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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, 18 May 2008 10:49:00 -0600

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/2008/May/18/t12111293997iaxqxtlmnc3wpq.htm/, Retrieved Mon, 20 May 2024 00:09:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12791, Retrieved Mon, 20 May 2024 00:09:11 +0000

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No (this computation is public)

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Estimated Impact

150

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

-       [Standard Deviation-Mean Plot] [Deviation Mean Pl...] [2008-05-18 16:49:00] [88615a9036e6e98ff64037322024b7ad] [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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12791&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12791&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' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	120.075	0.0331662479035574	0.0700000000000074
2	120.22	0.0355902608401013	0.0699999999999932
3	120.26	0.0216024689946973	0.0500000000000114
4	120.3475	0.0411298755975134	0.0900000000000034
5	120.4325	0.0499165971062383	0.109999999999999
6	120.7225	0.177458915433027	0.409999999999997
7	121.0675	0.0623832242407123	0.150000000000006
8	121.515	0.252520626220243	0.529999999999987
9	121.77	0.0346410161513748	0.0799999999999983
10	121.8925	0.0861684396980719	0.170000000000002
11	122.3975	0.151959424408839	0.339999999999989
12	122.6425	0.0684957419601129	0.159999999999997
13	122.55	0.121106014163897	0.259999999999991
14	122.435	0.0506622805119015	0.109999999999999
15	122.4325	0.0722841614740008	0.129999999999995
16	122.5325	0.0262995563967631	0.0499999999999972
17	122.9425	0.152178623115513	0.329999999999998
18	123.0875	0.0221735578260879	0.0500000000000114
19	123.3775	0.457411193566572	0.97999999999999
20	124.24	0.255212329900678	0.469999999999999
21	124.8175	0.161322658049018	0.390000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 120.075 & 0.0331662479035574 & 0.0700000000000074 \tabularnewline
2 & 120.22 & 0.0355902608401013 & 0.0699999999999932 \tabularnewline
3 & 120.26 & 0.0216024689946973 & 0.0500000000000114 \tabularnewline
4 & 120.3475 & 0.0411298755975134 & 0.0900000000000034 \tabularnewline
5 & 120.4325 & 0.0499165971062383 & 0.109999999999999 \tabularnewline
6 & 120.7225 & 0.177458915433027 & 0.409999999999997 \tabularnewline
7 & 121.0675 & 0.0623832242407123 & 0.150000000000006 \tabularnewline
8 & 121.515 & 0.252520626220243 & 0.529999999999987 \tabularnewline
9 & 121.77 & 0.0346410161513748 & 0.0799999999999983 \tabularnewline
10 & 121.8925 & 0.0861684396980719 & 0.170000000000002 \tabularnewline
11 & 122.3975 & 0.151959424408839 & 0.339999999999989 \tabularnewline
12 & 122.6425 & 0.0684957419601129 & 0.159999999999997 \tabularnewline
13 & 122.55 & 0.121106014163897 & 0.259999999999991 \tabularnewline
14 & 122.435 & 0.0506622805119015 & 0.109999999999999 \tabularnewline
15 & 122.4325 & 0.0722841614740008 & 0.129999999999995 \tabularnewline
16 & 122.5325 & 0.0262995563967631 & 0.0499999999999972 \tabularnewline
17 & 122.9425 & 0.152178623115513 & 0.329999999999998 \tabularnewline
18 & 123.0875 & 0.0221735578260879 & 0.0500000000000114 \tabularnewline
19 & 123.3775 & 0.457411193566572 & 0.97999999999999 \tabularnewline
20 & 124.24 & 0.255212329900678 & 0.469999999999999 \tabularnewline
21 & 124.8175 & 0.161322658049018 & 0.390000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12791&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]120.075[/C][C]0.0331662479035574[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]2[/C][C]120.22[/C][C]0.0355902608401013[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]3[/C][C]120.26[/C][C]0.0216024689946973[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]4[/C][C]120.3475[/C][C]0.0411298755975134[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]5[/C][C]120.4325[/C][C]0.0499165971062383[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]6[/C][C]120.7225[/C][C]0.177458915433027[/C][C]0.409999999999997[/C][/ROW]
[ROW][C]7[/C][C]121.0675[/C][C]0.0623832242407123[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]8[/C][C]121.515[/C][C]0.252520626220243[/C][C]0.529999999999987[/C][/ROW]
[ROW][C]9[/C][C]121.77[/C][C]0.0346410161513748[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]10[/C][C]121.8925[/C][C]0.0861684396980719[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]11[/C][C]122.3975[/C][C]0.151959424408839[/C][C]0.339999999999989[/C][/ROW]
[ROW][C]12[/C][C]122.6425[/C][C]0.0684957419601129[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]13[/C][C]122.55[/C][C]0.121106014163897[/C][C]0.259999999999991[/C][/ROW]
[ROW][C]14[/C][C]122.435[/C][C]0.0506622805119015[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]15[/C][C]122.4325[/C][C]0.0722841614740008[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]16[/C][C]122.5325[/C][C]0.0262995563967631[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]17[/C][C]122.9425[/C][C]0.152178623115513[/C][C]0.329999999999998[/C][/ROW]
[ROW][C]18[/C][C]123.0875[/C][C]0.0221735578260879[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]19[/C][C]123.3775[/C][C]0.457411193566572[/C][C]0.97999999999999[/C][/ROW]
[ROW][C]20[/C][C]124.24[/C][C]0.255212329900678[/C][C]0.469999999999999[/C][/ROW]
[ROW][C]21[/C][C]124.8175[/C][C]0.161322658049018[/C][C]0.390000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12791&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	120.075	0.0331662479035574	0.0700000000000074
2	120.22	0.0355902608401013	0.0699999999999932
3	120.26	0.0216024689946973	0.0500000000000114
4	120.3475	0.0411298755975134	0.0900000000000034
5	120.4325	0.0499165971062383	0.109999999999999
6	120.7225	0.177458915433027	0.409999999999997
7	121.0675	0.0623832242407123	0.150000000000006
8	121.515	0.252520626220243	0.529999999999987
9	121.77	0.0346410161513748	0.0799999999999983
10	121.8925	0.0861684396980719	0.170000000000002
11	122.3975	0.151959424408839	0.339999999999989
12	122.6425	0.0684957419601129	0.159999999999997
13	122.55	0.121106014163897	0.259999999999991
14	122.435	0.0506622805119015	0.109999999999999
15	122.4325	0.0722841614740008	0.129999999999995
16	122.5325	0.0262995563967631	0.0499999999999972
17	122.9425	0.152178623115513	0.329999999999998
18	123.0875	0.0221735578260879	0.0500000000000114
19	123.3775	0.457411193566572	0.97999999999999
20	124.24	0.255212329900678	0.469999999999999
21	124.8175	0.161322658049018	0.390000000000001

