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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, 15 Aug 2010 13:14:31 +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/15/t1281878060j0z4dcpj5to9ta3.htm/, Retrieved Sun, 28 Apr 2024 16:25:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78858, Retrieved Sun, 28 Apr 2024 16:25:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Sebastien Delforge

Estimated Impact

165

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

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-08-15 13:14:31] [923770d86edf74ed976a539eae527e37] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78858&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78858&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78858&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	73.25	1.70782512765993	4
2	80.25	12.5266382827424	26
3	67	1.4142135623731	3
4	76.5	1.91485421551268	4
5	94.25	8.0156097709407	17
6	84.5	2.38047614284762	5
7	91.25	6.07590871118606	14
8	97.5	11.4455231422596	28
9	82.75	7.54431353183752	16
10	96.5	5.97215762238964	14
11	108	7.78888096369861	16
12	102.25	6.7515430335097	15
13	119.25	3.86221007541882	8
14	146	9.59166304662544	22
15	128.25	4.42530601578392	9
16	136	4.54606056566195	11
17	179.25	10.5316981853197	25
18	159.25	5.61990510002912	11
19	167.5	4.04145188432738	9
20	204.25	10.4363148029688	25
21	180	9.55684745788763	19
22	197	2.94392028877595	7
23	234.75	9.21502396451939	22
24	201.25	5.31507290636732	12
25	216.25	4.3493294502333	10
26	247	16.2685791225499	35
27	207.5	7.18795288428261	16
28	232	5.35412613473634	11
29	270.5	13.076696830622	27
30	233.5	6.45497224367903	14

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 73.25 & 1.70782512765993 & 4 \tabularnewline
2 & 80.25 & 12.5266382827424 & 26 \tabularnewline
3 & 67 & 1.4142135623731 & 3 \tabularnewline
4 & 76.5 & 1.91485421551268 & 4 \tabularnewline
5 & 94.25 & 8.0156097709407 & 17 \tabularnewline
6 & 84.5 & 2.38047614284762 & 5 \tabularnewline
7 & 91.25 & 6.07590871118606 & 14 \tabularnewline
8 & 97.5 & 11.4455231422596 & 28 \tabularnewline
9 & 82.75 & 7.54431353183752 & 16 \tabularnewline
10 & 96.5 & 5.97215762238964 & 14 \tabularnewline
11 & 108 & 7.78888096369861 & 16 \tabularnewline
12 & 102.25 & 6.7515430335097 & 15 \tabularnewline
13 & 119.25 & 3.86221007541882 & 8 \tabularnewline
14 & 146 & 9.59166304662544 & 22 \tabularnewline
15 & 128.25 & 4.42530601578392 & 9 \tabularnewline
16 & 136 & 4.54606056566195 & 11 \tabularnewline
17 & 179.25 & 10.5316981853197 & 25 \tabularnewline
18 & 159.25 & 5.61990510002912 & 11 \tabularnewline
19 & 167.5 & 4.04145188432738 & 9 \tabularnewline
20 & 204.25 & 10.4363148029688 & 25 \tabularnewline
21 & 180 & 9.55684745788763 & 19 \tabularnewline
22 & 197 & 2.94392028877595 & 7 \tabularnewline
23 & 234.75 & 9.21502396451939 & 22 \tabularnewline
24 & 201.25 & 5.31507290636732 & 12 \tabularnewline
25 & 216.25 & 4.3493294502333 & 10 \tabularnewline
26 & 247 & 16.2685791225499 & 35 \tabularnewline
27 & 207.5 & 7.18795288428261 & 16 \tabularnewline
28 & 232 & 5.35412613473634 & 11 \tabularnewline
29 & 270.5 & 13.076696830622 & 27 \tabularnewline
30 & 233.5 & 6.45497224367903 & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78858&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]73.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]80.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]67[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]76.5[/C][C]1.91485421551268[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]94.25[/C][C]8.0156097709407[/C][C]17[/C][/ROW]
[ROW][C]6[/C][C]84.5[/C][C]2.38047614284762[/C][C]5[/C][/ROW]
[ROW][C]7[/C][C]91.25[/C][C]6.07590871118606[/C][C]14[/C][/ROW]
[ROW][C]8[/C][C]97.5[/C][C]11.4455231422596[/C][C]28[/C][/ROW]
[ROW][C]9[/C][C]82.75[/C][C]7.54431353183752[/C][C]16[/C][/ROW]
[ROW][C]10[/C][C]96.5[/C][C]5.97215762238964[/C][C]14[/C][/ROW]
[ROW][C]11[/C][C]108[/C][C]7.78888096369861[/C][C]16[/C][/ROW]
[ROW][C]12[/C][C]102.25[/C][C]6.7515430335097[/C][C]15[/C][/ROW]
[ROW][C]13[/C][C]119.25[/C][C]3.86221007541882[/C][C]8[/C][/ROW]
[ROW][C]14[/C][C]146[/C][C]9.59166304662544[/C][C]22[/C][/ROW]
[ROW][C]15[/C][C]128.25[/C][C]4.42530601578392[/C][C]9[/C][/ROW]
[ROW][C]16[/C][C]136[/C][C]4.54606056566195[/C][C]11[/C][/ROW]
[ROW][C]17[/C][C]179.25[/C][C]10.5316981853197[/C][C]25[/C][/ROW]
[ROW][C]18[/C][C]159.25[/C][C]5.61990510002912[/C][C]11[/C][/ROW]
[ROW][C]19[/C][C]167.5[/C][C]4.04145188432738[/C][C]9[/C][/ROW]
[ROW][C]20[/C][C]204.25[/C][C]10.4363148029688[/C][C]25[/C][/ROW]
[ROW][C]21[/C][C]180[/C][C]9.55684745788763[/C][C]19[/C][/ROW]
[ROW][C]22[/C][C]197[/C][C]2.94392028877595[/C][C]7[/C][/ROW]
[ROW][C]23[/C][C]234.75[/C][C]9.21502396451939[/C][C]22[/C][/ROW]
[ROW][C]24[/C][C]201.25[/C][C]5.31507290636732[/C][C]12[/C][/ROW]
[ROW][C]25[/C][C]216.25[/C][C]4.3493294502333[/C][C]10[/C][/ROW]
[ROW][C]26[/C][C]247[/C][C]16.2685791225499[/C][C]35[/C][/ROW]
[ROW][C]27[/C][C]207.5[/C][C]7.18795288428261[/C][C]16[/C][/ROW]
[ROW][C]28[/C][C]232[/C][C]5.35412613473634[/C][C]11[/C][/ROW]
[ROW][C]29[/C][C]270.5[/C][C]13.076696830622[/C][C]27[/C][/ROW]
[ROW][C]30[/C][C]233.5[/C][C]6.45497224367903[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78858&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78858&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	73.25	1.70782512765993	4
2	80.25	12.5266382827424	26
3	67	1.4142135623731	3
4	76.5	1.91485421551268	4
5	94.25	8.0156097709407	17
6	84.5	2.38047614284762	5
7	91.25	6.07590871118606	14
8	97.5	11.4455231422596	28
9	82.75	7.54431353183752	16
10	96.5	5.97215762238964	14
11	108	7.78888096369861	16
12	102.25	6.7515430335097	15
13	119.25	3.86221007541882	8
14	146	9.59166304662544	22
15	128.25	4.42530601578392	9
16	136	4.54606056566195	11
17	179.25	10.5316981853197	25
18	159.25	5.61990510002912	11
19	167.5	4.04145188432738	9
20	204.25	10.4363148029688	25
21	180	9.55684745788763	19
22	197	2.94392028877595	7
23	234.75	9.21502396451939	22
24	201.25	5.31507290636732	12
25	216.25	4.3493294502333	10
26	247	16.2685791225499	35
27	207.5	7.18795288428261	16
28	232	5.35412613473634	11
29	270.5	13.076696830622	27
30	233.5	6.45497224367903	14

