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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, 08 Jan 2009 04:29:09 -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/2009/Jan/08/t1231414272yxysjmkoof2944e.htm/, Retrieved Wed, 08 May 2024 19:00:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36821, Retrieved Wed, 08 May 2024 19:00:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

237

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

-       [Standard Deviation-Mean Plot] [2MAR03A_Robbe Ley...] [2009-01-08 11:29:09] [5cfda051308d8cc79b9da3748118f98f] [Current]
-   P     [Standard Deviation-Mean Plot] [Robbe Leys_2MAR03...] [2009-01-27 16:39:47] [74be16979710d4c4e7c6647856088456] 

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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=36821&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=36821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36821&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	261.166666666667	37.8523767317512	107.6
2	271.708333333333	37.1613058370552	112.7
3	299.133333333333	40.8037060111263	119.7
4	336.916666666667	41.2957588254496	117
5	382.233333333333	48.2497165951796	147.3
6	431.458333333333	60.9725341792714	195.2
7	483.233333333333	47.8139639803599	123.2
8	492.266666666667	53.0648374132718	157.4
9	495.225	51.821601761147	148.4
10	463.15	54.4829998506623	148.3
11	473.683333333333	55.5360298010274	181.5
12	481.675	62.5962694938401	176.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 261.166666666667 & 37.8523767317512 & 107.6 \tabularnewline
2 & 271.708333333333 & 37.1613058370552 & 112.7 \tabularnewline
3 & 299.133333333333 & 40.8037060111263 & 119.7 \tabularnewline
4 & 336.916666666667 & 41.2957588254496 & 117 \tabularnewline
5 & 382.233333333333 & 48.2497165951796 & 147.3 \tabularnewline
6 & 431.458333333333 & 60.9725341792714 & 195.2 \tabularnewline
7 & 483.233333333333 & 47.8139639803599 & 123.2 \tabularnewline
8 & 492.266666666667 & 53.0648374132718 & 157.4 \tabularnewline
9 & 495.225 & 51.821601761147 & 148.4 \tabularnewline
10 & 463.15 & 54.4829998506623 & 148.3 \tabularnewline
11 & 473.683333333333 & 55.5360298010274 & 181.5 \tabularnewline
12 & 481.675 & 62.5962694938401 & 176.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36821&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]261.166666666667[/C][C]37.8523767317512[/C][C]107.6[/C][/ROW]
[ROW][C]2[/C][C]271.708333333333[/C][C]37.1613058370552[/C][C]112.7[/C][/ROW]
[ROW][C]3[/C][C]299.133333333333[/C][C]40.8037060111263[/C][C]119.7[/C][/ROW]
[ROW][C]4[/C][C]336.916666666667[/C][C]41.2957588254496[/C][C]117[/C][/ROW]
[ROW][C]5[/C][C]382.233333333333[/C][C]48.2497165951796[/C][C]147.3[/C][/ROW]
[ROW][C]6[/C][C]431.458333333333[/C][C]60.9725341792714[/C][C]195.2[/C][/ROW]
[ROW][C]7[/C][C]483.233333333333[/C][C]47.8139639803599[/C][C]123.2[/C][/ROW]
[ROW][C]8[/C][C]492.266666666667[/C][C]53.0648374132718[/C][C]157.4[/C][/ROW]
[ROW][C]9[/C][C]495.225[/C][C]51.821601761147[/C][C]148.4[/C][/ROW]
[ROW][C]10[/C][C]463.15[/C][C]54.4829998506623[/C][C]148.3[/C][/ROW]
[ROW][C]11[/C][C]473.683333333333[/C][C]55.5360298010274[/C][C]181.5[/C][/ROW]
[ROW][C]12[/C][C]481.675[/C][C]62.5962694938401[/C][C]176.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36821&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	261.166666666667	37.8523767317512	107.6
2	271.708333333333	37.1613058370552	112.7
3	299.133333333333	40.8037060111263	119.7
4	336.916666666667	41.2957588254496	117
5	382.233333333333	48.2497165951796	147.3
6	431.458333333333	60.9725341792714	195.2
7	483.233333333333	47.8139639803599	123.2
8	492.266666666667	53.0648374132718	157.4
9	495.225	51.821601761147	148.4
10	463.15	54.4829998506623	148.3
11	473.683333333333	55.5360298010274	181.5
12	481.675	62.5962694938401	176.4

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	17.1720954283701
beta	0.079145695236861
S.D.	0.0163763213206841
T-STAT	4.83293492396831
p-value	0.000688743839909684

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 17.1720954283701 \tabularnewline
beta & 0.079145695236861 \tabularnewline
S.D. & 0.0163763213206841 \tabularnewline
T-STAT & 4.83293492396831 \tabularnewline
p-value & 0.000688743839909684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36821&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.1720954283701[/C][/ROW]
[ROW][C]beta[/C][C]0.079145695236861[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0163763213206841[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.83293492396831[/C][/ROW]
[ROW][C]p-value[/C][C]0.000688743839909684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36821&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36821&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	17.1720954283701
beta	0.079145695236861
S.D.	0.0163763213206841
T-STAT	4.83293492396831
p-value	0.000688743839909684

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.0647864102481687
beta	0.638565360052714
S.D.	0.110565013804647
T-STAT	5.7754739775185
p-value	0.000178835422947581
Lambda	0.361434639947286

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0647864102481687 \tabularnewline
beta & 0.638565360052714 \tabularnewline
S.D. & 0.110565013804647 \tabularnewline
T-STAT & 5.7754739775185 \tabularnewline
p-value & 0.000178835422947581 \tabularnewline
Lambda & 0.361434639947286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36821&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0647864102481687[/C][/ROW]
[ROW][C]beta[/C][C]0.638565360052714[/C][/ROW]
[ROW][C]S.D.[/C][C]0.110565013804647[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.7754739775185[/C][/ROW]
[ROW][C]p-value[/C][C]0.000178835422947581[/C][/ROW]
[ROW][C]Lambda[/C][C]0.361434639947286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36821&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36821&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	0.0647864102481687
beta	0.638565360052714
S.D.	0.110565013804647
T-STAT	5.7754739775185
p-value	0.000178835422947581
Lambda	0.361434639947286

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