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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

Fri, 30 Jul 2010 12:56:30 +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/Jul/30/t1280494576ldp9r3ltjq0z9t7.htm/, Retrieved Thu, 02 May 2024 02:43:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78197, Retrieved Thu, 02 May 2024 02:43:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

239

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

-     [Central Tendency] [Centrummaten omze...] [2010-07-30 11:59:49] [f5ecd041e4b32af12787a4e421b18aaf]
- RMP     [Standard Deviation-Mean Plot] [SD Mean Plot omze...] [2010-07-30 12:56:30] [05b8da000f2ebbd12b039a4b088dd3f2] [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	'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78197&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78197&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	54.25	1.70782512765993	4
2	61.25	12.5266382827424	26
3	48	1.4142135623731	3
4	37	5.22812904711937	11
5	41.75	14.7507061977837	32
6	35.5	5.44671154612273	11
7	35.5	4.20317340430616	10
8	37	14.7873820085459	32
9	34.75	4.27200187265877	10
10	28.5	2.88675134594813	7
11	47	9.2736184954957	17
12	48.25	7.88986691902975	18
13	47.5	9.57427107756338	22
14	66.25	2.3629078131263	5
15	68	7.78888096369861	19
16	70.5	8.38649708360608	20
17	100	4.32049379893857	10
18	105	9.20144916122817	21
19	105	10.6144555520604	25
20	132.75	7.41057802513857	17
21	140.75	8.84590300647707	18
22	134.25	7.45542308211501	17
23	154.25	7.36545993132812	17
24	160	11.2249721603218	23
25	158.75	6.29152869605896	15
26	174.25	3.947573094109	8
27	182.25	14.7507061977837	27
28	184.75	7.45542308211501	17
29	201	4.69041575982343	9
30	204.25	11.056672193748	23

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 54.25 & 1.70782512765993 & 4 \tabularnewline
2 & 61.25 & 12.5266382827424 & 26 \tabularnewline
3 & 48 & 1.4142135623731 & 3 \tabularnewline
4 & 37 & 5.22812904711937 & 11 \tabularnewline
5 & 41.75 & 14.7507061977837 & 32 \tabularnewline
6 & 35.5 & 5.44671154612273 & 11 \tabularnewline
7 & 35.5 & 4.20317340430616 & 10 \tabularnewline
8 & 37 & 14.7873820085459 & 32 \tabularnewline
9 & 34.75 & 4.27200187265877 & 10 \tabularnewline
10 & 28.5 & 2.88675134594813 & 7 \tabularnewline
11 & 47 & 9.2736184954957 & 17 \tabularnewline
12 & 48.25 & 7.88986691902975 & 18 \tabularnewline
13 & 47.5 & 9.57427107756338 & 22 \tabularnewline
14 & 66.25 & 2.3629078131263 & 5 \tabularnewline
15 & 68 & 7.78888096369861 & 19 \tabularnewline
16 & 70.5 & 8.38649708360608 & 20 \tabularnewline
17 & 100 & 4.32049379893857 & 10 \tabularnewline
18 & 105 & 9.20144916122817 & 21 \tabularnewline
19 & 105 & 10.6144555520604 & 25 \tabularnewline
20 & 132.75 & 7.41057802513857 & 17 \tabularnewline
21 & 140.75 & 8.84590300647707 & 18 \tabularnewline
22 & 134.25 & 7.45542308211501 & 17 \tabularnewline
23 & 154.25 & 7.36545993132812 & 17 \tabularnewline
24 & 160 & 11.2249721603218 & 23 \tabularnewline
25 & 158.75 & 6.29152869605896 & 15 \tabularnewline
26 & 174.25 & 3.947573094109 & 8 \tabularnewline
27 & 182.25 & 14.7507061977837 & 27 \tabularnewline
28 & 184.75 & 7.45542308211501 & 17 \tabularnewline
29 & 201 & 4.69041575982343 & 9 \tabularnewline
30 & 204.25 & 11.056672193748 & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78197&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]54.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]61.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]48[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]37[/C][C]5.22812904711937[/C][C]11[/C][/ROW]
[ROW][C]5[/C][C]41.75[/C][C]14.7507061977837[/C][C]32[/C][/ROW]
[ROW][C]6[/C][C]35.5[/C][C]5.44671154612273[/C][C]11[/C][/ROW]
[ROW][C]7[/C][C]35.5[/C][C]4.20317340430616[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]37[/C][C]14.7873820085459[/C][C]32[/C][/ROW]
[ROW][C]9[/C][C]34.75[/C][C]4.27200187265877[/C][C]10[/C][/ROW]
[ROW][C]10[/C][C]28.5[/C][C]2.88675134594813[/C][C]7[/C][/ROW]
[ROW][C]11[/C][C]47[/C][C]9.2736184954957[/C][C]17[/C][/ROW]
[ROW][C]12[/C][C]48.25[/C][C]7.88986691902975[/C][C]18[/C][/ROW]
[ROW][C]13[/C][C]47.5[/C][C]9.57427107756338[/C][C]22[/C][/ROW]
[ROW][C]14[/C][C]66.25[/C][C]2.3629078131263[/C][C]5[/C][/ROW]
[ROW][C]15[/C][C]68[/C][C]7.78888096369861[/C][C]19[/C][/ROW]
[ROW][C]16[/C][C]70.5[/C][C]8.38649708360608[/C][C]20[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]4.32049379893857[/C][C]10[/C][/ROW]
[ROW][C]18[/C][C]105[/C][C]9.20144916122817[/C][C]21[/C][/ROW]
[ROW][C]19[/C][C]105[/C][C]10.6144555520604[/C][C]25[/C][/ROW]
[ROW][C]20[/C][C]132.75[/C][C]7.41057802513857[/C][C]17[/C][/ROW]
[ROW][C]21[/C][C]140.75[/C][C]8.84590300647707[/C][C]18[/C][/ROW]
[ROW][C]22[/C][C]134.25[/C][C]7.45542308211501[/C][C]17[/C][/ROW]
[ROW][C]23[/C][C]154.25[/C][C]7.36545993132812[/C][C]17[/C][/ROW]
[ROW][C]24[/C][C]160[/C][C]11.2249721603218[/C][C]23[/C][/ROW]
[ROW][C]25[/C][C]158.75[/C][C]6.29152869605896[/C][C]15[/C][/ROW]
[ROW][C]26[/C][C]174.25[/C][C]3.947573094109[/C][C]8[/C][/ROW]
[ROW][C]27[/C][C]182.25[/C][C]14.7507061977837[/C][C]27[/C][/ROW]
[ROW][C]28[/C][C]184.75[/C][C]7.45542308211501[/C][C]17[/C][/ROW]
[ROW][C]29[/C][C]201[/C][C]4.69041575982343[/C][C]9[/C][/ROW]
[ROW][C]30[/C][C]204.25[/C][C]11.056672193748[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78197&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	54.25	1.70782512765993	4
2	61.25	12.5266382827424	26
3	48	1.4142135623731	3
4	37	5.22812904711937	11
5	41.75	14.7507061977837	32
6	35.5	5.44671154612273	11
7	35.5	4.20317340430616	10
8	37	14.7873820085459	32
9	34.75	4.27200187265877	10
10	28.5	2.88675134594813	7
11	47	9.2736184954957	17
12	48.25	7.88986691902975	18
13	47.5	9.57427107756338	22
14	66.25	2.3629078131263	5
15	68	7.78888096369861	19
16	70.5	8.38649708360608	20
17	100	4.32049379893857	10
18	105	9.20144916122817	21
19	105	10.6144555520604	25
20	132.75	7.41057802513857	17
21	140.75	8.84590300647707	18
22	134.25	7.45542308211501	17
23	154.25	7.36545993132812	17
24	160	11.2249721603218	23
25	158.75	6.29152869605896	15
26	174.25	3.947573094109	8
27	182.25	14.7507061977837	27
28	184.75	7.45542308211501	17
29	201	4.69041575982343	9
30	204.25	11.056672193748	23

