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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

Mon, 04 Jan 2010 10:59:35 -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/2010/Jan/04/t1262628017fz8d97zhgmal74o.htm/, Retrieved Fri, 03 May 2024 13:02:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71589, Retrieved Fri, 03 May 2024 13:02:09 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

172

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

-       [Standard Deviation-Mean Plot] [KDGP2W83] [2010-01-04 17:59:35] [3f12ab8801f7554f488f56dad3cd0b03] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71589&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71589&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' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	47.325	0.767571929311296	1.80000000000000
2	50.575	1.25266382827424	2.9
3	54.2	0.852447456836295	2
4	56.05	0.544671154612271	1.20000000000000
5	58.525	0.818026079453868	1.9
6	60.025	0.206155281280883	0.5
7	59.675	0.309569593683446	0.700000000000003
8	59.15	0.129099444873580	0.299999999999997
9	59.45	0.100000000000001	0.200000000000003
10	60.15	0.525991127935316	1
11	61.725	0.499165971062398	1.10000000000000
12	62.975	0.434932945023330	1
13	64.7	0.648074069840789	1.50000000000001
14	68.25	1.60519988371127	3.7
15	72.975	1.35738719604982	3.19999999999999
16	76.45	1.16761865920913	2.70000000000000
17	81.675	2.29401394939089	5.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 47.325 & 0.767571929311296 & 1.80000000000000 \tabularnewline
2 & 50.575 & 1.25266382827424 & 2.9 \tabularnewline
3 & 54.2 & 0.852447456836295 & 2 \tabularnewline
4 & 56.05 & 0.544671154612271 & 1.20000000000000 \tabularnewline
5 & 58.525 & 0.818026079453868 & 1.9 \tabularnewline
6 & 60.025 & 0.206155281280883 & 0.5 \tabularnewline
7 & 59.675 & 0.309569593683446 & 0.700000000000003 \tabularnewline
8 & 59.15 & 0.129099444873580 & 0.299999999999997 \tabularnewline
9 & 59.45 & 0.100000000000001 & 0.200000000000003 \tabularnewline
10 & 60.15 & 0.525991127935316 & 1 \tabularnewline
11 & 61.725 & 0.499165971062398 & 1.10000000000000 \tabularnewline
12 & 62.975 & 0.434932945023330 & 1 \tabularnewline
13 & 64.7 & 0.648074069840789 & 1.50000000000001 \tabularnewline
14 & 68.25 & 1.60519988371127 & 3.7 \tabularnewline
15 & 72.975 & 1.35738719604982 & 3.19999999999999 \tabularnewline
16 & 76.45 & 1.16761865920913 & 2.70000000000000 \tabularnewline
17 & 81.675 & 2.29401394939089 & 5.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71589&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]47.325[/C][C]0.767571929311296[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]2[/C][C]50.575[/C][C]1.25266382827424[/C][C]2.9[/C][/ROW]
[ROW][C]3[/C][C]54.2[/C][C]0.852447456836295[/C][C]2[/C][/ROW]
[ROW][C]4[/C][C]56.05[/C][C]0.544671154612271[/C][C]1.20000000000000[/C][/ROW]
[ROW][C]5[/C][C]58.525[/C][C]0.818026079453868[/C][C]1.9[/C][/ROW]
[ROW][C]6[/C][C]60.025[/C][C]0.206155281280883[/C][C]0.5[/C][/ROW]
[ROW][C]7[/C][C]59.675[/C][C]0.309569593683446[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]8[/C][C]59.15[/C][C]0.129099444873580[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]9[/C][C]59.45[/C][C]0.100000000000001[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]10[/C][C]60.15[/C][C]0.525991127935316[/C][C]1[/C][/ROW]
[ROW][C]11[/C][C]61.725[/C][C]0.499165971062398[/C][C]1.10000000000000[/C][/ROW]
[ROW][C]12[/C][C]62.975[/C][C]0.434932945023330[/C][C]1[/C][/ROW]
[ROW][C]13[/C][C]64.7[/C][C]0.648074069840789[/C][C]1.50000000000001[/C][/ROW]
[ROW][C]14[/C][C]68.25[/C][C]1.60519988371127[/C][C]3.7[/C][/ROW]
[ROW][C]15[/C][C]72.975[/C][C]1.35738719604982[/C][C]3.19999999999999[/C][/ROW]
[ROW][C]16[/C][C]76.45[/C][C]1.16761865920913[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]17[/C][C]81.675[/C][C]2.29401394939089[/C][C]5.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71589&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	47.325	0.767571929311296	1.80000000000000
2	50.575	1.25266382827424	2.9
3	54.2	0.852447456836295	2
4	56.05	0.544671154612271	1.20000000000000
5	58.525	0.818026079453868	1.9
6	60.025	0.206155281280883	0.5
7	59.675	0.309569593683446	0.700000000000003
8	59.15	0.129099444873580	0.299999999999997
9	59.45	0.100000000000001	0.200000000000003
10	60.15	0.525991127935316	1
11	61.725	0.499165971062398	1.10000000000000
12	62.975	0.434932945023330	1
13	64.7	0.648074069840789	1.50000000000001
14	68.25	1.60519988371127	3.7
15	72.975	1.35738719604982	3.19999999999999
16	76.45	1.16761865920913	2.70000000000000
17	81.675	2.29401394939089	5.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-1.59671188198858
beta	0.0385782854364651
S.D.	0.0138862031001811
T-STAT	2.7781737857458
p-value	0.0140653024811080

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.59671188198858 \tabularnewline
beta & 0.0385782854364651 \tabularnewline
S.D. & 0.0138862031001811 \tabularnewline
T-STAT & 2.7781737857458 \tabularnewline
p-value & 0.0140653024811080 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71589&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.59671188198858[/C][/ROW]
[ROW][C]beta[/C][C]0.0385782854364651[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0138862031001811[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.7781737857458[/C][/ROW]
[ROW][C]p-value[/C][C]0.0140653024811080[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71589&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	-1.59671188198858
beta	0.0385782854364651
S.D.	0.0138862031001811
T-STAT	2.7781737857458
p-value	0.0140653024811080

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-9.4747642533617
beta	2.17310454397155
S.D.	1.50723534675546
T-STAT	1.44178183496656
p-value	0.169916194098469
Lambda	-1.17310454397155

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.4747642533617 \tabularnewline
beta & 2.17310454397155 \tabularnewline
S.D. & 1.50723534675546 \tabularnewline
T-STAT & 1.44178183496656 \tabularnewline
p-value & 0.169916194098469 \tabularnewline
Lambda & -1.17310454397155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71589&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.4747642533617[/C][/ROW]
[ROW][C]beta[/C][C]2.17310454397155[/C][/ROW]
[ROW][C]S.D.[/C][C]1.50723534675546[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.44178183496656[/C][/ROW]
[ROW][C]p-value[/C][C]0.169916194098469[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.17310454397155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71589&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71589&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	-9.4747642533617
beta	2.17310454397155
S.D.	1.50723534675546
T-STAT	1.44178183496656
p-value	0.169916194098469
Lambda	-1.17310454397155

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 50 ;

Parameters (R input):

par1 = 4 ;

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