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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, 14 Dec 2014 15:39:05 +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/2014/Dec/14/t14185715982h6a1bxh3jz1oat.htm/, Retrieved Thu, 16 May 2024 21:35:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267697, Retrieved Thu, 16 May 2024 21:35:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

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] [] [2014-12-14 15:39:05] [42cc6d0d468769986f2f8c7c7fdc2d20] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12
6.3
11.3
11.9
9.3
9.6
10
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1
4.35
12.7
18.1
17.85
16.6
12.6
17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6
18.9
14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1
11.6
17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85
14.6
13.85
18.95
15.6
14.85
11.75
18.45
15.9
17.1
16.1
19.9
10.95
18.45
15.1
15
11.35
15.95
18.1
14.6
15.4
15.4
17.6
13.35
19.1
15.35
7.6
13.4
13.9
19.1
15.25
12.9
16.1
17.35
13.15
12.15
12.6
10.35
15.4
9.6
18.2
13.6
14.85
14.75
14.1
14.9
16.25
19.25
13.6
13.6
15.65
12.75
14.6
9.85
12.65
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
18.15
11.15
15.65
17.75
7.65
12.35
15.6
19.3
15.2
17.1
15.6
18.4
19.05
18.55
19.1
13.1
12.85
9.5
4.5
11.85
13.6
11.7
12.4
13.35
11.4
14.9
19.9
11.2
14.6
17.6
14.05
16.1
13.35
11.85
11.95
14.75
15.15
13.2
16.85
7.85
7.7
12.6
7.85
10.95
12.35
9.95
14.9
16.65
13.4
13.95
15.7
16.85
10.95
15.35
12.2
15.1
17.75
15.2
14.6
16.65
8.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267697&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267697&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
110.81666666666672.873019739619358.4
210.48333333333332.405989999727327.5
311.10833333333332.079973047610937.8
410.71666666666672.090164557825027.1
510.91666666666672.762355165543728.6
611.50833333333332.412263491311678.3
710.95833333333332.9348868131600210.3
810.00833333333332.190665458602747.6
910.01666666666672.834794632078429.3
1013.09166666666674.7879979367606514.75
1114.93333333333332.367232113415988.3
1214.77916666666672.969577436524459.8
1315.36666666666672.387784569745598.35
1416.09166666666672.745312809907548.95
1514.93.0950106476538811.5
1614.30416666666672.432026683216868.75
1714.86252.449594122224419.65
1813.82916666666672.644931545198839.35
1915.11253.2753296156126211.65
2013.71666666666674.4300283876236614.6
2114.18752.649195847113548.7
2212.00833333333333.156222809663869.15
2314.80833333333331.953881141510796.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10.8166666666667 & 2.87301973961935 & 8.4 \tabularnewline
2 & 10.4833333333333 & 2.40598999972732 & 7.5 \tabularnewline
3 & 11.1083333333333 & 2.07997304761093 & 7.8 \tabularnewline
4 & 10.7166666666667 & 2.09016455782502 & 7.1 \tabularnewline
5 & 10.9166666666667 & 2.76235516554372 & 8.6 \tabularnewline
6 & 11.5083333333333 & 2.41226349131167 & 8.3 \tabularnewline
7 & 10.9583333333333 & 2.93488681316002 & 10.3 \tabularnewline
8 & 10.0083333333333 & 2.19066545860274 & 7.6 \tabularnewline
9 & 10.0166666666667 & 2.83479463207842 & 9.3 \tabularnewline
10 & 13.0916666666667 & 4.78799793676065 & 14.75 \tabularnewline
11 & 14.9333333333333 & 2.36723211341598 & 8.3 \tabularnewline
12 & 14.7791666666667 & 2.96957743652445 & 9.8 \tabularnewline
13 & 15.3666666666667 & 2.38778456974559 & 8.35 \tabularnewline
14 & 16.0916666666667 & 2.74531280990754 & 8.95 \tabularnewline
15 & 14.9 & 3.09501064765388 & 11.5 \tabularnewline
16 & 14.3041666666667 & 2.43202668321686 & 8.75 \tabularnewline
17 & 14.8625 & 2.44959412222441 & 9.65 \tabularnewline
18 & 13.8291666666667 & 2.64493154519883 & 9.35 \tabularnewline
19 & 15.1125 & 3.27532961561262 & 11.65 \tabularnewline
20 & 13.7166666666667 & 4.43002838762366 & 14.6 \tabularnewline
21 & 14.1875 & 2.64919584711354 & 8.7 \tabularnewline
22 & 12.0083333333333 & 3.15622280966386 & 9.15 \tabularnewline
23 & 14.8083333333333 & 1.95388114151079 & 6.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267697&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]10.8166666666667[/C][C]2.87301973961935[/C][C]8.4[/C][/ROW]
[ROW][C]2[/C][C]10.4833333333333[/C][C]2.40598999972732[/C][C]7.5[/C][/ROW]
[ROW][C]3[/C][C]11.1083333333333[/C][C]2.07997304761093[/C][C]7.8[/C][/ROW]
[ROW][C]4[/C][C]10.7166666666667[/C][C]2.09016455782502[/C][C]7.1[/C][/ROW]
[ROW][C]5[/C][C]10.9166666666667[/C][C]2.76235516554372[/C][C]8.6[/C][/ROW]
[ROW][C]6[/C][C]11.5083333333333[/C][C]2.41226349131167[/C][C]8.3[/C][/ROW]
[ROW][C]7[/C][C]10.9583333333333[/C][C]2.93488681316002[/C][C]10.3[/C][/ROW]
[ROW][C]8[/C][C]10.0083333333333[/C][C]2.19066545860274[/C][C]7.6[/C][/ROW]
[ROW][C]9[/C][C]10.0166666666667[/C][C]2.83479463207842[/C][C]9.3[/C][/ROW]
[ROW][C]10[/C][C]13.0916666666667[/C][C]4.78799793676065[/C][C]14.75[/C][/ROW]
[ROW][C]11[/C][C]14.9333333333333[/C][C]2.36723211341598[/C][C]8.3[/C][/ROW]
[ROW][C]12[/C][C]14.7791666666667[/C][C]2.96957743652445[/C][C]9.8[/C][/ROW]
[ROW][C]13[/C][C]15.3666666666667[/C][C]2.38778456974559[/C][C]8.35[/C][/ROW]
[ROW][C]14[/C][C]16.0916666666667[/C][C]2.74531280990754[/C][C]8.95[/C][/ROW]
[ROW][C]15[/C][C]14.9[/C][C]3.09501064765388[/C][C]11.5[/C][/ROW]
[ROW][C]16[/C][C]14.3041666666667[/C][C]2.43202668321686[/C][C]8.75[/C][/ROW]
[ROW][C]17[/C][C]14.8625[/C][C]2.44959412222441[/C][C]9.65[/C][/ROW]
[ROW][C]18[/C][C]13.8291666666667[/C][C]2.64493154519883[/C][C]9.35[/C][/ROW]
[ROW][C]19[/C][C]15.1125[/C][C]3.27532961561262[/C][C]11.65[/C][/ROW]
[ROW][C]20[/C][C]13.7166666666667[/C][C]4.43002838762366[/C][C]14.6[/C][/ROW]
[ROW][C]21[/C][C]14.1875[/C][C]2.64919584711354[/C][C]8.7[/C][/ROW]
[ROW][C]22[/C][C]12.0083333333333[/C][C]3.15622280966386[/C][C]9.15[/C][/ROW]
[ROW][C]23[/C][C]14.8083333333333[/C][C]1.95388114151079[/C][C]6.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267697&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
110.81666666666672.873019739619358.4
210.48333333333332.405989999727327.5
311.10833333333332.079973047610937.8
410.71666666666672.090164557825027.1
510.91666666666672.762355165543728.6
611.50833333333332.412263491311678.3
710.95833333333332.9348868131600210.3
810.00833333333332.190665458602747.6
910.01666666666672.834794632078429.3
1013.09166666666674.7879979367606514.75
1114.93333333333332.367232113415988.3
1214.77916666666672.969577436524459.8
1315.36666666666672.387784569745598.35
1416.09166666666672.745312809907548.95
1514.93.0950106476538811.5
1614.30416666666672.432026683216868.75
1714.86252.449594122224419.65
1813.82916666666672.644931545198839.35
1915.11253.2753296156126211.65
2013.71666666666674.4300283876236614.6
2114.18752.649195847113548.7
2212.00833333333333.156222809663869.15
2314.80833333333331.953881141510796.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.2328332119387
beta0.042117325842264
S.D.0.072529629778435
T-STAT0.580691311549843
p-value0.567628612292431

