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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

Thu, 17 Dec 2009 16:11:21 -0700

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/Dec/18/t1261091540kntfcjwrwlajot0.htm/, Retrieved Sat, 27 Apr 2024 06:03:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69146, Retrieved Sat, 27 Apr 2024 06:03:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

151

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

-       [Standard Deviation-Mean Plot] [] [2009-12-17 23:11:21] [e24e91da8d334fb8882bf413603fde71] [Current]

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Dataseries X:

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Histogram

Boxplots

6,8
7,5
7,6
7,8
8
8,1
8,2
8,3
8,2
8
7,9
7,6
7,6
8,3
8,4
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,4
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3

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	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69146&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69146&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	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.425	0.434932945023330	1
2	8.15	0.129099444873581	0.300000000000001
3	7.925	0.25	0.6
4	8.175	0.386221007541883	0.8
5	8.575	0.236290781312630	0.5
6	7.95	0.732575365861197	1.6
7	8.7	0.898146239020499	1.9
8	8.425	0.221735578260834	0.5
9	8.35	0.238047614284762	0.5
10	8.475	0.386221007541882	0.799999999999999
11	8.525	0.125830573921179	0.299999999999999
12	8.525	0.170782512765993	0.399999999999999
13	8.1	0.0816496580927723	0.199999999999999
14	7.95	0.0577350269189624	0.0999999999999996
15	7.9	0.141421356237309	0.3
16	7.25	0.208166599946613	0.5
17	7.125	0.15	0.3
18	6.6	0.439696865275764	1
19	7.4	0.621825270205921	1.4
20	7.025	0.47169905660283	1.1
21	7.75	0.33166247903554	0.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.425 & 0.434932945023330 & 1 \tabularnewline
2 & 8.15 & 0.129099444873581 & 0.300000000000001 \tabularnewline
3 & 7.925 & 0.25 & 0.6 \tabularnewline
4 & 8.175 & 0.386221007541883 & 0.8 \tabularnewline
5 & 8.575 & 0.236290781312630 & 0.5 \tabularnewline
6 & 7.95 & 0.732575365861197 & 1.6 \tabularnewline
7 & 8.7 & 0.898146239020499 & 1.9 \tabularnewline
8 & 8.425 & 0.221735578260834 & 0.5 \tabularnewline
9 & 8.35 & 0.238047614284762 & 0.5 \tabularnewline
10 & 8.475 & 0.386221007541882 & 0.799999999999999 \tabularnewline
11 & 8.525 & 0.125830573921179 & 0.299999999999999 \tabularnewline
12 & 8.525 & 0.170782512765993 & 0.399999999999999 \tabularnewline
13 & 8.1 & 0.0816496580927723 & 0.199999999999999 \tabularnewline
14 & 7.95 & 0.0577350269189624 & 0.0999999999999996 \tabularnewline
15 & 7.9 & 0.141421356237309 & 0.3 \tabularnewline
16 & 7.25 & 0.208166599946613 & 0.5 \tabularnewline
17 & 7.125 & 0.15 & 0.3 \tabularnewline
18 & 6.6 & 0.439696865275764 & 1 \tabularnewline
19 & 7.4 & 0.621825270205921 & 1.4 \tabularnewline
20 & 7.025 & 0.47169905660283 & 1.1 \tabularnewline
21 & 7.75 & 0.33166247903554 & 0.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69146&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]7.425[/C][C]0.434932945023330[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]8.15[/C][C]0.129099444873581[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]3[/C][C]7.925[/C][C]0.25[/C][C]0.6[/C][/ROW]
[ROW][C]4[/C][C]8.175[/C][C]0.386221007541883[/C][C]0.8[/C][/ROW]
[ROW][C]5[/C][C]8.575[/C][C]0.236290781312630[/C][C]0.5[/C][/ROW]
[ROW][C]6[/C][C]7.95[/C][C]0.732575365861197[/C][C]1.6[/C][/ROW]
[ROW][C]7[/C][C]8.7[/C][C]0.898146239020499[/C][C]1.9[/C][/ROW]
[ROW][C]8[/C][C]8.425[/C][C]0.221735578260834[/C][C]0.5[/C][/ROW]
[ROW][C]9[/C][C]8.35[/C][C]0.238047614284762[/C][C]0.5[/C][/ROW]
[ROW][C]10[/C][C]8.475[/C][C]0.386221007541882[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]11[/C][C]8.525[/C][C]0.125830573921179[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]12[/C][C]8.525[/C][C]0.170782512765993[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]0.0816496580927723[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]14[/C][C]7.95[/C][C]0.0577350269189624[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]0.141421356237309[/C][C]0.3[/C][/ROW]
[ROW][C]16[/C][C]7.25[/C][C]0.208166599946613[/C][C]0.5[/C][/ROW]
[ROW][C]17[/C][C]7.125[/C][C]0.15[/C][C]0.3[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]0.439696865275764[/C][C]1[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]0.621825270205921[/C][C]1.4[/C][/ROW]
[ROW][C]20[/C][C]7.025[/C][C]0.47169905660283[/C][C]1.1[/C][/ROW]
[ROW][C]21[/C][C]7.75[/C][C]0.33166247903554[/C][C]0.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69146&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	7.425	0.434932945023330	1
2	8.15	0.129099444873581	0.300000000000001
3	7.925	0.25	0.6
4	8.175	0.386221007541883	0.8
5	8.575	0.236290781312630	0.5
6	7.95	0.732575365861197	1.6
7	8.7	0.898146239020499	1.9
8	8.425	0.221735578260834	0.5
9	8.35	0.238047614284762	0.5
10	8.475	0.386221007541882	0.799999999999999
11	8.525	0.125830573921179	0.299999999999999
12	8.525	0.170782512765993	0.399999999999999
13	8.1	0.0816496580927723	0.199999999999999
14	7.95	0.0577350269189624	0.0999999999999996
15	7.9	0.141421356237309	0.3
16	7.25	0.208166599946613	0.5
17	7.125	0.15	0.3
18	6.6	0.439696865275764	1
19	7.4	0.621825270205921	1.4
20	7.025	0.47169905660283	1.1
21	7.75	0.33166247903554	0.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.576137663647091
beta	-0.0323821500533099
S.D.	0.0864659757174759
T-STAT	-0.374507426587277
p-value	0.712174039065062

