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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 computationFri, 27 Nov 2009 13:49:04 -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/2009/Nov/27/t125935501884yzekjv1p6oqxh.htm/, Retrieved Sun, 28 Apr 2024 18:54:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61273, Retrieved Sun, 28 Apr 2024 18:54:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-   PD        [Standard Deviation-Mean Plot] [Methode 4] [2009-11-27 18:02:48] [76ab39dc7a55316678260825bd5ad46c]
-    D            [Standard Deviation-Mean Plot] [methode 4] [2009-11-27 20:49:04] [986e3c28a4248c495afaef9fd432264f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98.71
98.54
98.2
96.92
99.06
99.65
99.82
99.99
100.33
99.31
101.1
101.1
100.93
100.85
100.93
99.6
101.88
101.81
102.38
102.74
102.82
101.72
103.47
102.98
102.68
102.9
103.03
101.29
103.69
103.68
104.2
104.08
104.16
103.05
104.66
104.46
104.95
105.85
106.23
104.86
107.44
108.23
108.45
109.39
110.15
109.13
110.28
110.17
109.99
109.26
109.11
107.06
109.53
108.92
109.24
109.12
109
107.23
109.49
109.04

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61273&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61273&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
198.09250.8099125467192931.78999999999999
299.630.4045573712919640.929999999999993
3100.460.8482531068810341.78999999999999
4100.57750.6527569736637611.33000000000001
5102.20250.4391184350491310.929999999999993
6102.74750.7387094602525861.75
7102.4750.8030981675154441.73999999999999
8103.91250.2672545602978550.519999999999996
9104.08250.71834880107091.61
10105.47250.6744071470558421.37000000000000
11108.37750.80230397398161.95000000000000
12109.93250.5380442980523731.15000000000001
13108.8551.256887690554202.92999999999999
14109.20250.2551306854666180.61
15108.690.9983653305946322.25999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.0925 & 0.809912546719293 & 1.78999999999999 \tabularnewline
2 & 99.63 & 0.404557371291964 & 0.929999999999993 \tabularnewline
3 & 100.46 & 0.848253106881034 & 1.78999999999999 \tabularnewline
4 & 100.5775 & 0.652756973663761 & 1.33000000000001 \tabularnewline
5 & 102.2025 & 0.439118435049131 & 0.929999999999993 \tabularnewline
6 & 102.7475 & 0.738709460252586 & 1.75 \tabularnewline
7 & 102.475 & 0.803098167515444 & 1.73999999999999 \tabularnewline
8 & 103.9125 & 0.267254560297855 & 0.519999999999996 \tabularnewline
9 & 104.0825 & 0.7183488010709 & 1.61 \tabularnewline
10 & 105.4725 & 0.674407147055842 & 1.37000000000000 \tabularnewline
11 & 108.3775 & 0.8023039739816 & 1.95000000000000 \tabularnewline
12 & 109.9325 & 0.538044298052373 & 1.15000000000001 \tabularnewline
13 & 108.855 & 1.25688769055420 & 2.92999999999999 \tabularnewline
14 & 109.2025 & 0.255130685466618 & 0.61 \tabularnewline
15 & 108.69 & 0.998365330594632 & 2.25999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61273&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]98.0925[/C][C]0.809912546719293[/C][C]1.78999999999999[/C][/ROW]
[ROW][C]2[/C][C]99.63[/C][C]0.404557371291964[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]3[/C][C]100.46[/C][C]0.848253106881034[/C][C]1.78999999999999[/C][/ROW]
[ROW][C]4[/C][C]100.5775[/C][C]0.652756973663761[/C][C]1.33000000000001[/C][/ROW]
[ROW][C]5[/C][C]102.2025[/C][C]0.439118435049131[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]6[/C][C]102.7475[/C][C]0.738709460252586[/C][C]1.75[/C][/ROW]
[ROW][C]7[/C][C]102.475[/C][C]0.803098167515444[/C][C]1.73999999999999[/C][/ROW]
[ROW][C]8[/C][C]103.9125[/C][C]0.267254560297855[/C][C]0.519999999999996[/C][/ROW]
[ROW][C]9[/C][C]104.0825[/C][C]0.7183488010709[/C][C]1.61[/C][/ROW]
[ROW][C]10[/C][C]105.4725[/C][C]0.674407147055842[/C][C]1.37000000000000[/C][/ROW]
[ROW][C]11[/C][C]108.3775[/C][C]0.8023039739816[/C][C]1.95000000000000[/C][/ROW]
[ROW][C]12[/C][C]109.9325[/C][C]0.538044298052373[/C][C]1.15000000000001[/C][/ROW]
[ROW][C]13[/C][C]108.855[/C][C]1.25688769055420[/C][C]2.92999999999999[/C][/ROW]
[ROW][C]14[/C][C]109.2025[/C][C]0.255130685466618[/C][C]0.61[/C][/ROW]
[ROW][C]15[/C][C]108.69[/C][C]0.998365330594632[/C][C]2.25999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61273&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
198.09250.8099125467192931.78999999999999
299.630.4045573712919640.929999999999993
3100.460.8482531068810341.78999999999999
4100.57750.6527569736637611.33000000000001
5102.20250.4391184350491310.929999999999993
6102.74750.7387094602525861.75
7102.4750.8030981675154441.73999999999999
8103.91250.2672545602978550.519999999999996
9104.08250.71834880107091.61
10105.47250.6744071470558421.37000000000000
11108.37750.80230397398161.95000000000000
12109.93250.5380442980523731.15000000000001
13108.8551.256887690554202.92999999999999
14109.20250.2551306854666180.61
15108.690.9983653305946322.25999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.255220419502996
beta0.00897000392468391
S.D.0.0190287158792478
T-STAT0.471393024185429
p-value0.645173109242674

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.255220419502996 \tabularnewline
beta & 0.00897000392468391 \tabularnewline
S.D. & 0.0190287158792478 \tabularnewline
T-STAT & 0.471393024185429 \tabularnewline
p-value & 0.645173109242674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61273&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.255220419502996[/C][/ROW]
[ROW][C]beta[/C][C]0.00897000392468391[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0190287158792478[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.471393024185429[/C][/ROW]
[ROW][C]p-value[/C][C]0.645173109242674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61273&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61273&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-0.255220419502996
beta0.00897000392468391
S.D.0.0190287158792478
T-STAT0.471393024185429
p-value0.645173109242674






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.57661737384327
beta0.237784570848646
S.D.3.38216194518612
T-STAT0.0703054953317916
p-value0.945020526200753
Lambda0.762215429151355

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.57661737384327 \tabularnewline
beta & 0.237784570848646 \tabularnewline
S.D. & 3.38216194518612 \tabularnewline
T-STAT & 0.0703054953317916 \tabularnewline
p-value & 0.945020526200753 \tabularnewline
Lambda & 0.762215429151355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61273&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.57661737384327[/C][/ROW]
[ROW][C]beta[/C][C]0.237784570848646[/C][/ROW]
[ROW][C]S.D.[/C][C]3.38216194518612[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0703054953317916[/C][/ROW]
[ROW][C]p-value[/C][C]0.945020526200753[/C][/ROW]
[ROW][C]Lambda[/C][C]0.762215429151355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61273&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61273&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-1.57661737384327
beta0.237784570848646
S.D.3.38216194518612
T-STAT0.0703054953317916
p-value0.945020526200753
Lambda0.762215429151355


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')