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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 computationTue, 14 Dec 2010 16:20:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292343936eaaytp6954fds97.htm/, Retrieved Thu, 02 May 2024 15:53:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109845, Retrieved Thu, 02 May 2024 15:53:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- R PD          [Standard Deviation-Mean Plot] [WS9 - Standard De...] [2010-12-07 09:15:36] [1f5baf2b24e732d76900bb8178fc04e7]
-    D              [Standard Deviation-Mean Plot] [Paper - Standard ...] [2010-12-14 16:20:25] [ee4a783fb13f41eb2e9bc8a0c4f26279] [Current]
-    D                [Standard Deviation-Mean Plot] [paper Standard De...] [2010-12-26 15:54:48] [eeb33d252044f8583501f5ba0605ad6d]
-    D                [Standard Deviation-Mean Plot] [paper lambda waar...] [2010-12-26 16:00:23] [eeb33d252044f8583501f5ba0605ad6d]
-   PD                  [Standard Deviation-Mean Plot] [paper Standard De...] [2010-12-26 17:09:45] [eeb33d252044f8583501f5ba0605ad6d]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10.81
9.12
11.03
12.74
9.98
11.62
9.40
9.27
7.76
8.78
10.65
10.95
12.36
10.85
11.84
12.14
11.65
8.86
7.63
7.38
7.25
8.03
7.75
7.16
7.18
7.51
7.07
7.11
8.98
9.53
10.54
11.31
10.36
11.44
10.45
10.69
11.28
11.96
13.52
12.89
14.03
16.27
16.17
17.25
19.38
26.20
33.53
32.20
38.45
44.86
41.67
36.06
39.76
36.81
42.65
46.89
53.61
57.59
67.82
71.89
75.51
68.49
62.72
70.39
59.77
57.27
67.96
67.85
76.98
81.08
91.66
84.84
85.73
84.61
92.91
99.80
121.19
122.04
131.76
138.48
153.47
189.95
182.22
198.08
135.36
125.02
143.50
173.95
188.75
167.44
158.95
169.53
113.66
107.59
92.67
85.35
90.13
89.31
105.12
125.83
135.81
142.43
163.39
168.21
185.35
188.50
199.91
210.73
192.06
204.62
235.00
261.09
256.88
251.53
257.25
243.10
283.75

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109845&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109845&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
110.17583333333331.380931558657774.98
29.408333333333332.155993056715645.2
39.34751.709099310907784.37
418.72333333333337.7234852393478622.25
548.171666666666712.035228466565335.83
672.043333333333310.322288623374334.39
7133.35333333333340.334396404723113.47
8138.48083333333333.9982388469898103.4
9150.39333333333342.1521168094219121.42

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10.1758333333333 & 1.38093155865777 & 4.98 \tabularnewline
2 & 9.40833333333333 & 2.15599305671564 & 5.2 \tabularnewline
3 & 9.3475 & 1.70909931090778 & 4.37 \tabularnewline
4 & 18.7233333333333 & 7.72348523934786 & 22.25 \tabularnewline
5 & 48.1716666666667 & 12.0352284665653 & 35.83 \tabularnewline
6 & 72.0433333333333 & 10.3222886233743 & 34.39 \tabularnewline
7 & 133.353333333333 & 40.334396404723 & 113.47 \tabularnewline
8 & 138.480833333333 & 33.9982388469898 & 103.4 \tabularnewline
9 & 150.393333333333 & 42.1521168094219 & 121.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109845&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]10.1758333333333[/C][C]1.38093155865777[/C][C]4.98[/C][/ROW]
[ROW][C]2[/C][C]9.40833333333333[/C][C]2.15599305671564[/C][C]5.2[/C][/ROW]
[ROW][C]3[/C][C]9.3475[/C][C]1.70909931090778[/C][C]4.37[/C][/ROW]
[ROW][C]4[/C][C]18.7233333333333[/C][C]7.72348523934786[/C][C]22.25[/C][/ROW]
[ROW][C]5[/C][C]48.1716666666667[/C][C]12.0352284665653[/C][C]35.83[/C][/ROW]
[ROW][C]6[/C][C]72.0433333333333[/C][C]10.3222886233743[/C][C]34.39[/C][/ROW]
[ROW][C]7[/C][C]133.353333333333[/C][C]40.334396404723[/C][C]113.47[/C][/ROW]
[ROW][C]8[/C][C]138.480833333333[/C][C]33.9982388469898[/C][C]103.4[/C][/ROW]
[ROW][C]9[/C][C]150.393333333333[/C][C]42.1521168094219[/C][C]121.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109845&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
110.17583333333331.380931558657774.98
29.408333333333332.155993056715645.2
39.34751.709099310907784.37
418.72333333333337.7234852393478622.25
548.171666666666712.035228466565335.83
672.043333333333310.322288623374334.39
7133.35333333333340.334396404723113.47
8138.48083333333333.9982388469898103.4
9150.39333333333342.1521168094219121.42






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.18084814300883
beta0.275275546166156
S.D.0.0242646556040649
T-STAT11.3447126824269
p-value9.26027671396061e-06

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.18084814300883 \tabularnewline
beta & 0.275275546166156 \tabularnewline
S.D. & 0.0242646556040649 \tabularnewline
T-STAT & 11.3447126824269 \tabularnewline
p-value & 9.26027671396061e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109845&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.18084814300883[/C][/ROW]
[ROW][C]beta[/C][C]0.275275546166156[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0242646556040649[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.3447126824269[/C][/ROW]
[ROW][C]p-value[/C][C]9.26027671396061e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109845&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109845&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)
alpha-1.18084814300883
beta0.275275546166156
S.D.0.0242646556040649
T-STAT11.3447126824269
p-value9.26027671396061e-06






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.7900749036487
beta1.08721671308954
S.D.0.10640382531625
T-STAT10.2178348368411
p-value1.85576453976231e-05
Lambda-0.0872167130895398

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.7900749036487 \tabularnewline
beta & 1.08721671308954 \tabularnewline
S.D. & 0.10640382531625 \tabularnewline
T-STAT & 10.2178348368411 \tabularnewline
p-value & 1.85576453976231e-05 \tabularnewline
Lambda & -0.0872167130895398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109845&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.7900749036487[/C][/ROW]
[ROW][C]beta[/C][C]1.08721671308954[/C][/ROW]
[ROW][C]S.D.[/C][C]0.10640382531625[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.2178348368411[/C][/ROW]
[ROW][C]p-value[/C][C]1.85576453976231e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0872167130895398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109845&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109845&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-1.7900749036487
beta1.08721671308954
S.D.0.10640382531625
T-STAT10.2178348368411
p-value1.85576453976231e-05
Lambda-0.0872167130895398


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')