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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sat, 05 Dec 2009 11:22:12 -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/05/t1260037382lwy65qle0e2kkop.htm/, Retrieved Tue, 30 Apr 2024 04:24:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64294, Retrieved Tue, 30 Apr 2024 04:24:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

175

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-    D    [Standard Deviation-Mean Plot] [Stap 1 workshop 5] [2009-12-04 18:21:41] [a542c511726eba04a1fc2f4bd37a90f8]
- R PD        [Standard Deviation-Mean Plot] [] [2009-12-05 18:22:12] [0744dbfa8cdb263e2e292d0a5ee9dc89] [Current]

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Dataseries X:

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Histogram

Boxplots

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

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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64294&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64294&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

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	8.15	0.129099444873581	0.300000000000001
2	7.6	0.316227766016838	0.7
3	7.3	0.658280588604383	1.4
4	7.5	0.432049379893857	1
5	6.45	0.288675134594813	0.7
6	7.15	0.129099444873581	0.3
7	7.2	0.244948974278318	0.5
8	7.7	0.355902608401044	0.8
9	7.95	0.0577350269189624	0.0999999999999996
10	8.1	0.0816496580927723	0.199999999999999
11	8.35	0.264575131106459	0.6
12	8.575	0.149999999999999	0.299999999999999
13	8.625	0.0957427107756335	0.199999999999999
14	8.175	0.25	0.6
15	8.4	0.182574185835055	0.4
16	9.025	0.320156211871643	0.600000000000001
17	7.6	0.483045891539648	1.1
18	8.675	0.221735578260835	0.5
19	8.375	0.0499999999999998	0.0999999999999996
20	7.775	0.206155281280883	0.4
21	8.2	0.081649658092773	0.200000000000001
22	7.725	0.221735578260835	0.5
23	7.025	0.221735578260834	0.5
24	7.525	0.0957427107756335	0.199999999999999
25	6.725	0.57373048260195	1.3
26	6.175	0.15	0.3
27	6.45	0.310912635102961	0.7
28	7.05	0.208166599946613	0.5
29	6.55	0.238047614284762	0.5
30	7.55	0.264575131106459	0.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.15 & 0.129099444873581 & 0.300000000000001 \tabularnewline
2 & 7.6 & 0.316227766016838 & 0.7 \tabularnewline
3 & 7.3 & 0.658280588604383 & 1.4 \tabularnewline
4 & 7.5 & 0.432049379893857 & 1 \tabularnewline
5 & 6.45 & 0.288675134594813 & 0.7 \tabularnewline
6 & 7.15 & 0.129099444873581 & 0.3 \tabularnewline
7 & 7.2 & 0.244948974278318 & 0.5 \tabularnewline
8 & 7.7 & 0.355902608401044 & 0.8 \tabularnewline
9 & 7.95 & 0.0577350269189624 & 0.0999999999999996 \tabularnewline
10 & 8.1 & 0.0816496580927723 & 0.199999999999999 \tabularnewline
11 & 8.35 & 0.264575131106459 & 0.6 \tabularnewline
12 & 8.575 & 0.149999999999999 & 0.299999999999999 \tabularnewline
13 & 8.625 & 0.0957427107756335 & 0.199999999999999 \tabularnewline
14 & 8.175 & 0.25 & 0.6 \tabularnewline
15 & 8.4 & 0.182574185835055 & 0.4 \tabularnewline
16 & 9.025 & 0.320156211871643 & 0.600000000000001 \tabularnewline
17 & 7.6 & 0.483045891539648 & 1.1 \tabularnewline
18 & 8.675 & 0.221735578260835 & 0.5 \tabularnewline
19 & 8.375 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
20 & 7.775 & 0.206155281280883 & 0.4 \tabularnewline
21 & 8.2 & 0.081649658092773 & 0.200000000000001 \tabularnewline
22 & 7.725 & 0.221735578260835 & 0.5 \tabularnewline
23 & 7.025 & 0.221735578260834 & 0.5 \tabularnewline
24 & 7.525 & 0.0957427107756335 & 0.199999999999999 \tabularnewline
25 & 6.725 & 0.57373048260195 & 1.3 \tabularnewline
26 & 6.175 & 0.15 & 0.3 \tabularnewline
27 & 6.45 & 0.310912635102961 & 0.7 \tabularnewline
28 & 7.05 & 0.208166599946613 & 0.5 \tabularnewline
29 & 6.55 & 0.238047614284762 & 0.5 \tabularnewline
30 & 7.55 & 0.264575131106459 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64294&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]8.15[/C][C]0.129099444873581[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]2[/C][C]7.6[/C][C]0.316227766016838[/C][C]0.7[/C][/ROW]
[ROW][C]3[/C][C]7.3[/C][C]0.658280588604383[/C][C]1.4[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]0.432049379893857[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]6.45[/C][C]0.288675134594813[/C][C]0.7[/C][/ROW]
[ROW][C]6[/C][C]7.15[/C][C]0.129099444873581[/C][C]0.3[/C][/ROW]
[ROW][C]7[/C][C]7.2[/C][C]0.244948974278318[/C][C]0.5[/C][/ROW]
[ROW][C]8[/C][C]7.7[/C][C]0.355902608401044[/C][C]0.8[/C][/ROW]
[ROW][C]9[/C][C]7.95[/C][C]0.0577350269189624[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]10[/C][C]8.1[/C][C]0.0816496580927723[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]11[/C][C]8.35[/C][C]0.264575131106459[/C][C]0.6[/C][/ROW]
[ROW][C]12[/C][C]8.575[/C][C]0.149999999999999[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]13[/C][C]8.625[/C][C]0.0957427107756335[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]14[/C][C]8.175[/C][C]0.25[/C][C]0.6[/C][/ROW]
[ROW][C]15[/C][C]8.4[/C][C]0.182574185835055[/C][C]0.4[/C][/ROW]
[ROW][C]16[/C][C]9.025[/C][C]0.320156211871643[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]17[/C][C]7.6[/C][C]0.483045891539648[/C][C]1.1[/C][/ROW]
[ROW][C]18[/C][C]8.675[/C][C]0.221735578260835[/C][C]0.5[/C][/ROW]
[ROW][C]19[/C][C]8.375[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]20[/C][C]7.775[/C][C]0.206155281280883[/C][C]0.4[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]0.081649658092773[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]22[/C][C]7.725[/C][C]0.221735578260835[/C][C]0.5[/C][/ROW]
[ROW][C]23[/C][C]7.025[/C][C]0.221735578260834[/C][C]0.5[/C][/ROW]
[ROW][C]24[/C][C]7.525[/C][C]0.0957427107756335[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]25[/C][C]6.725[/C][C]0.57373048260195[/C][C]1.3[/C][/ROW]
[ROW][C]26[/C][C]6.175[/C][C]0.15[/C][C]0.3[/C][/ROW]
[ROW][C]27[/C][C]6.45[/C][C]0.310912635102961[/C][C]0.7[/C][/ROW]
[ROW][C]28[/C][C]7.05[/C][C]0.208166599946613[/C][C]0.5[/C][/ROW]
[ROW][C]29[/C][C]6.55[/C][C]0.238047614284762[/C][C]0.5[/C][/ROW]
[ROW][C]30[/C][C]7.55[/C][C]0.264575131106459[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64294&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	8.15	0.129099444873581	0.300000000000001
2	7.6	0.316227766016838	0.7
3	7.3	0.658280588604383	1.4
4	7.5	0.432049379893857	1
5	6.45	0.288675134594813	0.7
6	7.15	0.129099444873581	0.3
7	7.2	0.244948974278318	0.5
8	7.7	0.355902608401044	0.8
9	7.95	0.0577350269189624	0.0999999999999996
10	8.1	0.0816496580927723	0.199999999999999
11	8.35	0.264575131106459	0.6
12	8.575	0.149999999999999	0.299999999999999
13	8.625	0.0957427107756335	0.199999999999999
14	8.175	0.25	0.6
15	8.4	0.182574185835055	0.4
16	9.025	0.320156211871643	0.600000000000001
17	7.6	0.483045891539648	1.1
18	8.675	0.221735578260835	0.5
19	8.375	0.0499999999999998	0.0999999999999996
20	7.775	0.206155281280883	0.4
21	8.2	0.081649658092773	0.200000000000001
22	7.725	0.221735578260835	0.5
23	7.025	0.221735578260834	0.5
24	7.525	0.0957427107756335	0.199999999999999
25	6.725	0.57373048260195	1.3
26	6.175	0.15	0.3
27	6.45	0.310912635102961	0.7
28	7.05	0.208166599946613	0.5
29	6.55	0.238047614284762	0.5
30	7.55	0.264575131106459	0.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.707126061864245
beta	-0.0606567944710483
S.D.	0.035579954414141
T-STAT	-1.7048024785254
p-value	0.0993045170626934

