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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Fri, 27 Nov 2009 09:40:00 -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/Nov/27/t1259340086fk02rp1vrmc11zd.htm/, Retrieved Mon, 29 Apr 2024 05:52:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60981, Retrieved Mon, 29 Apr 2024 05:52:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-       [Standard Deviation-Mean Plot] [] [2009-11-27 16:40:00] [477c9cb8e7bda18f2375c22a66069c90] [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=60981&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=60981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60981&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	98.8	8.07052249444442	16.6
2	81.175	7.53983863664645	18.2
3	86.075	28.9459697827982	64.7
4	97.775	6.56067831858872	13.8
5	85.125	12.6090906359922	26.8
6	84.525	27.4969543768033	61.2
7	102.1	5.71722543430523	13.1
8	90.175	12.2222133838352	28.8
9	87	24.686163465931	55.9
10	103.625	7.28211278865321	15.7
11	87.525	11.433977144167	26.9
12	92.15	23.9953467711277	52.5
13	96.2	11.4510552643268	22.3
14	84	13.7625094610927	31
15	81.925	21.7199409145912	50.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.8 & 8.07052249444442 & 16.6 \tabularnewline
2 & 81.175 & 7.53983863664645 & 18.2 \tabularnewline
3 & 86.075 & 28.9459697827982 & 64.7 \tabularnewline
4 & 97.775 & 6.56067831858872 & 13.8 \tabularnewline
5 & 85.125 & 12.6090906359922 & 26.8 \tabularnewline
6 & 84.525 & 27.4969543768033 & 61.2 \tabularnewline
7 & 102.1 & 5.71722543430523 & 13.1 \tabularnewline
8 & 90.175 & 12.2222133838352 & 28.8 \tabularnewline
9 & 87 & 24.686163465931 & 55.9 \tabularnewline
10 & 103.625 & 7.28211278865321 & 15.7 \tabularnewline
11 & 87.525 & 11.433977144167 & 26.9 \tabularnewline
12 & 92.15 & 23.9953467711277 & 52.5 \tabularnewline
13 & 96.2 & 11.4510552643268 & 22.3 \tabularnewline
14 & 84 & 13.7625094610927 & 31 \tabularnewline
15 & 81.925 & 21.7199409145912 & 50.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60981&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]98.8[/C][C]8.07052249444442[/C][C]16.6[/C][/ROW]
[ROW][C]2[/C][C]81.175[/C][C]7.53983863664645[/C][C]18.2[/C][/ROW]
[ROW][C]3[/C][C]86.075[/C][C]28.9459697827982[/C][C]64.7[/C][/ROW]
[ROW][C]4[/C][C]97.775[/C][C]6.56067831858872[/C][C]13.8[/C][/ROW]
[ROW][C]5[/C][C]85.125[/C][C]12.6090906359922[/C][C]26.8[/C][/ROW]
[ROW][C]6[/C][C]84.525[/C][C]27.4969543768033[/C][C]61.2[/C][/ROW]
[ROW][C]7[/C][C]102.1[/C][C]5.71722543430523[/C][C]13.1[/C][/ROW]
[ROW][C]8[/C][C]90.175[/C][C]12.2222133838352[/C][C]28.8[/C][/ROW]
[ROW][C]9[/C][C]87[/C][C]24.686163465931[/C][C]55.9[/C][/ROW]
[ROW][C]10[/C][C]103.625[/C][C]7.28211278865321[/C][C]15.7[/C][/ROW]
[ROW][C]11[/C][C]87.525[/C][C]11.433977144167[/C][C]26.9[/C][/ROW]
[ROW][C]12[/C][C]92.15[/C][C]23.9953467711277[/C][C]52.5[/C][/ROW]
[ROW][C]13[/C][C]96.2[/C][C]11.4510552643268[/C][C]22.3[/C][/ROW]
[ROW][C]14[/C][C]84[/C][C]13.7625094610927[/C][C]31[/C][/ROW]
[ROW][C]15[/C][C]81.925[/C][C]21.7199409145912[/C][C]50.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60981&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	98.8	8.07052249444442	16.6
2	81.175	7.53983863664645	18.2
3	86.075	28.9459697827982	64.7
4	97.775	6.56067831858872	13.8
5	85.125	12.6090906359922	26.8
6	84.525	27.4969543768033	61.2
7	102.1	5.71722543430523	13.1
8	90.175	12.2222133838352	28.8
9	87	24.686163465931	55.9
10	103.625	7.28211278865321	15.7
11	87.525	11.433977144167	26.9
12	92.15	23.9953467711277	52.5
13	96.2	11.4510552643268	22.3
14	84	13.7625094610927	31
15	81.925	21.7199409145912	50.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	68.7547115927264
beta	-0.594788650223715
S.D.	0.256108159065179
T-STAT	-2.32241195436629
p-value	0.0370825609401785

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 68.7547115927264 \tabularnewline
beta & -0.594788650223715 \tabularnewline
S.D. & 0.256108159065179 \tabularnewline
T-STAT & -2.32241195436629 \tabularnewline
p-value & 0.0370825609401785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60981&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]68.7547115927264[/C][/ROW]
[ROW][C]beta[/C][C]-0.594788650223715[/C][/ROW]
[ROW][C]S.D.[/C][C]0.256108159065179[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.32241195436629[/C][/ROW]
[ROW][C]p-value[/C][C]0.0370825609401785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60981&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	68.7547115927264
beta	-0.594788650223715
S.D.	0.256108159065179
T-STAT	-2.32241195436629
p-value	0.0370825609401785

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	21.0515166093518
beta	-4.10677899748551
S.D.	1.52192429305732
T-STAT	-2.69841214587331
p-value	0.018249133432482
Lambda	5.10677899748551

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 21.0515166093518 \tabularnewline
beta & -4.10677899748551 \tabularnewline
S.D. & 1.52192429305732 \tabularnewline
T-STAT & -2.69841214587331 \tabularnewline
p-value & 0.018249133432482 \tabularnewline
Lambda & 5.10677899748551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60981&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.0515166093518[/C][/ROW]
[ROW][C]beta[/C][C]-4.10677899748551[/C][/ROW]
[ROW][C]S.D.[/C][C]1.52192429305732[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.69841214587331[/C][/ROW]
[ROW][C]p-value[/C][C]0.018249133432482[/C][/ROW]
[ROW][C]Lambda[/C][C]5.10677899748551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60981&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60981&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	21.0515166093518
beta	-4.10677899748551
S.D.	1.52192429305732
T-STAT	-2.69841214587331
p-value	0.018249133432482
Lambda	5.10677899748551

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code