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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, 19 Aug 2009 09:25:16 -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/2009/Aug/19/t1250695573gxwtjb6vha5trp6.htm/, Retrieved Tue, 07 May 2024 09:01:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42953, Retrieved Tue, 07 May 2024 09:01:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

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

-     [Central Tendency] [Thomas Van den Bo...] [2009-04-22 20:03:59] [29fb2afdd4eca1705c3ee13bfc104084]
- RMPD  [(Partial) Autocorrelation Function] [Thomas Van den Bo...] [2009-08-19 14:06:37] [f85cc8f00ef4b762f0a6fdfddc793773]
- RM        [Standard Deviation-Mean Plot] [Thomas Van den Bo...] [2009-08-19 15:25:16] [50e97696ebad247f45d73cd9926afb25] [Current]

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Dataseries X:

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Histogram

Boxplots

5.93
5.9
5.9
5.94
5.86
5.92
5.9
5.91
5.84
5.84
5.83
5.82
5.8
5.91
5.92
5.96
5.9
5.92
6.09
6.31
6.25
6.23
6.22
6.19
6.15
6.12
6.13
6.1
6.05
6.07
6.09
6.17
6.12
6.12
6.13
6.19
6.24
6.41
6.5
6.53
6.58
6.53
6.51
6.51
6.49
6.49
6.49
6.53
6.65
6.61
6.52
6.62
6.6
6.61
6.63
6.62
6.6
6.59
6.59
6.52
6.52
6.61
6.59
6.6
6.48
6.53
6.56
6.56
6.49
6.45
6.44
6.43

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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42953&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42953&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.9175	0.0206155281280882	0.04
2	5.8975	0.0262995563967657	0.0599999999999996
3	5.8325	0.00957427107756318	0.0199999999999996
4	5.8975	0.0684957419601151	0.16
5	6.055	0.190175357674612	0.409999999999999
6	6.2225	0.0249999999999999	0.0599999999999996
7	6.125	0.0208166599946616	0.0500000000000007
8	6.095	0.0525991127935316	0.12
9	6.14	0.0336650164612071	0.0700000000000003
10	6.42	0.130384048104053	0.29
11	6.5325	0.0330403793359985	0.0700000000000003
12	6.5	0.02	0.04
13	6.6	0.0559761854124892	0.130000000000001
14	6.615	0.0129099444873581	0.0300000000000002
15	6.575	0.0369684550213648	0.08
16	6.58	0.0408248290463865	0.0900000000000007
17	6.5325	0.0377491721763534	0.0799999999999992
18	6.4525	0.0262995563967659	0.0600000000000005