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.707126061864245 \tabularnewline
beta & -0.0606567944710483 \tabularnewline
S.D. & 0.035579954414141 \tabularnewline
T-STAT & -1.7048024785254 \tabularnewline
p-value & 0.0993045170626934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64294&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.707126061864245[/C][/ROW]
[ROW][C]beta[/C][C]-0.0606567944710483[/C][/ROW]
[ROW][C]S.D.[/C][C]0.035579954414141[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.7048024785254[/C][/ROW]
[ROW][C]p-value[/C][C]0.0993045170626934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64294&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64294&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	0.707126061864245
beta	-0.0606567944710483
S.D.	0.035579954414141
T-STAT	-1.7048024785254
p-value	0.0993045170626934

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.79605653753526
beta	-2.16428895830434
S.D.	1.16108122978550
T-STAT	-1.86402889202177
p-value	0.0728346094192418
Lambda	3.16428895830434

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.79605653753526 \tabularnewline
beta & -2.16428895830434 \tabularnewline
S.D. & 1.16108122978550 \tabularnewline
T-STAT & -1.86402889202177 \tabularnewline
p-value & 0.0728346094192418 \tabularnewline
Lambda & 3.16428895830434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64294&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.79605653753526[/C][/ROW]
[ROW][C]beta[/C][C]-2.16428895830434[/C][/ROW]
[ROW][C]S.D.[/C][C]1.16108122978550[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.86402889202177[/C][/ROW]
[ROW][C]p-value[/C][C]0.0728346094192418[/C][/ROW]
[ROW][C]Lambda[/C][C]3.16428895830434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64294&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64294&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	2.79605653753526
beta	-2.16428895830434
S.D.	1.16108122978550
T-STAT	-1.86402889202177
p-value	0.0728346094192418
Lambda	3.16428895830434

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code