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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 28 Apr 2014 08:28:20 -0400

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/2014/Apr/28/t1398688107355y7lsbizbmdrx.htm/, Retrieved Fri, 17 May 2024 04:17:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234672, Retrieved Fri, 17 May 2024 04:17:38 +0000

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

-       [Standard Deviation-Mean Plot] [] [2014-04-28 12:28:20] [a17c9baa293c9bc97942594e3a0541eb] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234672&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]2 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=234672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234672&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	302.775	18.244208296433	48.5
2	245.4	15.9160296556648	52.5
3	202.283333333333	9.43695187049614	30.9
4	175.316666666667	5.70595117293153	17.7
5	184.308333333333	12.3330640838751	36.3
6	253.591666666667	26.6429747975072	79.4
7	312.05	13.9615380762488	40.2
8	321.158333333333	7.37655479245295	23.6
9	276.991666666667	14.8808270990397	44.4
10	214.208333333333	16.1130358481083	51.1
11	173.383333333333	7.28982271056815	23.5
12	225.25	32.4369177999951	94.1
13	266.708333333333	6.11175593475889	19.2
14	259.783333333333	4.60865457261628	14.4
15	303.166666666667	19.4340999900752	60.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 302.775 & 18.244208296433 & 48.5 \tabularnewline
2 & 245.4 & 15.9160296556648 & 52.5 \tabularnewline
3 & 202.283333333333 & 9.43695187049614 & 30.9 \tabularnewline
4 & 175.316666666667 & 5.70595117293153 & 17.7 \tabularnewline
5 & 184.308333333333 & 12.3330640838751 & 36.3 \tabularnewline
6 & 253.591666666667 & 26.6429747975072 & 79.4 \tabularnewline
7 & 312.05 & 13.9615380762488 & 40.2 \tabularnewline
8 & 321.158333333333 & 7.37655479245295 & 23.6 \tabularnewline
9 & 276.991666666667 & 14.8808270990397 & 44.4 \tabularnewline
10 & 214.208333333333 & 16.1130358481083 & 51.1 \tabularnewline
11 & 173.383333333333 & 7.28982271056815 & 23.5 \tabularnewline
12 & 225.25 & 32.4369177999951 & 94.1 \tabularnewline
13 & 266.708333333333 & 6.11175593475889 & 19.2 \tabularnewline
14 & 259.783333333333 & 4.60865457261628 & 14.4 \tabularnewline
15 & 303.166666666667 & 19.4340999900752 & 60.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234672&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]302.775[/C][C]18.244208296433[/C][C]48.5[/C][/ROW]
[ROW][C]2[/C][C]245.4[/C][C]15.9160296556648[/C][C]52.5[/C][/ROW]
[ROW][C]3[/C][C]202.283333333333[/C][C]9.43695187049614[/C][C]30.9[/C][/ROW]
[ROW][C]4[/C][C]175.316666666667[/C][C]5.70595117293153[/C][C]17.7[/C][/ROW]
[ROW][C]5[/C][C]184.308333333333[/C][C]12.3330640838751[/C][C]36.3[/C][/ROW]
[ROW][C]6[/C][C]253.591666666667[/C][C]26.6429747975072[/C][C]79.4[/C][/ROW]
[ROW][C]7[/C][C]312.05[/C][C]13.9615380762488[/C][C]40.2[/C][/ROW]
[ROW][C]8[/C][C]321.158333333333[/C][C]7.37655479245295[/C][C]23.6[/C][/ROW]
[ROW][C]9[/C][C]276.991666666667[/C][C]14.8808270990397[/C][C]44.4[/C][/ROW]
[ROW][C]10[/C][C]214.208333333333[/C][C]16.1130358481083[/C][C]51.1[/C][/ROW]
[ROW][C]11[/C][C]173.383333333333[/C][C]7.28982271056815[/C][C]23.5[/C][/ROW]
[ROW][C]12[/C][C]225.25[/C][C]32.4369177999951[/C][C]94.1[/C][/ROW]
[ROW][C]13[/C][C]266.708333333333[/C][C]6.11175593475889[/C][C]19.2[/C][/ROW]
[ROW][C]14[/C][C]259.783333333333[/C][C]4.60865457261628[/C][C]14.4[/C][/ROW]
[ROW][C]15[/C][C]303.166666666667[/C][C]19.4340999900752[/C][C]60.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234672&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	302.775	18.244208296433	48.5
2	245.4	15.9160296556648	52.5
3	202.283333333333	9.43695187049614	30.9
4	175.316666666667	5.70595117293153	17.7
5	184.308333333333	12.3330640838751	36.3
6	253.591666666667	26.6429747975072	79.4
7	312.05	13.9615380762488	40.2
8	321.158333333333	7.37655479245295	23.6
9	276.991666666667	14.8808270990397	44.4
10	214.208333333333	16.1130358481083	51.1
11	173.383333333333	7.28982271056815	23.5
12	225.25	32.4369177999951	94.1
13	266.708333333333	6.11175593475889	19.2
14	259.783333333333	4.60865457261628	14.4
15	303.166666666667	19.4340999900752	60.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	8.41222227035664
beta	0.0226858303172908
S.D.	0.0433962201757694
T-STAT	0.522760512906551
p-value	0.609935171008513

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.41222227035664 \tabularnewline
beta & 0.0226858303172908 \tabularnewline
S.D. & 0.0433962201757694 \tabularnewline
T-STAT & 0.522760512906551 \tabularnewline
p-value & 0.609935171008513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234672&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.41222227035664[/C][/ROW]
[ROW][C]beta[/C][C]0.0226858303172908[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0433962201757694[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.522760512906551[/C][/ROW]
[ROW][C]p-value[/C][C]0.609935171008513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234672&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234672&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	8.41222227035664
beta	0.0226858303172908
S.D.	0.0433962201757694
T-STAT	0.522760512906551
p-value	0.609935171008513

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.81397859856102
beta	0.601419795289097
S.D.	0.74687432500142
T-STAT	0.80524898922982
p-value	0.435157428804319
Lambda	0.398580204710903

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.81397859856102 \tabularnewline
beta & 0.601419795289097 \tabularnewline
S.D. & 0.74687432500142 \tabularnewline
T-STAT & 0.80524898922982 \tabularnewline
p-value & 0.435157428804319 \tabularnewline
Lambda & 0.398580204710903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234672&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.81397859856102[/C][/ROW]
[ROW][C]beta[/C][C]0.601419795289097[/C][/ROW]
[ROW][C]S.D.[/C][C]0.74687432500142[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.80524898922982[/C][/ROW]
[ROW][C]p-value[/C][C]0.435157428804319[/C][/ROW]
[ROW][C]Lambda[/C][C]0.398580204710903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234672&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234672&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	-0.81397859856102
beta	0.601419795289097
S.D.	0.74687432500142
T-STAT	0.80524898922982
p-value	0.435157428804319
Lambda	0.398580204710903

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