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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

Sun, 18 May 2008 14:10:49 -0600

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/May/18/t12111414876cfkq64tccmujr0.htm/, Retrieved Tue, 14 May 2024 01:06:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12828, Retrieved Tue, 14 May 2024 01:06:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-       [Standard Deviation-Mean Plot] [Spreidings -en ge...] [2008-05-18 20:10:49] [6461440fa2a8ea0ebac8d11789a457eb] [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=12828&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=12828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12828&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	48.0575	0.0236290781312651	0.0500000000000043
2	48.15	0.0199999999999996	0.0399999999999991
3	48.13	0.0355902608401039	0.0799999999999983
4	48.26	0.150996688705415	0.32
5	48.525	0.0100000000000016	0.0200000000000031
6	48.6625	0.0170782512765994	0.0399999999999991
7	48.75	0.141656862405839	0.300000000000004
8	49.0325	0.0150000000000006	0.0300000000000011
9	49.16	0.0852447456836272	0.199999999999996
10	49.31	0.0812403840463603	0.170000000000002
11	49.4475	0.0125830573921187	0.0300000000000011
12	49.665	0.0645497224367908	0.140000000000001
13	49.8575	0.165806111668620	0.390000000000001
14	50.2025	0.0613052471924995	0.130000000000003
15	50.8625	0.335099487714719	0.68

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 48.0575 & 0.0236290781312651 & 0.0500000000000043 \tabularnewline
2 & 48.15 & 0.0199999999999996 & 0.0399999999999991 \tabularnewline
3 & 48.13 & 0.0355902608401039 & 0.0799999999999983 \tabularnewline
4 & 48.26 & 0.150996688705415 & 0.32 \tabularnewline
5 & 48.525 & 0.0100000000000016 & 0.0200000000000031 \tabularnewline
6 & 48.6625 & 0.0170782512765994 & 0.0399999999999991 \tabularnewline
7 & 48.75 & 0.141656862405839 & 0.300000000000004 \tabularnewline
8 & 49.0325 & 0.0150000000000006 & 0.0300000000000011 \tabularnewline
9 & 49.16 & 0.0852447456836272 & 0.199999999999996 \tabularnewline
10 & 49.31 & 0.0812403840463603 & 0.170000000000002 \tabularnewline
11 & 49.4475 & 0.0125830573921187 & 0.0300000000000011 \tabularnewline
12 & 49.665 & 0.0645497224367908 & 0.140000000000001 \tabularnewline
13 & 49.8575 & 0.165806111668620 & 0.390000000000001 \tabularnewline
14 & 50.2025 & 0.0613052471924995 & 0.130000000000003 \tabularnewline
15 & 50.8625 & 0.335099487714719 & 0.68 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12828&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]48.0575[/C][C]0.0236290781312651[/C][C]0.0500000000000043[/C][/ROW]
[ROW][C]2[/C][C]48.15[/C][C]0.0199999999999996[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]3[/C][C]48.13[/C][C]0.0355902608401039[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]4[/C][C]48.26[/C][C]0.150996688705415[/C][C]0.32[/C][/ROW]
[ROW][C]5[/C][C]48.525[/C][C]0.0100000000000016[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]6[/C][C]48.6625[/C][C]0.0170782512765994[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]7[/C][C]48.75[/C][C]0.141656862405839[/C][C]0.300000000000004[/C][/ROW]
[ROW][C]8[/C][C]49.0325[/C][C]0.0150000000000006[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]9[/C][C]49.16[/C][C]0.0852447456836272[/C][C]0.199999999999996[/C][/ROW]
[ROW][C]10[/C][C]49.31[/C][C]0.0812403840463603[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]11[/C][C]49.4475[/C][C]0.0125830573921187[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]12[/C][C]49.665[/C][C]0.0645497224367908[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]13[/C][C]49.8575[/C][C]0.165806111668620[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]14[/C][C]50.2025[/C][C]0.0613052471924995[/C][C]0.130000000000003[/C][/ROW]
[ROW][C]15[/C][C]50.8625[/C][C]0.335099487714719[/C][C]0.68[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12828&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	48.0575	0.0236290781312651	0.0500000000000043
2	48.15	0.0199999999999996	0.0399999999999991
3	48.13	0.0355902608401039	0.0799999999999983
4	48.26	0.150996688705415	0.32
5	48.525	0.0100000000000016	0.0200000000000031
6	48.6625	0.0170782512765994	0.0399999999999991
7	48.75	0.141656862405839	0.300000000000004
8	49.0325	0.0150000000000006	0.0300000000000011
9	49.16	0.0852447456836272	0.199999999999996
10	49.31	0.0812403840463603	0.170000000000002
11	49.4475	0.0125830573921187	0.0300000000000011
12	49.665	0.0645497224367908	0.140000000000001
13	49.8575	0.165806111668620	0.390000000000001
14	50.2025	0.0613052471924995	0.130000000000003
15	50.8625	0.335099487714719	0.68

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-3.03274931313501
beta	0.0634598080956958
S.D.	0.0235068797433955
T-STAT	2.69962703635839
p-value	0.0182069097631191

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.03274931313501 \tabularnewline
beta & 0.0634598080956958 \tabularnewline
S.D. & 0.0235068797433955 \tabularnewline
T-STAT & 2.69962703635839 \tabularnewline
p-value & 0.0182069097631191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12828&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.03274931313501[/C][/ROW]
[ROW][C]beta[/C][C]0.0634598080956958[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0235068797433955[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.69962703635839[/C][/ROW]
[ROW][C]p-value[/C][C]0.0182069097631191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12828&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	-3.03274931313501
beta	0.0634598080956958
S.D.	0.0235068797433955
T-STAT	2.69962703635839
p-value	0.0182069097631191

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-130.360721811010
beta	32.7058193090422
S.D.	15.4502789562659
T-STAT	2.11684328817754
p-value	0.054130450728377
Lambda	-31.7058193090422

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -130.360721811010 \tabularnewline
beta & 32.7058193090422 \tabularnewline
S.D. & 15.4502789562659 \tabularnewline
T-STAT & 2.11684328817754 \tabularnewline
p-value & 0.054130450728377 \tabularnewline
Lambda & -31.7058193090422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12828&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-130.360721811010[/C][/ROW]
[ROW][C]beta[/C][C]32.7058193090422[/C][/ROW]
[ROW][C]S.D.[/C][C]15.4502789562659[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.11684328817754[/C][/ROW]
[ROW][C]p-value[/C][C]0.054130450728377[/C][/ROW]
[ROW][C]Lambda[/C][C]-31.7058193090422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12828&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12828&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	-130.360721811010
beta	32.7058193090422
S.D.	15.4502789562659
T-STAT	2.11684328817754
p-value	0.054130450728377
Lambda	-31.7058193090422

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

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')

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Figures (Output of Computation)

Input Parameters & R Code