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.9175 & 0.0206155281280882 & 0.04 \tabularnewline
2 & 5.8975 & 0.0262995563967657 & 0.0599999999999996 \tabularnewline
3 & 5.8325 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
4 & 5.8975 & 0.0684957419601151 & 0.16 \tabularnewline
5 & 6.055 & 0.190175357674612 & 0.409999999999999 \tabularnewline
6 & 6.2225 & 0.0249999999999999 & 0.0599999999999996 \tabularnewline
7 & 6.125 & 0.0208166599946616 & 0.0500000000000007 \tabularnewline
8 & 6.095 & 0.0525991127935316 & 0.12 \tabularnewline
9 & 6.14 & 0.0336650164612071 & 0.0700000000000003 \tabularnewline
10 & 6.42 & 0.130384048104053 & 0.29 \tabularnewline
11 & 6.5325 & 0.0330403793359985 & 0.0700000000000003 \tabularnewline
12 & 6.5 & 0.02 & 0.04 \tabularnewline
13 & 6.6 & 0.0559761854124892 & 0.130000000000001 \tabularnewline
14 & 6.615 & 0.0129099444873581 & 0.0300000000000002 \tabularnewline
15 & 6.575 & 0.0369684550213648 & 0.08 \tabularnewline
16 & 6.58 & 0.0408248290463865 & 0.0900000000000007 \tabularnewline
17 & 6.5325 & 0.0377491721763534 & 0.0799999999999992 \tabularnewline
18 & 6.4525 & 0.0262995563967659 & 0.0600000000000005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42953&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]5.9175[/C][C]0.0206155281280882[/C][C]0.04[/C][/ROW]
[ROW][C]2[/C][C]5.8975[/C][C]0.0262995563967657[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]3[/C][C]5.8325[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]4[/C][C]5.8975[/C][C]0.0684957419601151[/C][C]0.16[/C][/ROW]
[ROW][C]5[/C][C]6.055[/C][C]0.190175357674612[/C][C]0.409999999999999[/C][/ROW]
[ROW][C]6[/C][C]6.2225[/C][C]0.0249999999999999[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]7[/C][C]6.125[/C][C]0.0208166599946616[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]8[/C][C]6.095[/C][C]0.0525991127935316[/C][C]0.12[/C][/ROW]
[ROW][C]9[/C][C]6.14[/C][C]0.0336650164612071[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]10[/C][C]6.42[/C][C]0.130384048104053[/C][C]0.29[/C][/ROW]
[ROW][C]11[/C][C]6.5325[/C][C]0.0330403793359985[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]12[/C][C]6.5[/C][C]0.02[/C][C]0.04[/C][/ROW]
[ROW][C]13[/C][C]6.6[/C][C]0.0559761854124892[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]14[/C][C]6.615[/C][C]0.0129099444873581[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]15[/C][C]6.575[/C][C]0.0369684550213648[/C][C]0.08[/C][/ROW]
[ROW][C]16[/C][C]6.58[/C][C]0.0408248290463865[/C][C]0.0900000000000007[/C][/ROW]
[ROW][C]17[/C][C]6.5325[/C][C]0.0377491721763534[/C][C]0.0799999999999992[/C][/ROW]
[ROW][C]18[/C][C]6.4525[/C][C]0.0262995563967659[/C][C]0.0600000000000005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42953&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	5.9175	0.0206155281280882	0.04
2	5.8975	0.0262995563967657	0.0599999999999996
3	5.8325	0.00957427107756318	0.0199999999999996
4	5.8975	0.0684957419601151	0.16
5	6.055	0.190175357674612	0.409999999999999
6	6.2225	0.0249999999999999	0.0599999999999996
7	6.125	0.0208166599946616	0.0500000000000007
8	6.095	0.0525991127935316	0.12
9	6.14	0.0336650164612071	0.0700000000000003
10	6.42	0.130384048104053	0.29
11	6.5325	0.0330403793359985	0.0700000000000003
12	6.5	0.02	0.04
13	6.6	0.0559761854124892	0.130000000000001
14	6.615	0.0129099444873581	0.0300000000000002
15	6.575	0.0369684550213648	0.08
16	6.58	0.0408248290463865	0.0900000000000007
17	6.5325	0.0377491721763534	0.0799999999999992
18	6.4525	0.0262995563967659	0.0600000000000005

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.125033251268306
beta	-0.0124719418387662
S.D.	0.0395871786397053
T-STAT	-0.315050030523192
p-value	0.756795251276602

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.125033251268306 \tabularnewline
beta & -0.0124719418387662 \tabularnewline
S.D. & 0.0395871786397053 \tabularnewline
T-STAT & -0.315050030523192 \tabularnewline
p-value & 0.756795251276602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42953&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.125033251268306[/C][/ROW]
[ROW][C]beta[/C][C]-0.0124719418387662[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0395871786397053[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.315050030523192[/C][/ROW]
[ROW][C]p-value[/C][C]0.756795251276602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42953&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42953&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	0.125033251268306
beta	-0.0124719418387662
S.D.	0.0395871786397053
T-STAT	-0.315050030523192
p-value	0.756795251276602

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.91147659222553
beta	0.847181189540098
S.D.	4.05021825508909
T-STAT	0.209169268464882
p-value	0.836955992473364
Lambda	0.152818810459902

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.91147659222553 \tabularnewline
beta & 0.847181189540098 \tabularnewline
S.D. & 4.05021825508909 \tabularnewline
T-STAT & 0.209169268464882 \tabularnewline
p-value & 0.836955992473364 \tabularnewline
Lambda & 0.152818810459902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42953&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.91147659222553[/C][/ROW]
[ROW][C]beta[/C][C]0.847181189540098[/C][/ROW]
[ROW][C]S.D.[/C][C]4.05021825508909[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.209169268464882[/C][/ROW]
[ROW][C]p-value[/C][C]0.836955992473364[/C][/ROW]
[ROW][C]Lambda[/C][C]0.152818810459902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42953&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42953&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	-4.91147659222553
beta	0.847181189540098
S.D.	4.05021825508909
T-STAT	0.209169268464882
p-value	0.836955992473364
Lambda	0.152818810459902

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0 ;

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