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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, 07 Dec 2008 10:58:18 -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/07/t1228672739u0ymt9re28zncza.htm/, Retrieved Sat, 18 May 2024 11:33:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30199, Retrieved Sat, 18 May 2024 11:33:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:37:06] [a0d819c22534897f04a2f0b92f1eb36a]
-    D      [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:58:18] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
- RM          [Variance Reduction Matrix] [s2] [2008-12-07 18:02:35] [a0d819c22534897f04a2f0b92f1eb36a]
- RMP           [(Partial) Autocorrelation Function] [S2 ACF] [2008-12-07 18:10:24] [a0d819c22534897f04a2f0b92f1eb36a]
-   P             [(Partial) Autocorrelation Function] [s2] [2008-12-07 18:12:59] [a0d819c22534897f04a2f0b92f1eb36a]
-   P               [(Partial) Autocorrelation Function] [s2 ACF] [2008-12-07 18:25:03] [a0d819c22534897f04a2f0b92f1eb36a]
-                     [(Partial) Autocorrelation Function] [s2 acf d1D1] [2008-12-07 18:26:56] [a0d819c22534897f04a2f0b92f1eb36a]
- RM                    [Spectral Analysis] [S2 SA - d0 D0 L1] [2008-12-07 18:29:54] [a0d819c22534897f04a2f0b92f1eb36a]
-                         [Spectral Analysis] [s2 SA d1D1 L1] [2008-12-07 18:32:14] [a0d819c22534897f04a2f0b92f1eb36a]
-                           [Spectral Analysis] [s3] [2008-12-07 18:39:13] [a0d819c22534897f04a2f0b92f1eb36a]
-                             [Spectral Analysis] [s3 sa] [2008-12-07 18:42:05] [a0d819c22534897f04a2f0b92f1eb36a]
- RM                            [(Partial) Autocorrelation Function] [s4] [2008-12-07 18:48:27] [a0d819c22534897f04a2f0b92f1eb36a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105

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=30199&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=30199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30199&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
1137.16666666666716.519043188961948
2133.58333333333316.188988026845145
3127.83333333333313.992422191596439
4111.511.658005443003137
5103.08333333333311.626445820810536

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 137.166666666667 & 16.5190431889619 & 48 \tabularnewline
2 & 133.583333333333 & 16.1889880268451 & 45 \tabularnewline
3 & 127.833333333333 & 13.9924221915964 & 39 \tabularnewline
4 & 111.5 & 11.6580054430031 & 37 \tabularnewline
5 & 103.083333333333 & 11.6264458208105 & 36 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30199&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]137.166666666667[/C][C]16.5190431889619[/C][C]48[/C][/ROW]
[ROW][C]2[/C][C]133.583333333333[/C][C]16.1889880268451[/C][C]45[/C][/ROW]
[ROW][C]3[/C][C]127.833333333333[/C][C]13.9924221915964[/C][C]39[/C][/ROW]
[ROW][C]4[/C][C]111.5[/C][C]11.6580054430031[/C][C]37[/C][/ROW]
[ROW][C]5[/C][C]103.083333333333[/C][C]11.6264458208105[/C][C]36[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30199&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
1137.16666666666716.519043188961948
2133.58333333333316.188988026845145
3127.83333333333313.992422191596439
4111.511.658005443003137
5103.08333333333311.626445820810536






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.87620271550662
beta0.153899295866404
S.D.0.0262352265049625
T-STAT5.86613177657504
p-value0.00987982527735116

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.87620271550662 \tabularnewline
beta & 0.153899295866404 \tabularnewline
S.D. & 0.0262352265049625 \tabularnewline
T-STAT & 5.86613177657504 \tabularnewline
p-value & 0.00987982527735116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30199&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.87620271550662[/C][/ROW]
[ROW][C]beta[/C][C]0.153899295866404[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0262352265049625[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.86613177657504[/C][/ROW]
[ROW][C]p-value[/C][C]0.00987982527735116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30199&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-4.87620271550662
beta0.153899295866404
S.D.0.0262352265049625
T-STAT5.86613177657504
p-value0.00987982527735116






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.7325835096635
beta1.32408700206543
S.D.0.228972207459787
T-STAT5.78274113157588
p-value0.0102845427483849
Lambda-0.324087002065433

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.7325835096635 \tabularnewline
beta & 1.32408700206543 \tabularnewline
S.D. & 0.228972207459787 \tabularnewline
T-STAT & 5.78274113157588 \tabularnewline
p-value & 0.0102845427483849 \tabularnewline
Lambda & -0.324087002065433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30199&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.7325835096635[/C][/ROW]
[ROW][C]beta[/C][C]1.32408700206543[/C][/ROW]
[ROW][C]S.D.[/C][C]0.228972207459787[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.78274113157588[/C][/ROW]
[ROW][C]p-value[/C][C]0.0102845427483849[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.324087002065433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30199&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-3.7325835096635
beta1.32408700206543
S.D.0.228972207459787
T-STAT5.78274113157588
p-value0.0102845427483849
Lambda-0.324087002065433


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')