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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

Wed, 24 Dec 2008 04:57:02 -0700

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/2008/Dec/24/t1230119879nny71nv2d1zgxnq.htm/, Retrieved Sun, 19 May 2024 09:20:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36488, Retrieved Sun, 19 May 2024 09:20:55 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

171

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

-       [Standard Deviation-Mean Plot] [SD Mean Plot] [2008-12-24 11:57:02] [52492148dbcac26917ed19e489351f79] [Current]

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Dataseries X:

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Histogram

Boxplots

0.2
0.8
1.2
4.5
0.4
5.9
6.5
12.8
4.2
-3.3
-12.5
-16.3
-10.5
-11.8
-11.4
-17.7
-17.3
-18.6
-17.9
-21.4
-19.4
-15.5
-7.7
-0.7
-1.6
1.4
0.7
9.5
1.4
4.1
6.6
18.4
16.9
9.2
-4.3
-5.9
-7.7
-5.4
-2.3
-4.8
2.3
-5.2
-10
-17.1
-14.4
-3.9
3.7
6.5
0.9
-4.1
-7
-12.2
-2.5
4.4
13.7
12.3
13.4
2.2
1.7
-7.2
-4.8
-2.9
-2.4
-2.5
-5.3
-7.1
-8
-8.9
-7.7
-1.1
4
9.6
10.9
13

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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36488&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36488&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36488&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' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	0.366666666666667	8.04694559030527	29.1
2	-14.1583333333333	5.93333546135474	20.7
3	4.7	7.71433140919607	24.3
4	-4.85833333333333	6.9856291879483	23.6
5	1.3	8.52216361772483	25.9
6	-3.09166666666667	5.38625495351292	18.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.366666666666667 & 8.04694559030527 & 29.1 \tabularnewline
2 & -14.1583333333333 & 5.93333546135474 & 20.7 \tabularnewline
3 & 4.7 & 7.71433140919607 & 24.3 \tabularnewline
4 & -4.85833333333333 & 6.9856291879483 & 23.6 \tabularnewline
5 & 1.3 & 8.52216361772483 & 25.9 \tabularnewline
6 & -3.09166666666667 & 5.38625495351292 & 18.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36488&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]0.366666666666667[/C][C]8.04694559030527[/C][C]29.1[/C][/ROW]
[ROW][C]2[/C][C]-14.1583333333333[/C][C]5.93333546135474[/C][C]20.7[/C][/ROW]
[ROW][C]3[/C][C]4.7[/C][C]7.71433140919607[/C][C]24.3[/C][/ROW]
[ROW][C]4[/C][C]-4.85833333333333[/C][C]6.9856291879483[/C][C]23.6[/C][/ROW]
[ROW][C]5[/C][C]1.3[/C][C]8.52216361772483[/C][C]25.9[/C][/ROW]
[ROW][C]6[/C][C]-3.09166666666667[/C][C]5.38625495351292[/C][C]18.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36488&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36488&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	0.366666666666667	8.04694559030527	29.1
2	-14.1583333333333	5.93333546135474	20.7
3	4.7	7.71433140919607	24.3
4	-4.85833333333333	6.9856291879483	23.6
5	1.3	8.52216361772483	25.9
6	-3.09166666666667	5.38625495351292	18.5

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	7.43086989417796
beta	0.126832767285904
S.D.	0.0690946373769558
T-STAT	1.83563836646178
p-value	0.140306508105811

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.43086989417796 \tabularnewline
beta & 0.126832767285904 \tabularnewline
S.D. & 0.0690946373769558 \tabularnewline
T-STAT & 1.83563836646178 \tabularnewline
p-value & 0.140306508105811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36488&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.43086989417796[/C][/ROW]
[ROW][C]beta[/C][C]0.126832767285904[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0690946373769558[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.83563836646178[/C][/ROW]
[ROW][C]p-value[/C][C]0.140306508105811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36488&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36488&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	7.43086989417796
beta	0.126832767285904
S.D.	0.0690946373769558
T-STAT	1.83563836646178
p-value	0.140306508105811

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.09483914954302
beta	-0.0167051471663808
S.D.	0.0354535452947992
T-STAT	-0.471184109444517
p-value	0.719677017569235
Lambda	1.01670514716638

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.09483914954302 \tabularnewline
beta & -0.0167051471663808 \tabularnewline
S.D. & 0.0354535452947992 \tabularnewline
T-STAT & -0.471184109444517 \tabularnewline
p-value & 0.719677017569235 \tabularnewline
Lambda & 1.01670514716638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36488&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.09483914954302[/C][/ROW]
[ROW][C]beta[/C][C]-0.0167051471663808[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0354535452947992[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.471184109444517[/C][/ROW]
[ROW][C]p-value[/C][C]0.719677017569235[/C][/ROW]
[ROW][C]Lambda[/C][C]1.01670514716638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36488&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36488&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	2.09483914954302
beta	-0.0167051471663808
S.D.	0.0354535452947992
T-STAT	-0.471184109444517
p-value	0.719677017569235
Lambda	1.01670514716638

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