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.52416735566198
beta	0.0108360589387273
S.D.	0.0119381816432811
T-STAT	0.90768085647498
p-value	0.371793068112088

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.52416735566198 \tabularnewline
beta & 0.0108360589387273 \tabularnewline
S.D. & 0.0119381816432811 \tabularnewline
T-STAT & 0.90768085647498 \tabularnewline
p-value & 0.371793068112088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78197&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.52416735566198[/C][/ROW]
[ROW][C]beta[/C][C]0.0108360589387273[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0119381816432811[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.90768085647498[/C][/ROW]
[ROW][C]p-value[/C][C]0.371793068112088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78197&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	6.52416735566198
beta	0.0108360589387273
S.D.	0.0119381816432811
T-STAT	0.90768085647498
p-value	0.371793068112088

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.820099156023386
beta	0.240682166280659
S.D.	0.171327696472634
T-STAT	1.40480594344011
p-value	0.171076418269002
Lambda	0.759317833719341

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.820099156023386 \tabularnewline
beta & 0.240682166280659 \tabularnewline
S.D. & 0.171327696472634 \tabularnewline
T-STAT & 1.40480594344011 \tabularnewline
p-value & 0.171076418269002 \tabularnewline
Lambda & 0.759317833719341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78197&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.820099156023386[/C][/ROW]
[ROW][C]beta[/C][C]0.240682166280659[/C][/ROW]
[ROW][C]S.D.[/C][C]0.171327696472634[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.40480594344011[/C][/ROW]
[ROW][C]p-value[/C][C]0.171076418269002[/C][/ROW]
[ROW][C]Lambda[/C][C]0.759317833719341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78197&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	0.820099156023386
beta	0.240682166280659
S.D.	0.171327696472634
T-STAT	1.40480594344011
p-value	0.171076418269002
Lambda	0.759317833719341

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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