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Free Statistics

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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 23 Nov 2014 09:37:52 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/23/t14167355060dkus3mh5yr93bm.htm/, Retrieved Mon, 20 May 2024 02:33:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257937, Retrieved Mon, 20 May 2024 02:33:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [] [2014-11-23 09:37:52] [4b199ad8119df16cb977784959786033] [Current]

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Dataseries X:

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Histogram

Boxplots

1.11
1.11
1.2
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.9
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1
0.99
1.03
1.02
1.07
1.13
1.15
1.16
1.14
1.15
1.15
1.16
1.17
1.22
1.26
1.29
1.36
1.38
1.37
1.37
1.37
1.36
1.38
1.4
1.44
1.42
1.45
1.45
1.49
1.48
1.44
1.39
1.41
1.48
1.51
1.49
1.46
1.43
1.42
1.43
1.42
1.39
1.36
1.36
1.39
1.39
1.43
1.38
1.36
1.38

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257937&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257937&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1.19583333333333	0.125586502845528	0.42
2	0.954166666666667	0.0331548250522065	0.1
3	1.12916666666667	0.0591543948007451	0.2
4	1.36666666666667	0.0496044963748858	0.18
5	1.45666666666667	0.0355050145839438	0.12
6	1.3925	0.0266714010948738	0.0699999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.19583333333333 & 0.125586502845528 & 0.42 \tabularnewline
2 & 0.954166666666667 & 0.0331548250522065 & 0.1 \tabularnewline
3 & 1.12916666666667 & 0.0591543948007451 & 0.2 \tabularnewline
4 & 1.36666666666667 & 0.0496044963748858 & 0.18 \tabularnewline
5 & 1.45666666666667 & 0.0355050145839438 & 0.12 \tabularnewline
6 & 1.3925 & 0.0266714010948738 & 0.0699999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257937&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]1.19583333333333[/C][C]0.125586502845528[/C][C]0.42[/C][/ROW]
[ROW][C]2[/C][C]0.954166666666667[/C][C]0.0331548250522065[/C][C]0.1[/C][/ROW]
[ROW][C]3[/C][C]1.12916666666667[/C][C]0.0591543948007451[/C][C]0.2[/C][/ROW]
[ROW][C]4[/C][C]1.36666666666667[/C][C]0.0496044963748858[/C][C]0.18[/C][/ROW]
[ROW][C]5[/C][C]1.45666666666667[/C][C]0.0355050145839438[/C][C]0.12[/C][/ROW]
[ROW][C]6[/C][C]1.3925[/C][C]0.0266714010948738[/C][C]0.0699999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257937&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1.19583333333333	0.125586502845528	0.42
2	0.954166666666667	0.0331548250522065	0.1
3	1.12916666666667	0.0591543948007451	0.2
4	1.36666666666667	0.0496044963748858	0.18
5	1.45666666666667	0.0355050145839438	0.12
6	1.3925	0.0266714010948738	0.0699999999999998

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.100040405510284
beta	-0.0360995061120106
S.D.	0.0942241260924308
T-STAT	-0.383123809252401
p-value	0.721118320227093

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.100040405510284 \tabularnewline
beta & -0.0360995061120106 \tabularnewline
S.D. & 0.0942241260924308 \tabularnewline
T-STAT & -0.383123809252401 \tabularnewline
p-value & 0.721118320227093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257937&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.100040405510284[/C][/ROW]
[ROW][C]beta[/C][C]-0.0360995061120106[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0942241260924308[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.383123809252401[/C][/ROW]
[ROW][C]p-value[/C][C]0.721118320227093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257937&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257937&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.100040405510284
beta	-0.0360995061120106
S.D.	0.0942241260924308
T-STAT	-0.383123809252401
p-value	0.721118320227093

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.92740519091681
beta	-0.558052817864129
S.D.	1.71626505819279
T-STAT	-0.325155380400131
p-value	0.761359961967392
Lambda	1.55805281786413

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.92740519091681 \tabularnewline
beta & -0.558052817864129 \tabularnewline
S.D. & 1.71626505819279 \tabularnewline
T-STAT & -0.325155380400131 \tabularnewline
p-value & 0.761359961967392 \tabularnewline
Lambda & 1.55805281786413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257937&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.92740519091681[/C][/ROW]
[ROW][C]beta[/C][C]-0.558052817864129[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71626505819279[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.325155380400131[/C][/ROW]
[ROW][C]p-value[/C][C]0.761359961967392[/C][/ROW]
[ROW][C]Lambda[/C][C]1.55805281786413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257937&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257937&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.92740519091681
beta	-0.558052817864129
S.D.	1.71626505819279
T-STAT	-0.325155380400131
p-value	0.761359961967392
Lambda	1.55805281786413

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code