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.2328332119387 \tabularnewline
beta & 0.042117325842264 \tabularnewline
S.D. & 0.072529629778435 \tabularnewline
T-STAT & 0.580691311549843 \tabularnewline
p-value & 0.567628612292431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267697&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.2328332119387[/C][/ROW]
[ROW][C]beta[/C][C]0.042117325842264[/C][/ROW]
[ROW][C]S.D.[/C][C]0.072529629778435[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.580691311549843[/C][/ROW]
[ROW][C]p-value[/C][C]0.567628612292431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267697&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267697&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)
alpha2.2328332119387
beta0.042117325842264
S.D.0.072529629778435
T-STAT0.580691311549843
p-value0.567628612292431






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.465840887679622
beta0.208589444642763
S.D.0.292496061148042
T-STAT0.713135909673629
p-value0.483611798951894
Lambda0.791410555357237

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.465840887679622 \tabularnewline
beta & 0.208589444642763 \tabularnewline
S.D. & 0.292496061148042 \tabularnewline
T-STAT & 0.713135909673629 \tabularnewline
p-value & 0.483611798951894 \tabularnewline
Lambda & 0.791410555357237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267697&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.465840887679622[/C][/ROW]
[ROW][C]beta[/C][C]0.208589444642763[/C][/ROW]
[ROW][C]S.D.[/C][C]0.292496061148042[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.713135909673629[/C][/ROW]
[ROW][C]p-value[/C][C]0.483611798951894[/C][/ROW]
[ROW][C]Lambda[/C][C]0.791410555357237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267697&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267697&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)
alpha0.465840887679622
beta0.208589444642763
S.D.0.292496061148042
T-STAT0.713135909673629
p-value0.483611798951894
Lambda0.791410555357237


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')