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Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 13 Dec 2016 13:31:07 +0100

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/2016/Dec/13/t148163234796hmmnhpjnoilcb.htm/, Retrieved Sat, 04 May 2024 23:53:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299087, Retrieved Sat, 04 May 2024 23:53:42 +0000

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Estimated Impact

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

-     [Variance Reduction Matrix] [] [2015-10-08 08:22:46] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [Standard Deviation-Mean Plot] [SDM] [2016-12-13 12:31:07] [36884fbde1107444791dd71ee0072a5a] [Current]

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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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299087&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299087&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	3522.16666666667	1056.98841769979	3782
2	3120.25	676.137307867943	2244
3	3404.16666666667	860.550757399356	3050
4	4688.75	2030.45884312792	6682
5	3107.75	1587.19455901972	6036
6	3726.58333333333	1782.21743690949	6958
7	4123.75	1935.08266795457	5791
8	4956.91666666667	1631.39803171353	5574
9	7257.91666666667	3261.90514488733	12058
10	13433.6666666667	4634.56143523524	14709

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3522.16666666667 & 1056.98841769979 & 3782 \tabularnewline
2 & 3120.25 & 676.137307867943 & 2244 \tabularnewline
3 & 3404.16666666667 & 860.550757399356 & 3050 \tabularnewline
4 & 4688.75 & 2030.45884312792 & 6682 \tabularnewline
5 & 3107.75 & 1587.19455901972 & 6036 \tabularnewline
6 & 3726.58333333333 & 1782.21743690949 & 6958 \tabularnewline
7 & 4123.75 & 1935.08266795457 & 5791 \tabularnewline
8 & 4956.91666666667 & 1631.39803171353 & 5574 \tabularnewline
9 & 7257.91666666667 & 3261.90514488733 & 12058 \tabularnewline
10 & 13433.6666666667 & 4634.56143523524 & 14709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299087&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]3522.16666666667[/C][C]1056.98841769979[/C][C]3782[/C][/ROW]
[ROW][C]2[/C][C]3120.25[/C][C]676.137307867943[/C][C]2244[/C][/ROW]
[ROW][C]3[/C][C]3404.16666666667[/C][C]860.550757399356[/C][C]3050[/C][/ROW]
[ROW][C]4[/C][C]4688.75[/C][C]2030.45884312792[/C][C]6682[/C][/ROW]
[ROW][C]5[/C][C]3107.75[/C][C]1587.19455901972[/C][C]6036[/C][/ROW]
[ROW][C]6[/C][C]3726.58333333333[/C][C]1782.21743690949[/C][C]6958[/C][/ROW]
[ROW][C]7[/C][C]4123.75[/C][C]1935.08266795457[/C][C]5791[/C][/ROW]
[ROW][C]8[/C][C]4956.91666666667[/C][C]1631.39803171353[/C][C]5574[/C][/ROW]
[ROW][C]9[/C][C]7257.91666666667[/C][C]3261.90514488733[/C][C]12058[/C][/ROW]
[ROW][C]10[/C][C]13433.6666666667[/C][C]4634.56143523524[/C][C]14709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299087&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	3522.16666666667	1056.98841769979	3782
2	3120.25	676.137307867943	2244
3	3404.16666666667	860.550757399356	3050
4	4688.75	2030.45884312792	6682
5	3107.75	1587.19455901972	6036
6	3726.58333333333	1782.21743690949	6958
7	4123.75	1935.08266795457	5791
8	4956.91666666667	1631.39803171353	5574
9	7257.91666666667	3261.90514488733	12058
10	13433.6666666667	4634.56143523524	14709

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	129.863126733806
beta	0.353665474788667
S.D.	0.0455248792815981
T-STAT	7.76861971672759
p-value	5.39071441843862e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 129.863126733806 \tabularnewline
beta & 0.353665474788667 \tabularnewline
S.D. & 0.0455248792815981 \tabularnewline
T-STAT & 7.76861971672759 \tabularnewline
p-value & 5.39071441843862e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299087&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]129.863126733806[/C][/ROW]
[ROW][C]beta[/C][C]0.353665474788667[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0455248792815981[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.76861971672759[/C][/ROW]
[ROW][C]p-value[/C][C]5.39071441843862e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299087&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299087&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	129.863126733806
beta	0.353665474788667
S.D.	0.0455248792815981
T-STAT	7.76861971672759
p-value	5.39071441843862e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.80970105835196
beta	1.09503295929662
S.D.	0.225018211433845
T-STAT	4.86641926588485
p-value	0.00124561549202018
Lambda	-0.0950329592966159

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.80970105835196 \tabularnewline
beta & 1.09503295929662 \tabularnewline
S.D. & 0.225018211433845 \tabularnewline
T-STAT & 4.86641926588485 \tabularnewline
p-value & 0.00124561549202018 \tabularnewline
Lambda & -0.0950329592966159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299087&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.80970105835196[/C][/ROW]
[ROW][C]beta[/C][C]1.09503295929662[/C][/ROW]
[ROW][C]S.D.[/C][C]0.225018211433845[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.86641926588485[/C][/ROW]
[ROW][C]p-value[/C][C]0.00124561549202018[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0950329592966159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299087&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299087&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	-1.80970105835196
beta	1.09503295929662
S.D.	0.225018211433845
T-STAT	4.86641926588485
p-value	0.00124561549202018
Lambda	-0.0950329592966159

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 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