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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 computationSun, 26 Dec 2010 16:37:02 +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/26/t1293381323y8bvlrkjy90e80d.htm/, Retrieved Mon, 06 May 2024 18:43:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115720, Retrieved Mon, 06 May 2024 18:43:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [W6_3] [2010-12-14 20:35:43] [7318566ef3ec88988be4d1362d0cf918]
- R  D  [(Partial) Autocorrelation Function] [Paper_Autocorrelatie] [2010-12-26 16:04:05] [7318566ef3ec88988be4d1362d0cf918]
- RMP     [Spectral Analysis] [Paper_SA] [2010-12-26 16:18:43] [7318566ef3ec88988be4d1362d0cf918]
-   P       [Spectral Analysis] [Paper_SA2] [2010-12-26 16:27:12] [7318566ef3ec88988be4d1362d0cf918]
- RMP           [Standard Deviation-Mean Plot] [Paper_SDMP] [2010-12-26 16:37:02] [edf51d809b713abfc4095a7dca74558e] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112.52
112.39
112.24
112.10
109.85
111.89
111.88
111.48
110.98
110.42
107.90
109.46
109.11
109.26
109.99
110.17
110.28
109.13
110.15
109.39
108.45
108.23
107.44
104.86
106.23
105.85
104.95
104.46
104.66
103.05
104.16
104.08
104.20
103.68
103.69
101.29
103.03
102.90
102.68
102.98
103.47
101.72
102.82
102.74
102.38
101.81
101.88
99.60
100.93
100.85
100.93
101.10
101.10
99.31
100.33
99.99
99.82
99.65
99.06
96.92
98.20
98.54
98.71
98.20
98.29
96.67
97.69
97.78
97.44
96.92
96.84
95.05
96.33
96.33
96.16
96.50
96.33
94.71
95.82
95.47
95.82
95.99
95.73
93.77
94.71
94.62
94.79
94.88
94.79
93.43
94.37
94.62
94.45
94.37
94.20
92.66
93.51
93.60
93.60
93.77
93.60
92.41
93.60
93.34
92.92
92.07
91.89
90.27
91.72
91.98
91.81
91.98
91.30
89.93
90.87
90.53
90.27
90.10
89.68
87.89

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=115720&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=115720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115720&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
1111.09251.424628340687814.61999999999999
2108.8716666666671.532364977491475.42
3104.1916666666671.279963304398244.94
4102.3341666666671.01658482035183.87000000000000
599.99916666666671.205377785617694.17999999999999
697.52751.032306552426083.66
795.74666666666670.791308850556912.73000000000000
894.32416666666670.6516616290590382.22
992.88166666666671.050755860696423.5
1090.67166666666671.207242035937014.09

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 111.0925 & 1.42462834068781 & 4.61999999999999 \tabularnewline
2 & 108.871666666667 & 1.53236497749147 & 5.42 \tabularnewline
3 & 104.191666666667 & 1.27996330439824 & 4.94 \tabularnewline
4 & 102.334166666667 & 1.0165848203518 & 3.87000000000000 \tabularnewline
5 & 99.9991666666667 & 1.20537778561769 & 4.17999999999999 \tabularnewline
6 & 97.5275 & 1.03230655242608 & 3.66 \tabularnewline
7 & 95.7466666666667 & 0.79130885055691 & 2.73000000000000 \tabularnewline
8 & 94.3241666666667 & 0.651661629059038 & 2.22 \tabularnewline
9 & 92.8816666666667 & 1.05075586069642 & 3.5 \tabularnewline
10 & 90.6716666666667 & 1.20724203593701 & 4.09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115720&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]111.0925[/C][C]1.42462834068781[/C][C]4.61999999999999[/C][/ROW]
[ROW][C]2[/C][C]108.871666666667[/C][C]1.53236497749147[/C][C]5.42[/C][/ROW]
[ROW][C]3[/C][C]104.191666666667[/C][C]1.27996330439824[/C][C]4.94[/C][/ROW]
[ROW][C]4[/C][C]102.334166666667[/C][C]1.0165848203518[/C][C]3.87000000000000[/C][/ROW]
[ROW][C]5[/C][C]99.9991666666667[/C][C]1.20537778561769[/C][C]4.17999999999999[/C][/ROW]
[ROW][C]6[/C][C]97.5275[/C][C]1.03230655242608[/C][C]3.66[/C][/ROW]
[ROW][C]7[/C][C]95.7466666666667[/C][C]0.79130885055691[/C][C]2.73000000000000[/C][/ROW]
[ROW][C]8[/C][C]94.3241666666667[/C][C]0.651661629059038[/C][C]2.22[/C][/ROW]
[ROW][C]9[/C][C]92.8816666666667[/C][C]1.05075586069642[/C][C]3.5[/C][/ROW]
[ROW][C]10[/C][C]90.6716666666667[/C][C]1.20724203593701[/C][C]4.09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115720&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
1111.09251.424628340687814.61999999999999
2108.8716666666671.532364977491475.42
3104.1916666666671.279963304398244.94
4102.3341666666671.01658482035183.87000000000000
599.99916666666671.205377785617694.17999999999999
697.52751.032306552426083.66
795.74666666666670.791308850556912.73000000000000
894.32416666666670.6516616290590382.22
992.88166666666671.050755860696423.5
1090.67166666666671.207242035937014.09






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.60355047097439
beta0.0272920854452126
S.D.0.0101135040933368
T-STAT2.69857857309751
p-value0.0271336959050445

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.60355047097439 \tabularnewline
beta & 0.0272920854452126 \tabularnewline
S.D. & 0.0101135040933368 \tabularnewline
T-STAT & 2.69857857309751 \tabularnewline
p-value & 0.0271336959050445 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115720&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.60355047097439[/C][/ROW]
[ROW][C]beta[/C][C]0.0272920854452126[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0101135040933368[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.69857857309751[/C][/ROW]
[ROW][C]p-value[/C][C]0.0271336959050445[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115720&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-1.60355047097439
beta0.0272920854452126
S.D.0.0101135040933368
T-STAT2.69857857309751
p-value0.0271336959050445






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.0648285508143
beta2.42323244322424
S.D.1.05547487589148
T-STAT2.29586937460499
p-value0.050797314492478
Lambda-1.42323244322424

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.0648285508143 \tabularnewline
beta & 2.42323244322424 \tabularnewline
S.D. & 1.05547487589148 \tabularnewline
T-STAT & 2.29586937460499 \tabularnewline
p-value & 0.050797314492478 \tabularnewline
Lambda & -1.42323244322424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115720&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.0648285508143[/C][/ROW]
[ROW][C]beta[/C][C]2.42323244322424[/C][/ROW]
[ROW][C]S.D.[/C][C]1.05547487589148[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.29586937460499[/C][/ROW]
[ROW][C]p-value[/C][C]0.050797314492478[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.42323244322424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115720&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115720&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-11.0648285508143
beta2.42323244322424
S.D.1.05547487589148
T-STAT2.29586937460499
p-value0.050797314492478
Lambda-1.42323244322424


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')