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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 computationMon, 02 Dec 2013 12:20:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/02/t13860048490o8vlw5qx3n7ya4.htm/, Retrieved Thu, 25 Apr 2024 10:34:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230043, Retrieved Thu, 25 Apr 2024 10:34:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

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] [] [2013-12-02 17:20:36] [edf84888c7447b9af382ed711d9803fc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
107.2
107.56
107.72
108.14
108.16
108.16
108.16
108.1
108.95
110.49
110.72
110.82
110.82
110.75
110.71
110.86
110.84
110.84
110.84
110.92
111.46
112.46
113.04
113.15
113.15
113.21
113.37
113.47
113.71
113.71
113.71
113.8
115.46
117
117.94
118.08
118.08
118.47
118.49
118.45
118.54
118.55
118.55
118.55
119.04
121.37
122
122.14
122.14
122.03
121.91
122.23
121.73
121.83
121.83
122.49
123.02
125.98
126.13
126.39
126.39
126.57
126.87
127.26
126.82
126.7
126.7
126.7
128.53
130.37
130.39
130.65
130.65
130.65
130.85
130.89
130.85
131.6
131.6
131.6
132.53
133.05
133.49
133.46

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230043&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230043&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1108.6816666666671.275495150436833.61999999999999
2111.3908333333330.9330347195462722.44000000000001
3114.71751.89354465583374.92999999999999
4119.35251.522438982207654.06
5123.14251.858602236285994.66
6127.8291666666671.684315120232084.26000000000001
7131.7683333333331.091003152510522.84

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 108.681666666667 & 1.27549515043683 & 3.61999999999999 \tabularnewline
2 & 111.390833333333 & 0.933034719546272 & 2.44000000000001 \tabularnewline
3 & 114.7175 & 1.8935446558337 & 4.92999999999999 \tabularnewline
4 & 119.3525 & 1.52243898220765 & 4.06 \tabularnewline
5 & 123.1425 & 1.85860223628599 & 4.66 \tabularnewline
6 & 127.829166666667 & 1.68431512023208 & 4.26000000000001 \tabularnewline
7 & 131.768333333333 & 1.09100315251052 & 2.84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230043&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]108.681666666667[/C][C]1.27549515043683[/C][C]3.61999999999999[/C][/ROW]
[ROW][C]2[/C][C]111.390833333333[/C][C]0.933034719546272[/C][C]2.44000000000001[/C][/ROW]
[ROW][C]3[/C][C]114.7175[/C][C]1.8935446558337[/C][C]4.92999999999999[/C][/ROW]
[ROW][C]4[/C][C]119.3525[/C][C]1.52243898220765[/C][C]4.06[/C][/ROW]
[ROW][C]5[/C][C]123.1425[/C][C]1.85860223628599[/C][C]4.66[/C][/ROW]
[ROW][C]6[/C][C]127.829166666667[/C][C]1.68431512023208[/C][C]4.26000000000001[/C][/ROW]
[ROW][C]7[/C][C]131.768333333333[/C][C]1.09100315251052[/C][C]2.84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230043&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
1108.6816666666671.275495150436833.61999999999999
2111.3908333333330.9330347195462722.44000000000001
3114.71751.89354465583374.92999999999999
4119.35251.522438982207654.06
5123.14251.858602236285994.66
6127.8291666666671.684315120232084.26000000000001
7131.7683333333331.091003152510522.84






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.65419681883619
beta0.00678596611256623
S.D.0.0194323728560308
T-STAT0.349209340662698
p-value0.741157923510073

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.65419681883619 \tabularnewline
beta & 0.00678596611256623 \tabularnewline
S.D. & 0.0194323728560308 \tabularnewline
T-STAT & 0.349209340662698 \tabularnewline
p-value & 0.741157923510073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230043&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.65419681883619[/C][/ROW]
[ROW][C]beta[/C][C]0.00678596611256623[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0194323728560308[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.349209340662698[/C][/ROW]
[ROW][C]p-value[/C][C]0.741157923510073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230043&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230043&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)
alpha0.65419681883619
beta0.00678596611256623
S.D.0.0194323728560308
T-STAT0.349209340662698
p-value0.741157923510073






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.03994468635021
beta0.709288815060093
S.D.1.67928207198413
T-STAT0.422376220703674
p-value0.690298148597964
Lambda0.290711184939907

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.03994468635021 \tabularnewline
beta & 0.709288815060093 \tabularnewline
S.D. & 1.67928207198413 \tabularnewline
T-STAT & 0.422376220703674 \tabularnewline
p-value & 0.690298148597964 \tabularnewline
Lambda & 0.290711184939907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230043&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.03994468635021[/C][/ROW]
[ROW][C]beta[/C][C]0.709288815060093[/C][/ROW]
[ROW][C]S.D.[/C][C]1.67928207198413[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.422376220703674[/C][/ROW]
[ROW][C]p-value[/C][C]0.690298148597964[/C][/ROW]
[ROW][C]Lambda[/C][C]0.290711184939907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230043&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230043&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-3.03994468635021
beta0.709288815060093
S.D.1.67928207198413
T-STAT0.422376220703674
p-value0.690298148597964
Lambda0.290711184939907


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')