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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 18 Aug 2010 01:02:11 +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/Aug/18/t1282093317zqr3qia9fcb53p8.htm/, Retrieved Thu, 16 May 2024 11:59:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79176, Retrieved Thu, 16 May 2024 11:59:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

153

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

-     [Standard Deviation Plot] [] [2010-08-18 00:34:42] [0054c34847e75ef4340aed26951eb951]
- RMP   [Standard Deviation-Mean Plot] [] [2010-08-18 00:53:46] [0054c34847e75ef4340aed26951eb951]
-   PD      [Standard Deviation-Mean Plot] [] [2010-08-18 01:02:11] [ea4db07d8da34007b79212461ea6aa7b] [Current]

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Boxplots

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79176&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79176&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79176&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	156.25	1.70782512765993	4
2	152.25	1.25830573921179	3
3	156	1.41421356237310	3
4	153.5	2.38047614284762	5
5	151.5	5.44671154612273	12
6	144.25	3.30403793359983	7
7	144.5	4.65474668125631	11
8	143.75	6.29152869605896	14
9	141.75	7.58836829188814	18
10	135	2.44948974278318	5
11	128.5	8.34665601703261	20
12	119	6.68331255192114	16
13	107.75	5.18812747209113	11
14	102.75	6.18465843842649	13
15	87	6.48074069840786	13
16	69.5	3.87298334620742	9
17	72.75	5.1234753829798	12
18	65.5	5.32290647422377	11
19	62.25	6.80073525436772	14
20	77.75	5.85234995535981	14
21	89.25	13.6717470232106	30

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 156.25 & 1.70782512765993 & 4 \tabularnewline
2 & 152.25 & 1.25830573921179 & 3 \tabularnewline
3 & 156 & 1.41421356237310 & 3 \tabularnewline
4 & 153.5 & 2.38047614284762 & 5 \tabularnewline
5 & 151.5 & 5.44671154612273 & 12 \tabularnewline
6 & 144.25 & 3.30403793359983 & 7 \tabularnewline
7 & 144.5 & 4.65474668125631 & 11 \tabularnewline
8 & 143.75 & 6.29152869605896 & 14 \tabularnewline
9 & 141.75 & 7.58836829188814 & 18 \tabularnewline
10 & 135 & 2.44948974278318 & 5 \tabularnewline
11 & 128.5 & 8.34665601703261 & 20 \tabularnewline
12 & 119 & 6.68331255192114 & 16 \tabularnewline
13 & 107.75 & 5.18812747209113 & 11 \tabularnewline
14 & 102.75 & 6.18465843842649 & 13 \tabularnewline
15 & 87 & 6.48074069840786 & 13 \tabularnewline
16 & 69.5 & 3.87298334620742 & 9 \tabularnewline
17 & 72.75 & 5.1234753829798 & 12 \tabularnewline
18 & 65.5 & 5.32290647422377 & 11 \tabularnewline
19 & 62.25 & 6.80073525436772 & 14 \tabularnewline
20 & 77.75 & 5.85234995535981 & 14 \tabularnewline
21 & 89.25 & 13.6717470232106 & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79176&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]156.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]152.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]156[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]153.5[/C][C]2.38047614284762[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]151.5[/C][C]5.44671154612273[/C][C]12[/C][/ROW]
[ROW][C]6[/C][C]144.25[/C][C]3.30403793359983[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]144.5[/C][C]4.65474668125631[/C][C]11[/C][/ROW]
[ROW][C]8[/C][C]143.75[/C][C]6.29152869605896[/C][C]14[/C][/ROW]
[ROW][C]9[/C][C]141.75[/C][C]7.58836829188814[/C][C]18[/C][/ROW]
[ROW][C]10[/C][C]135[/C][C]2.44948974278318[/C][C]5[/C][/ROW]
[ROW][C]11[/C][C]128.5[/C][C]8.34665601703261[/C][C]20[/C][/ROW]
[ROW][C]12[/C][C]119[/C][C]6.68331255192114[/C][C]16[/C][/ROW]
[ROW][C]13[/C][C]107.75[/C][C]5.18812747209113[/C][C]11[/C][/ROW]
[ROW][C]14[/C][C]102.75[/C][C]6.18465843842649[/C][C]13[/C][/ROW]
[ROW][C]15[/C][C]87[/C][C]6.48074069840786[/C][C]13[/C][/ROW]
[ROW][C]16[/C][C]69.5[/C][C]3.87298334620742[/C][C]9[/C][/ROW]
[ROW][C]17[/C][C]72.75[/C][C]5.1234753829798[/C][C]12[/C][/ROW]
[ROW][C]18[/C][C]65.5[/C][C]5.32290647422377[/C][C]11[/C][/ROW]
[ROW][C]19[/C][C]62.25[/C][C]6.80073525436772[/C][C]14[/C][/ROW]
[ROW][C]20[/C][C]77.75[/C][C]5.85234995535981[/C][C]14[/C][/ROW]
[ROW][C]21[/C][C]89.25[/C][C]13.6717470232106[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79176&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79176&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	156.25	1.70782512765993	4
2	152.25	1.25830573921179	3
3	156	1.41421356237310	3
4	153.5	2.38047614284762	5
5	151.5	5.44671154612273	12
6	144.25	3.30403793359983	7
7	144.5	4.65474668125631	11
8	143.75	6.29152869605896	14
9	141.75	7.58836829188814	18
10	135	2.44948974278318	5
11	128.5	8.34665601703261	20
12	119	6.68331255192114	16
13	107.75	5.18812747209113	11
14	102.75	6.18465843842649	13
15	87	6.48074069840786	13
16	69.5	3.87298334620742	9
17	72.75	5.1234753829798	12
18	65.5	5.32290647422377	11
19	62.25	6.80073525436772	14
20	77.75	5.85234995535981	14
21	89.25	13.6717470232106	30

