833
83.166666666666672.124888588879787
9-2.752.094364733365147
100.08333333333333332.108783937953277






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.8873905520839
beta-0.00502597007423887
S.D.0.0700375833210032
T-STAT-0.0717610436557091
p-value0.944553680863893

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.8873905520839 \tabularnewline
beta & -0.00502597007423887 \tabularnewline
S.D. & 0.0700375833210032 \tabularnewline
T-STAT & -0.0717610436557091 \tabularnewline
p-value & 0.944553680863893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199264&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.8873905520839[/C][/ROW]
[ROW][C]beta[/C][C]-0.00502597007423887[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0700375833210032[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0717610436557091[/C][/ROW]
[ROW][C]p-value[/C][C]0.944553680863893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199264&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199264&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)
alpha1.8873905520839
beta-0.00502597007423887
S.D.0.0700375833210032
T-STAT-0.0717610436557091
p-value0.944553680863893






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.595617727442752
beta-0.0503043989881816
S.D.0.112078424283898
T-STAT-0.448832139723513
p-value0.667118045629786
Lambda1.05030439898818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.595617727442752 \tabularnewline
beta & -0.0503043989881816 \tabularnewline
S.D. & 0.112078424283898 \tabularnewline
T-STAT & -0.448832139723513 \tabularnewline
p-value & 0.667118045629786 \tabularnewline
Lambda & 1.05030439898818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199264&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.595617727442752[/C][/ROW]
[ROW][C]beta[/C][C]-0.0503043989881816[/C][/ROW]
[ROW][C]S.D.[/C][C]0.112078424283898[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.448832139723513[/C][/ROW]
[ROW][C]p-value[/C][C]0.667118045629786[/C][/ROW]
[ROW][C]Lambda[/C][C]1.05030439898818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199264&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199264&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)
alpha0.595617727442752
beta-0.0503043989881816
S.D.0.112078424283898
T-STAT-0.448832139723513
p-value0.667118045629786
Lambda1.05030439898818


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')