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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, 16 Jan 2011 13:42:18 +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/2011/Jan/16/t1295185223kaq4sv9uhr7ase7.htm/, Retrieved Thu, 16 May 2024 14:19:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117401, Retrieved Thu, 16 May 2024 14:19:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

149

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

-     [Univariate Data Series] [] [2011-01-16 11:37:06] [e35ce2e7ec49602a729c3c8722e619b0]
- RMPD  [Variability] [] [2011-01-16 13:09:43] [e35ce2e7ec49602a729c3c8722e619b0]
- RM D      [Standard Deviation-Mean Plot] [] [2011-01-16 13:42:18] [9ecedc6075144b73bec317d56fadfdf0] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117401&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117401&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	10726	136.613810917247	298
2	10512.75	96.8310384122777	218
3	11011.75	390.680069451548	707
4	12255	691.624657358792	1580
5	14543.25	517.221664279446	1119
6	16071.75	775.94088047995	1896
7	15394.5	417.208580928053	885
8	15790	450.981891728112	1043
9	15853.75	254.858620938486	577
10	16712.25	857.238346863539	2013
11	19348.75	1123.88059122548	2403
12	18648.5	362.350198932837	787
13	18848.75	704.242560012765	1571
14	21753	1832.06240796177	3945
15	21725.5	237.203850446545	545
16	22629.75	1230.88758625636	2853
17	26001.25	1125.55093917009	2413
18	30204	2033.21436810452	4911

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10726 & 136.613810917247 & 298 \tabularnewline
2 & 10512.75 & 96.8310384122777 & 218 \tabularnewline
3 & 11011.75 & 390.680069451548 & 707 \tabularnewline
4 & 12255 & 691.624657358792 & 1580 \tabularnewline
5 & 14543.25 & 517.221664279446 & 1119 \tabularnewline
6 & 16071.75 & 775.94088047995 & 1896 \tabularnewline
7 & 15394.5 & 417.208580928053 & 885 \tabularnewline
8 & 15790 & 450.981891728112 & 1043 \tabularnewline
9 & 15853.75 & 254.858620938486 & 577 \tabularnewline
10 & 16712.25 & 857.238346863539 & 2013 \tabularnewline
11 & 19348.75 & 1123.88059122548 & 2403 \tabularnewline
12 & 18648.5 & 362.350198932837 & 787 \tabularnewline
13 & 18848.75 & 704.242560012765 & 1571 \tabularnewline
14 & 21753 & 1832.06240796177 & 3945 \tabularnewline
15 & 21725.5 & 237.203850446545 & 545 \tabularnewline
16 & 22629.75 & 1230.88758625636 & 2853 \tabularnewline
17 & 26001.25 & 1125.55093917009 & 2413 \tabularnewline
18 & 30204 & 2033.21436810452 & 4911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117401&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]10726[/C][C]136.613810917247[/C][C]298[/C][/ROW]
[ROW][C]2[/C][C]10512.75[/C][C]96.8310384122777[/C][C]218[/C][/ROW]
[ROW][C]3[/C][C]11011.75[/C][C]390.680069451548[/C][C]707[/C][/ROW]
[ROW][C]4[/C][C]12255[/C][C]691.624657358792[/C][C]1580[/C][/ROW]
[ROW][C]5[/C][C]14543.25[/C][C]517.221664279446[/C][C]1119[/C][/ROW]
[ROW][C]6[/C][C]16071.75[/C][C]775.94088047995[/C][C]1896[/C][/ROW]
[ROW][C]7[/C][C]15394.5[/C][C]417.208580928053[/C][C]885[/C][/ROW]
[ROW][C]8[/C][C]15790[/C][C]450.981891728112[/C][C]1043[/C][/ROW]
[ROW][C]9[/C][C]15853.75[/C][C]254.858620938486[/C][C]577[/C][/ROW]
[ROW][C]10[/C][C]16712.25[/C][C]857.238346863539[/C][C]2013[/C][/ROW]
[ROW][C]11[/C][C]19348.75[/C][C]1123.88059122548[/C][C]2403[/C][/ROW]
[ROW][C]12[/C][C]18648.5[/C][C]362.350198932837[/C][C]787[/C][/ROW]
[ROW][C]13[/C][C]18848.75[/C][C]704.242560012765[/C][C]1571[/C][/ROW]
[ROW][C]14[/C][C]21753[/C][C]1832.06240796177[/C][C]3945[/C][/ROW]
[ROW][C]15[/C][C]21725.5[/C][C]237.203850446545[/C][C]545[/C][/ROW]
[ROW][C]16[/C][C]22629.75[/C][C]1230.88758625636[/C][C]2853[/C][/ROW]
[ROW][C]17[/C][C]26001.25[/C][C]1125.55093917009[/C][C]2413[/C][/ROW]
[ROW][C]18[/C][C]30204[/C][C]2033.21436810452[/C][C]4911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117401&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	10726	136.613810917247	298
2	10512.75	96.8310384122777	218
3	11011.75	390.680069451548	707
4	12255	691.624657358792	1580
5	14543.25	517.221664279446	1119
6	16071.75	775.94088047995	1896
7	15394.5	417.208580928053	885
8	15790	450.981891728112	1043
9	15853.75	254.858620938486	577
10	16712.25	857.238346863539	2013
11	19348.75	1123.88059122548	2403
12	18648.5	362.350198932837	787
13	18848.75	704.242560012765	1571
14	21753	1832.06240796177	3945
15	21725.5	237.203850446545	545
16	22629.75	1230.88758625636	2853
17	26001.25	1125.55093917009	2413
18	30204	2033.21436810452	4911

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-661.875245713468
beta	0.0790878437329446
S.D.	0.016549234748395
T-STAT	4.77894264812546
p-value	0.000204943622627993

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -661.875245713468 \tabularnewline
beta & 0.0790878437329446 \tabularnewline
S.D. & 0.016549234748395 \tabularnewline
T-STAT & 4.77894264812546 \tabularnewline
p-value & 0.000204943622627993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117401&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-661.875245713468[/C][/ROW]
[ROW][C]beta[/C][C]0.0790878437329446[/C][/ROW]
[ROW][C]S.D.[/C][C]0.016549234748395[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.77894264812546[/C][/ROW]
[ROW][C]p-value[/C][C]0.000204943622627993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117401&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	-661.875245713468
beta	0.0790878437329446
S.D.	0.016549234748395
T-STAT	4.77894264812546
p-value	0.000204943622627993

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-13.2405553655873
beta	2.00772342153798
S.D.	0.482972062587607
T-STAT	4.15701771812897
p-value	0.000742344313015657
Lambda	-1.00772342153798

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.2405553655873 \tabularnewline
beta & 2.00772342153798 \tabularnewline
S.D. & 0.482972062587607 \tabularnewline
T-STAT & 4.15701771812897 \tabularnewline
p-value & 0.000742344313015657 \tabularnewline
Lambda & -1.00772342153798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117401&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.2405553655873[/C][/ROW]
[ROW][C]beta[/C][C]2.00772342153798[/C][/ROW]
[ROW][C]S.D.[/C][C]0.482972062587607[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.15701771812897[/C][/ROW]
[ROW][C]p-value[/C][C]0.000742344313015657[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.00772342153798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117401&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117401&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	-13.2405553655873
beta	2.00772342153798
S.D.	0.482972062587607
T-STAT	4.15701771812897
p-value	0.000742344313015657
Lambda	-1.00772342153798

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 200 ; par2 = 12 ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code