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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 computationSun, 11 Jul 2010 15:29:06 +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/Jul/11/t12788621986kyx3wen45bx9tp.htm/, Retrieved Fri, 03 May 2024 07:59:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77994, Retrieved Fri, 03 May 2024 07:59:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsFebiri Lordina
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-07-11 15:29:06] [ee335b92128d1ec04d3c346475765c6a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
213
212
211
209
229
228
213
203
204
204
205
207
205
208
201
201
220
218
203
185
179
182
182
185
183
192
177
172
188
182
162
150
141
135
139
148
142
156
143
134
146
142
117
106
104
99
105
106
96
104
96
85
91
98
73
70
62
60
70
82
72
73
68
53
61
73
46
50
52
45
58
73
58
49
44
35
46
61
29
33
37
31
44
57
42
34
27
22
30
47
12
13
18
11
26
41
21
24
30
34
48
64
35
44
55
53
73
94
73
78
87
87
91
104
73
84
103
111
131
155

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=77994&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=77994&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77994&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
1211.58.7230103227560826
2197.41666666666714.406175022811541
3164.08333333333320.734066536777557
412520.644171530526957
582.2514.997727100524944
660.333333333333311.089170256141728
743.666666666666710.982079065735332
826.916666666666712.295293507039336
947.916666666666721.491894173188173
1098.083333333333324.688820927453882

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 211.5 & 8.72301032275608 & 26 \tabularnewline
2 & 197.416666666667 & 14.4061750228115 & 41 \tabularnewline
3 & 164.083333333333 & 20.7340665367775 & 57 \tabularnewline
4 & 125 & 20.6441715305269 & 57 \tabularnewline
5 & 82.25 & 14.9977271005249 & 44 \tabularnewline
6 & 60.3333333333333 & 11.0891702561417 & 28 \tabularnewline
7 & 43.6666666666667 & 10.9820790657353 & 32 \tabularnewline
8 & 26.9166666666667 & 12.2952935070393 & 36 \tabularnewline
9 & 47.9166666666667 & 21.4918941731881 & 73 \tabularnewline
10 & 98.0833333333333 & 24.6888209274538 & 82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77994&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]211.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]197.416666666667[/C][C]14.4061750228115[/C][C]41[/C][/ROW]
[ROW][C]3[/C][C]164.083333333333[/C][C]20.7340665367775[/C][C]57[/C][/ROW]
[ROW][C]4[/C][C]125[/C][C]20.6441715305269[/C][C]57[/C][/ROW]
[ROW][C]5[/C][C]82.25[/C][C]14.9977271005249[/C][C]44[/C][/ROW]
[ROW][C]6[/C][C]60.3333333333333[/C][C]11.0891702561417[/C][C]28[/C][/ROW]
[ROW][C]7[/C][C]43.6666666666667[/C][C]10.9820790657353[/C][C]32[/C][/ROW]
[ROW][C]8[/C][C]26.9166666666667[/C][C]12.2952935070393[/C][C]36[/C][/ROW]
[ROW][C]9[/C][C]47.9166666666667[/C][C]21.4918941731881[/C][C]73[/C][/ROW]
[ROW][C]10[/C][C]98.0833333333333[/C][C]24.6888209274538[/C][C]82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77994&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77994&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
1211.58.7230103227560826
2197.41666666666714.406175022811541
3164.08333333333320.734066536777557
412520.644171530526957
582.2514.997727100524944
660.333333333333311.089170256141728
743.666666666666710.982079065735332
826.916666666666712.295293507039336
947.916666666666721.491894173188173
1098.083333333333324.688820927453882






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha16.2307480090945
beta-0.00213312783981415
S.D.0.0291949264308633
T-STAT-0.0730650185012667
p-value0.943548158594884

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 16.2307480090945 \tabularnewline
beta & -0.00213312783981415 \tabularnewline
S.D. & 0.0291949264308633 \tabularnewline
T-STAT & -0.0730650185012667 \tabularnewline
p-value & 0.943548158594884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77994&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16.2307480090945[/C][/ROW]
[ROW][C]beta[/C][C]-0.00213312783981415[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0291949264308633[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0730650185012667[/C][/ROW]
[ROW][C]p-value[/C][C]0.943548158594884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77994&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77994&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)
alpha16.2307480090945
beta-0.00213312783981415
S.D.0.0291949264308633
T-STAT-0.0730650185012667
p-value0.943548158594884






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.50229824664207
beta0.048500102894159
S.D.0.177454604721633
T-STAT0.273309914782091
p-value0.791538222780966
Lambda0.95149989710584

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.50229824664207 \tabularnewline
beta & 0.048500102894159 \tabularnewline
S.D. & 0.177454604721633 \tabularnewline
T-STAT & 0.273309914782091 \tabularnewline
p-value & 0.791538222780966 \tabularnewline
Lambda & 0.95149989710584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77994&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.50229824664207[/C][/ROW]
[ROW][C]beta[/C][C]0.048500102894159[/C][/ROW]
[ROW][C]S.D.[/C][C]0.177454604721633[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.273309914782091[/C][/ROW]
[ROW][C]p-value[/C][C]0.791538222780966[/C][/ROW]
[ROW][C]Lambda[/C][C]0.95149989710584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77994&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77994&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)
alpha2.50229824664207
beta0.048500102894159
S.D.0.177454604721633
T-STAT0.273309914782091
p-value0.791538222780966
Lambda0.95149989710584


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')