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Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 02 Dec 2010 06:56:58 +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/2010/Dec/02/t1291273004wmimkbl0nm3pdrn.htm/, Retrieved Sun, 05 May 2024 11:44:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104195, Retrieved Sun, 05 May 2024 11:44:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83 - Sofie Baert

Estimated Impact

144

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

-       [Standard Deviation-Mean Plot] [] [2010-12-02 06:56:58] [1ce81d942cb901782da36327f25f651a] [Current]

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Dataseries X:

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Histogram

Boxplots

6.59
6.59
6.59
6.59
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.63
6.79
6.79
6.79
6.81
6.80
6.80
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.10
7.10
7.10
7.10
7.12
7.13
7.18
7.24
7.24
7.24
7.27
7.27
7.27
7.27
7.30
7.30
7.57
7.76
7.94
7.94
7.96

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104195&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104195&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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.61666666666667	0.0196946385566933	0.04
2	6.67	0.0723627226986633	0.16
3	6.8425	0.0252712556798503	0.08
4	6.955	0.0606779876216917	0.17
5	7.12166666666667	0.066583281184794	0.190000000000000
6	7.5075	0.305974597876122	0.72

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.61666666666667 & 0.0196946385566933 & 0.04 \tabularnewline
2 & 6.67 & 0.0723627226986633 & 0.16 \tabularnewline
3 & 6.8425 & 0.0252712556798503 & 0.08 \tabularnewline
4 & 6.955 & 0.0606779876216917 & 0.17 \tabularnewline
5 & 7.12166666666667 & 0.066583281184794 & 0.190000000000000 \tabularnewline
6 & 7.5075 & 0.305974597876122 & 0.72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104195&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]6.61666666666667[/C][C]0.0196946385566933[/C][C]0.04[/C][/ROW]
[ROW][C]2[/C][C]6.67[/C][C]0.0723627226986633[/C][C]0.16[/C][/ROW]
[ROW][C]3[/C][C]6.8425[/C][C]0.0252712556798503[/C][C]0.08[/C][/ROW]
[ROW][C]4[/C][C]6.955[/C][C]0.0606779876216917[/C][C]0.17[/C][/ROW]
[ROW][C]5[/C][C]7.12166666666667[/C][C]0.066583281184794[/C][C]0.190000000000000[/C][/ROW]
[ROW][C]6[/C][C]7.5075[/C][C]0.305974597876122[/C][C]0.72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104195&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	6.61666666666667	0.0196946385566933	0.04
2	6.67	0.0723627226986633	0.16
3	6.8425	0.0252712556798503	0.08
4	6.955	0.0606779876216917	0.17
5	7.12166666666667	0.066583281184794	0.190000000000000
6	7.5075	0.305974597876122	0.72

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-1.85451498580706
beta	0.279950161382295
S.D.	0.0833756413962964
T-STAT	3.35769724459032
p-value	0.0283653808345199

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.85451498580706 \tabularnewline
beta & 0.279950161382295 \tabularnewline
S.D. & 0.0833756413962964 \tabularnewline
T-STAT & 3.35769724459032 \tabularnewline
p-value & 0.0283653808345199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104195&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.85451498580706[/C][/ROW]
[ROW][C]beta[/C][C]0.279950161382295[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0833756413962964[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.35769724459032[/C][/ROW]
[ROW][C]p-value[/C][C]0.0283653808345199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104195&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	-1.85451498580706
beta	0.279950161382295
S.D.	0.0833756413962964
T-STAT	3.35769724459032
p-value	0.0283653808345199

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-36.3925338441108
beta	17.3213661881386
S.D.	5.70562838550475
T-STAT	3.03583847699297
p-value	0.0385591421846688
Lambda	-16.3213661881386

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -36.3925338441108 \tabularnewline
beta & 17.3213661881386 \tabularnewline
S.D. & 5.70562838550475 \tabularnewline
T-STAT & 3.03583847699297 \tabularnewline
p-value & 0.0385591421846688 \tabularnewline
Lambda & -16.3213661881386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104195&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-36.3925338441108[/C][/ROW]
[ROW][C]beta[/C][C]17.3213661881386[/C][/ROW]
[ROW][C]S.D.[/C][C]5.70562838550475[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.03583847699297[/C][/ROW]
[ROW][C]p-value[/C][C]0.0385591421846688[/C][/ROW]
[ROW][C]Lambda[/C][C]-16.3213661881386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104195&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104195&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	-36.3925338441108
beta	17.3213661881386
S.D.	5.70562838550475
T-STAT	3.03583847699297
p-value	0.0385591421846688
Lambda	-16.3213661881386

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