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-4.43180761669198
beta	0.0372407002474241
S.D.	0.0161455465899099
T-STAT	2.30656175311510
p-value	0.0325122182677801

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.43180761669198 \tabularnewline
beta & 0.0372407002474241 \tabularnewline
S.D. & 0.0161455465899099 \tabularnewline
T-STAT & 2.30656175311510 \tabularnewline
p-value & 0.0325122182677801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12791&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.43180761669198[/C][/ROW]
[ROW][C]beta[/C][C]0.0372407002474241[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0161455465899099[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.30656175311510[/C][/ROW]
[ROW][C]p-value[/C][C]0.0325122182677801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12791&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	-4.43180761669198
beta	0.0372407002474241
S.D.	0.0161455465899099
T-STAT	2.30656175311510
p-value	0.0325122182677801

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-193.311870630718
beta	39.70512684832
S.D.	15.8599836850787
T-STAT	2.5034784169214
p-value	0.0215815429889178
Lambda	-38.7051268483200

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -193.311870630718 \tabularnewline
beta & 39.70512684832 \tabularnewline
S.D. & 15.8599836850787 \tabularnewline
T-STAT & 2.5034784169214 \tabularnewline
p-value & 0.0215815429889178 \tabularnewline
Lambda & -38.7051268483200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12791&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-193.311870630718[/C][/ROW]
[ROW][C]beta[/C][C]39.70512684832[/C][/ROW]
[ROW][C]S.D.[/C][C]15.8599836850787[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.5034784169214[/C][/ROW]
[ROW][C]p-value[/C][C]0.0215815429889178[/C][/ROW]
[ROW][C]Lambda[/C][C]-38.7051268483200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12791&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12791&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	-193.311870630718
beta	39.70512684832
S.D.	15.8599836850787
T-STAT	2.5034784169214
p-value	0.0215815429889178
Lambda	-38.7051268483200

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code