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Author's title

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

Sun, 18 Dec 2016 16:13:41 +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/18/t1482074045mi6dhgucq2609q6.htm/, Retrieved Sat, 26 Apr 2025 04:42:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301129, Retrieved Sat, 26 Apr 2025 04:42:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

124

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

-       [Standard Deviation-Mean Plot] [Standaard deviati...] [2016-12-18 15:13:41] [33f2a624cfeb2efbc43d2c77b7c0dad6] [Current]

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Boxplots

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=301129&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=301129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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	4445.83333333333	553.984875627704	1780
2	3996.66666666667	634.455146825474	1980
3	3483.33333333333	670.648713537644	1940
4	3013.33333333333	395.137107006332	1260
5	2941.66666666667	380.999483018817	1260
6	2591.66666666667	364.587770535769	1120
7	2547.5	152.442239433945	470
8	2525.83333333333	206.461897578016	660
9	2581.66666666667	229.459179706359	750
10	NaN	NA	-Inf
11	NaN	NA	-Inf
12	NaN	NA	-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4445.83333333333 & 553.984875627704 & 1780 \tabularnewline
2 & 3996.66666666667 & 634.455146825474 & 1980 \tabularnewline
3 & 3483.33333333333 & 670.648713537644 & 1940 \tabularnewline
4 & 3013.33333333333 & 395.137107006332 & 1260 \tabularnewline
5 & 2941.66666666667 & 380.999483018817 & 1260 \tabularnewline
6 & 2591.66666666667 & 364.587770535769 & 1120 \tabularnewline
7 & 2547.5 & 152.442239433945 & 470 \tabularnewline
8 & 2525.83333333333 & 206.461897578016 & 660 \tabularnewline
9 & 2581.66666666667 & 229.459179706359 & 750 \tabularnewline
10 & NaN & NA & -Inf \tabularnewline
11 & NaN & NA & -Inf \tabularnewline
12 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&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]4445.83333333333[/C][C]553.984875627704[/C][C]1780[/C][/ROW]
[ROW][C]2[/C][C]3996.66666666667[/C][C]634.455146825474[/C][C]1980[/C][/ROW]
[ROW][C]3[/C][C]3483.33333333333[/C][C]670.648713537644[/C][C]1940[/C][/ROW]
[ROW][C]4[/C][C]3013.33333333333[/C][C]395.137107006332[/C][C]1260[/C][/ROW]
[ROW][C]5[/C][C]2941.66666666667[/C][C]380.999483018817[/C][C]1260[/C][/ROW]
[ROW][C]6[/C][C]2591.66666666667[/C][C]364.587770535769[/C][C]1120[/C][/ROW]
[ROW][C]7[/C][C]2547.5[/C][C]152.442239433945[/C][C]470[/C][/ROW]
[ROW][C]8[/C][C]2525.83333333333[/C][C]206.461897578016[/C][C]660[/C][/ROW]
[ROW][C]9[/C][C]2581.66666666667[/C][C]229.459179706359[/C][C]750[/C][/ROW]
[ROW][C]10[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]11[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]12[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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	4445.83333333333	553.984875627704	1780
2	3996.66666666667	634.455146825474	1980
3	3483.33333333333	670.648713537644	1940
4	3013.33333333333	395.137107006332	1260
5	2941.66666666667	380.999483018817	1260
6	2591.66666666667	364.587770535769	1120
7	2547.5	152.442239433945	470
8	2525.83333333333	206.461897578016	660
9	2581.66666666667	229.459179706359	750
10	NaN	NA	-Inf
11	NaN	NA	-Inf
12	NaN	NA	-Inf

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-296.792599054343
beta	0.222533456750836
S.D.	0.0556718876709218
T-STAT	3.99723210511988
p-value	0.00520823430244478

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -296.792599054343 \tabularnewline
beta & 0.222533456750836 \tabularnewline
S.D. & 0.0556718876709218 \tabularnewline
T-STAT & 3.99723210511988 \tabularnewline
p-value & 0.00520823430244478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-296.792599054343[/C][/ROW]
[ROW][C]beta[/C][C]0.222533456750836[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0556718876709218[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.99723210511988[/C][/ROW]
[ROW][C]p-value[/C][C]0.00520823430244478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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	-296.792599054343
beta	0.222533456750836
S.D.	0.0556718876709218
T-STAT	3.99723210511988
p-value	0.00520823430244478

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-10.5211403384711
beta	2.04294761262818
S.D.	0.517682481423202
T-STAT	3.9463332949026
p-value	0.00555805097815544
Lambda	-1.04294761262818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.5211403384711 \tabularnewline
beta & 2.04294761262818 \tabularnewline
S.D. & 0.517682481423202 \tabularnewline
T-STAT & 3.9463332949026 \tabularnewline
p-value & 0.00555805097815544 \tabularnewline
Lambda & -1.04294761262818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.5211403384711[/C][/ROW]
[ROW][C]beta[/C][C]2.04294761262818[/C][/ROW]
[ROW][C]S.D.[/C][C]0.517682481423202[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.9463332949026[/C][/ROW]
[ROW][C]p-value[/C][C]0.00555805097815544[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.04294761262818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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	-10.5211403384711
beta	2.04294761262818
S.D.	0.517682481423202
T-STAT	3.9463332949026
p-value	0.00555805097815544
Lambda	-1.04294761262818

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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