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.39038898226053
beta	0.0231756742215421
S.D.	0.0102167717755284
T-STAT	2.26839502053412
p-value	0.0312101796926725

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.39038898226053 \tabularnewline
beta & 0.0231756742215421 \tabularnewline
S.D. & 0.0102167717755284 \tabularnewline
T-STAT & 2.26839502053412 \tabularnewline
p-value & 0.0312101796926725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78858&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.39038898226053[/C][/ROW]
[ROW][C]beta[/C][C]0.0231756742215421[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0102167717755284[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.26839502053412[/C][/ROW]
[ROW][C]p-value[/C][C]0.0312101796926725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78858&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78858&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	3.39038898226053
beta	0.0231756742215421
S.D.	0.0102167717755284
T-STAT	2.26839502053412
p-value	0.0312101796926725

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.38912032874359
beta	0.640828090589077
S.D.	0.240868772684273
T-STAT	2.66048638620775
p-value	0.0127681807292279
Lambda	0.359171909410923

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.38912032874359 \tabularnewline
beta & 0.640828090589077 \tabularnewline
S.D. & 0.240868772684273 \tabularnewline
T-STAT & 2.66048638620775 \tabularnewline
p-value & 0.0127681807292279 \tabularnewline
Lambda & 0.359171909410923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78858&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.38912032874359[/C][/ROW]
[ROW][C]beta[/C][C]0.640828090589077[/C][/ROW]
[ROW][C]S.D.[/C][C]0.240868772684273[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66048638620775[/C][/ROW]
[ROW][C]p-value[/C][C]0.0127681807292279[/C][/ROW]
[ROW][C]Lambda[/C][C]0.359171909410923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78858&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78858&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	-1.38912032874359
beta	0.640828090589077
S.D.	0.240868772684273
T-STAT	2.66048638620775
p-value	0.0127681807292279
Lambda	0.359171909410923

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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