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.576137663647091 \tabularnewline
beta & -0.0323821500533099 \tabularnewline
S.D. & 0.0864659757174759 \tabularnewline
T-STAT & -0.374507426587277 \tabularnewline
p-value & 0.712174039065062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69146&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.576137663647091[/C][/ROW]
[ROW][C]beta[/C][C]-0.0323821500533099[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0864659757174759[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.374507426587277[/C][/ROW]
[ROW][C]p-value[/C][C]0.712174039065062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69146&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	0.576137663647091
beta	-0.0323821500533099
S.D.	0.0864659757174759
T-STAT	-0.374507426587277
p-value	0.712174039065062

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.95536028150524
beta	-1.60849990631394
S.D.	2.12590295606887
T-STAT	-0.756619629189616
p-value	0.458557786526279
Lambda	2.60849990631394

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.95536028150524 \tabularnewline
beta & -1.60849990631394 \tabularnewline
S.D. & 2.12590295606887 \tabularnewline
T-STAT & -0.756619629189616 \tabularnewline
p-value & 0.458557786526279 \tabularnewline
Lambda & 2.60849990631394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69146&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.95536028150524[/C][/ROW]
[ROW][C]beta[/C][C]-1.60849990631394[/C][/ROW]
[ROW][C]S.D.[/C][C]2.12590295606887[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.756619629189616[/C][/ROW]
[ROW][C]p-value[/C][C]0.458557786526279[/C][/ROW]
[ROW][C]Lambda[/C][C]2.60849990631394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69146&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	1.95536028150524
beta	-1.60849990631394
S.D.	2.12590295606887
T-STAT	-0.756619629189616
p-value	0.458557786526279
Lambda	2.60849990631394

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.0 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

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