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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, 08 Dec 2008 12:46:48 -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/08/t1228765764ynt36kwaxmsl1tk.htm/, Retrieved Thu, 16 May 2024 15:16:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30865, Retrieved Thu, 16 May 2024 15:16:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [74be16979710d4c4e7c6647856088456]
F RMP   [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [74be16979710d4c4e7c6647856088456]
- RMPD      [Standard Deviation-Mean Plot] [inter productie m...] [2008-12-08 19:46:48] [e1dd70d3b1099218056e8ae5041dcc2f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90,7
94,3
104,6
111,1
110,8
107,2
99
99
91
96,2
96,9
96,2
100,1
99
115,4
106,9
107,1
99,3
99,2
108,3
105,6
99,5
107,4
93,1
88,1
110,7
113,1
99,6
93,6
98,6
99,6
114,3
107,8
101,2
112,5
100,5
93,9
116,2
112
106,4
95,7
96
95,8
103
102,2
98,4
111,4
86,6
91,3
107,9
101,8
104,4
93,4
100,1
98,5
112,9
101,4
107,1
110,8
90,3
95,5
111,4
113
107,5
95,9
106,3
105,2
117,2
106,9
108,2
113
97,2
99,9
108,1
118,1
109,1
93,3
112,1
111,8
112,5
116,3
110,3
117,1
103,4
96,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30865&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30865&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.757.0875691434818720.4
2103.4083333333336.0361725280080322.3
3103.38.331430085689226.2
4101.4666666666678.722211284815929.6
5101.6583333333337.4041092194357422.6
6106.4416666666677.0619928082831121.7
7109.3333333333337.3438079462575224.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.75 & 7.08756914348187 & 20.4 \tabularnewline
2 & 103.408333333333 & 6.03617252800803 & 22.3 \tabularnewline
3 & 103.3 & 8.3314300856892 & 26.2 \tabularnewline
4 & 101.466666666667 & 8.7222112848159 & 29.6 \tabularnewline
5 & 101.658333333333 & 7.40410921943574 & 22.6 \tabularnewline
6 & 106.441666666667 & 7.06199280828311 & 21.7 \tabularnewline
7 & 109.333333333333 & 7.34380794625752 & 24.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30865&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]99.75[/C][C]7.08756914348187[/C][C]20.4[/C][/ROW]
[ROW][C]2[/C][C]103.408333333333[/C][C]6.03617252800803[/C][C]22.3[/C][/ROW]
[ROW][C]3[/C][C]103.3[/C][C]8.3314300856892[/C][C]26.2[/C][/ROW]
[ROW][C]4[/C][C]101.466666666667[/C][C]8.7222112848159[/C][C]29.6[/C][/ROW]
[ROW][C]5[/C][C]101.658333333333[/C][C]7.40410921943574[/C][C]22.6[/C][/ROW]
[ROW][C]6[/C][C]106.441666666667[/C][C]7.06199280828311[/C][C]21.7[/C][/ROW]
[ROW][C]7[/C][C]109.333333333333[/C][C]7.34380794625752[/C][C]24.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30865&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
199.757.0875691434818720.4
2103.4083333333336.0361725280080322.3
3103.38.331430085689226.2
4101.4666666666678.722211284815929.6
5101.6583333333337.4041092194357422.6
6106.4416666666677.0619928082831121.7
7109.3333333333337.3438079462575224.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha12.1562409328838
beta-0.0456414326448521
S.D.0.119071796028698
T-STAT-0.383310189037981
p-value0.717245978652446

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 12.1562409328838 \tabularnewline
beta & -0.0456414326448521 \tabularnewline
S.D. & 0.119071796028698 \tabularnewline
T-STAT & -0.383310189037981 \tabularnewline
p-value & 0.717245978652446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30865&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.1562409328838[/C][/ROW]
[ROW][C]beta[/C][C]-0.0456414326448521[/C][/ROW]
[ROW][C]S.D.[/C][C]0.119071796028698[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.383310189037981[/C][/ROW]
[ROW][C]p-value[/C][C]0.717245978652446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30865&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)
alpha12.1562409328838
beta-0.0456414326448521
S.D.0.119071796028698
T-STAT-0.383310189037981
p-value0.717245978652446






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha4.72084132837898
beta-0.586572614586132
S.D.1.69794188410344
T-STAT-0.345460948974622
p-value0.743807310650771
Lambda1.58657261458613

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.72084132837898 \tabularnewline
beta & -0.586572614586132 \tabularnewline
S.D. & 1.69794188410344 \tabularnewline
T-STAT & -0.345460948974622 \tabularnewline
p-value & 0.743807310650771 \tabularnewline
Lambda & 1.58657261458613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30865&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.72084132837898[/C][/ROW]
[ROW][C]beta[/C][C]-0.586572614586132[/C][/ROW]
[ROW][C]S.D.[/C][C]1.69794188410344[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.345460948974622[/C][/ROW]
[ROW][C]p-value[/C][C]0.743807310650771[/C][/ROW]
[ROW][C]Lambda[/C][C]1.58657261458613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30865&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30865&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)
alpha4.72084132837898
beta-0.586572614586132
S.D.1.69794188410344
T-STAT-0.345460948974622
p-value0.743807310650771
Lambda1.58657261458613


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')