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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

Wed, 26 May 2010 19:20:36 +0000

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/May/26/t1274901690vegtnbkevt62csp.htm/, Retrieved Fri, 03 May 2024 12:27:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76545, Retrieved Fri, 03 May 2024 12:27:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

100

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

-       [Standard Deviation-Mean Plot] [] [2010-05-26 19:20:36] [850dbf9e683f79d78a1e8310559edb6e] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76545&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76545&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	301.75	36.8996386612841	90
2	323	38.0438343668634	85
3	406	99.274031515464	227
4	264.25	14.3614066163451	30
5	261.25	38.3090502797098	80
6	366	73.5436378394941	162
7	202.5	35.1804870157687	80
8	183	54.9969696134857	123
9	278.5	77.4273853361974	189
10	201	38.0788655293195	79
11	206.5	34.0832314586905	82
12	286.5	49.8698305591667	113
13	222.25	16.4392822227736	39
14	232.75	66.8948179358212	144
15	305.75	100.07455554069	229
16	224	65.8432481985308	130
17	212.5	16.3605215890774	34
18	295.5	66.2746809372428	140
19	193	29.1776169920255	71

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 301.75 & 36.8996386612841 & 90 \tabularnewline
2 & 323 & 38.0438343668634 & 85 \tabularnewline
3 & 406 & 99.274031515464 & 227 \tabularnewline
4 & 264.25 & 14.3614066163451 & 30 \tabularnewline
5 & 261.25 & 38.3090502797098 & 80 \tabularnewline
6 & 366 & 73.5436378394941 & 162 \tabularnewline
7 & 202.5 & 35.1804870157687 & 80 \tabularnewline
8 & 183 & 54.9969696134857 & 123 \tabularnewline
9 & 278.5 & 77.4273853361974 & 189 \tabularnewline
10 & 201 & 38.0788655293195 & 79 \tabularnewline
11 & 206.5 & 34.0832314586905 & 82 \tabularnewline
12 & 286.5 & 49.8698305591667 & 113 \tabularnewline
13 & 222.25 & 16.4392822227736 & 39 \tabularnewline
14 & 232.75 & 66.8948179358212 & 144 \tabularnewline
15 & 305.75 & 100.07455554069 & 229 \tabularnewline
16 & 224 & 65.8432481985308 & 130 \tabularnewline
17 & 212.5 & 16.3605215890774 & 34 \tabularnewline
18 & 295.5 & 66.2746809372428 & 140 \tabularnewline
19 & 193 & 29.1776169920255 & 71 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76545&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]301.75[/C][C]36.8996386612841[/C][C]90[/C][/ROW]
[ROW][C]2[/C][C]323[/C][C]38.0438343668634[/C][C]85[/C][/ROW]
[ROW][C]3[/C][C]406[/C][C]99.274031515464[/C][C]227[/C][/ROW]
[ROW][C]4[/C][C]264.25[/C][C]14.3614066163451[/C][C]30[/C][/ROW]
[ROW][C]5[/C][C]261.25[/C][C]38.3090502797098[/C][C]80[/C][/ROW]
[ROW][C]6[/C][C]366[/C][C]73.5436378394941[/C][C]162[/C][/ROW]
[ROW][C]7[/C][C]202.5[/C][C]35.1804870157687[/C][C]80[/C][/ROW]
[ROW][C]8[/C][C]183[/C][C]54.9969696134857[/C][C]123[/C][/ROW]
[ROW][C]9[/C][C]278.5[/C][C]77.4273853361974[/C][C]189[/C][/ROW]
[ROW][C]10[/C][C]201[/C][C]38.0788655293195[/C][C]79[/C][/ROW]
[ROW][C]11[/C][C]206.5[/C][C]34.0832314586905[/C][C]82[/C][/ROW]
[ROW][C]12[/C][C]286.5[/C][C]49.8698305591667[/C][C]113[/C][/ROW]
[ROW][C]13[/C][C]222.25[/C][C]16.4392822227736[/C][C]39[/C][/ROW]
[ROW][C]14[/C][C]232.75[/C][C]66.8948179358212[/C][C]144[/C][/ROW]
[ROW][C]15[/C][C]305.75[/C][C]100.07455554069[/C][C]229[/C][/ROW]
[ROW][C]16[/C][C]224[/C][C]65.8432481985308[/C][C]130[/C][/ROW]
[ROW][C]17[/C][C]212.5[/C][C]16.3605215890774[/C][C]34[/C][/ROW]
[ROW][C]18[/C][C]295.5[/C][C]66.2746809372428[/C][C]140[/C][/ROW]
[ROW][C]19[/C][C]193[/C][C]29.1776169920255[/C][C]71[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76545&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	301.75	36.8996386612841	90
2	323	38.0438343668634	85
3	406	99.274031515464	227
4	264.25	14.3614066163451	30
5	261.25	38.3090502797098	80
6	366	73.5436378394941	162
7	202.5	35.1804870157687	80
8	183	54.9969696134857	123
9	278.5	77.4273853361974	189
10	201	38.0788655293195	79
11	206.5	34.0832314586905	82
12	286.5	49.8698305591667	113
13	222.25	16.4392822227736	39
14	232.75	66.8948179358212	144
15	305.75	100.07455554069	229
16	224	65.8432481985308	130
17	212.5	16.3605215890774	34
18	295.5	66.2746809372428	140
19	193	29.1776169920255	71

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-14.2799872050891
beta	0.246164488341652
S.D.	0.0826619295774086
T-STAT	2.97796687786161
p-value	0.00844184783695502

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -14.2799872050891 \tabularnewline
beta & 0.246164488341652 \tabularnewline
S.D. & 0.0826619295774086 \tabularnewline
T-STAT & 2.97796687786161 \tabularnewline
p-value & 0.00844184783695502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76545&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.2799872050891[/C][/ROW]
[ROW][C]beta[/C][C]0.246164488341652[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0826619295774086[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.97796687786161[/C][/ROW]
[ROW][C]p-value[/C][C]0.00844184783695502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76545&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76545&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	-14.2799872050891
beta	0.246164488341652
S.D.	0.0826619295774086
T-STAT	2.97796687786161
p-value	0.00844184783695502

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.01343119921062
beta	1.22400774329226
S.D.	0.544279980689484
T-STAT	2.24885681399068
p-value	0.0380691836217269
Lambda	-0.22400774329226

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.01343119921062 \tabularnewline
beta & 1.22400774329226 \tabularnewline
S.D. & 0.544279980689484 \tabularnewline
T-STAT & 2.24885681399068 \tabularnewline
p-value & 0.0380691836217269 \tabularnewline
Lambda & -0.22400774329226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76545&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.01343119921062[/C][/ROW]
[ROW][C]beta[/C][C]1.22400774329226[/C][/ROW]
[ROW][C]S.D.[/C][C]0.544279980689484[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.24885681399068[/C][/ROW]
[ROW][C]p-value[/C][C]0.0380691836217269[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.22400774329226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76545&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76545&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	-3.01343119921062
beta	1.22400774329226
S.D.	0.544279980689484
T-STAT	2.24885681399068
p-value	0.0380691836217269
Lambda	-0.22400774329226

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