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	9.46935048519517
beta	-0.0360999549369374
S.D.	0.0170094537146491
T-STAT	-2.12234652226644
p-value	0.0471751344559261

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.46935048519517 \tabularnewline
beta & -0.0360999549369374 \tabularnewline
S.D. & 0.0170094537146491 \tabularnewline
T-STAT & -2.12234652226644 \tabularnewline
p-value & 0.0471751344559261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79176&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.46935048519517[/C][/ROW]
[ROW][C]beta[/C][C]-0.0360999549369374[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0170094537146491[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.12234652226644[/C][/ROW]
[ROW][C]p-value[/C][C]0.0471751344559261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79176&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79176&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	9.46935048519517
beta	-0.0360999549369374
S.D.	0.0170094537146491
T-STAT	-2.12234652226644
p-value	0.0471751344559261

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	5.73564917670455
beta	-0.898127667993572
S.D.	0.380846926931775
T-STAT	-2.35823792836974
p-value	0.0292298983801372
Lambda	1.89812766799357

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.73564917670455 \tabularnewline
beta & -0.898127667993572 \tabularnewline
S.D. & 0.380846926931775 \tabularnewline
T-STAT & -2.35823792836974 \tabularnewline
p-value & 0.0292298983801372 \tabularnewline
Lambda & 1.89812766799357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79176&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.73564917670455[/C][/ROW]
[ROW][C]beta[/C][C]-0.898127667993572[/C][/ROW]
[ROW][C]S.D.[/C][C]0.380846926931775[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.35823792836974[/C][/ROW]
[ROW][C]p-value[/C][C]0.0292298983801372[/C][/ROW]
[ROW][C]Lambda[/C][C]1.89812766799357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79176&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79176&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	5.73564917670455
beta	-0.898127667993572
S.D.	0.380846926931775
T-STAT	-2.35823792836974
p-value	0.0292298983801372
Lambda	1.89812766799357

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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