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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

Thu, 11 Aug 2016 13:23:07 +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/Aug/11/t1470918213a1o3s8ji5nbt33q.htm/, Retrieved Sat, 25 May 2024 00:19:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296307, Retrieved Sat, 25 May 2024 00:19:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

120

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

-       [Standard Deviation-Mean Plot] [] [2016-08-11 12:23:07] [eed3b94f44ab74d862a61d666a631b56] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296307&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296307&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	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	168.583333333333	9.79293189762469	34
2	170.5	9.82112750424031	31
3	171.75	13.0879889419824	45
4	171	13.6847625946791	41
5	168.916666666667	16.8709450795973	52
6	166.083333333333	18.754191450705	57
7	167.333333333333	21.2103462460844	80
8	165.916666666667	21.9563961827376	80
9	164.916666666667	21.3603640304924	79

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 168.583333333333 & 9.79293189762469 & 34 \tabularnewline
2 & 170.5 & 9.82112750424031 & 31 \tabularnewline
3 & 171.75 & 13.0879889419824 & 45 \tabularnewline
4 & 171 & 13.6847625946791 & 41 \tabularnewline
5 & 168.916666666667 & 16.8709450795973 & 52 \tabularnewline
6 & 166.083333333333 & 18.754191450705 & 57 \tabularnewline
7 & 167.333333333333 & 21.2103462460844 & 80 \tabularnewline
8 & 165.916666666667 & 21.9563961827376 & 80 \tabularnewline
9 & 164.916666666667 & 21.3603640304924 & 79 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296307&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]168.583333333333[/C][C]9.79293189762469[/C][C]34[/C][/ROW]
[ROW][C]2[/C][C]170.5[/C][C]9.82112750424031[/C][C]31[/C][/ROW]
[ROW][C]3[/C][C]171.75[/C][C]13.0879889419824[/C][C]45[/C][/ROW]
[ROW][C]4[/C][C]171[/C][C]13.6847625946791[/C][C]41[/C][/ROW]
[ROW][C]5[/C][C]168.916666666667[/C][C]16.8709450795973[/C][C]52[/C][/ROW]
[ROW][C]6[/C][C]166.083333333333[/C][C]18.754191450705[/C][C]57[/C][/ROW]
[ROW][C]7[/C][C]167.333333333333[/C][C]21.2103462460844[/C][C]80[/C][/ROW]
[ROW][C]8[/C][C]165.916666666667[/C][C]21.9563961827376[/C][C]80[/C][/ROW]
[ROW][C]9[/C][C]164.916666666667[/C][C]21.3603640304924[/C][C]79[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296307&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	168.583333333333	9.79293189762469	34
2	170.5	9.82112750424031	31
3	171.75	13.0879889419824	45
4	171	13.6847625946791	41
5	168.916666666667	16.8709450795973	52
6	166.083333333333	18.754191450705	57
7	167.333333333333	21.2103462460844	80
8	165.916666666667	21.9563961827376	80
9	164.916666666667	21.3603640304924	79

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	281.138304778547
beta	-1.57340309510151
S.D.	0.465693745107381
T-STAT	-3.37862191973118
p-value	0.0117808271580478

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 281.138304778547 \tabularnewline
beta & -1.57340309510151 \tabularnewline
S.D. & 0.465693745107381 \tabularnewline
T-STAT & -3.37862191973118 \tabularnewline
p-value & 0.0117808271580478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296307&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]281.138304778547[/C][/ROW]
[ROW][C]beta[/C][C]-1.57340309510151[/C][/ROW]
[ROW][C]S.D.[/C][C]0.465693745107381[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.37862191973118[/C][/ROW]
[ROW][C]p-value[/C][C]0.0117808271580478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296307&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	281.138304778547
beta	-1.57340309510151
S.D.	0.465693745107381
T-STAT	-3.37862191973118
p-value	0.0117808271580478

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	87.2907470867535
beta	-16.4937412806704
S.D.	5.64337194840367
T-STAT	-2.92267485316752
p-value	0.0222550987301922
Lambda	17.4937412806704

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 87.2907470867535 \tabularnewline
beta & -16.4937412806704 \tabularnewline
S.D. & 5.64337194840367 \tabularnewline
T-STAT & -2.92267485316752 \tabularnewline
p-value & 0.0222550987301922 \tabularnewline
Lambda & 17.4937412806704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296307&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]87.2907470867535[/C][/ROW]
[ROW][C]beta[/C][C]-16.4937412806704[/C][/ROW]
[ROW][C]S.D.[/C][C]5.64337194840367[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.92267485316752[/C][/ROW]
[ROW][C]p-value[/C][C]0.0222550987301922[/C][/ROW]
[ROW][C]Lambda[/C][C]17.4937412806704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296307&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296307&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	87.2907470867535
beta	-16.4937412806704
S.D.	5.64337194840367
T-STAT	-2.92267485316752
p-value	0.0222550987301922
Lambda	17.4937412806704

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