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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

Mon, 26 Jul 2010 17:33:51 +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/26/t1280165621fyocc2pzs9drgxj.htm/, Retrieved Sat, 04 May 2024 11:29:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78128, Retrieved Sat, 04 May 2024 11:29:45 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Hoes Isabelle

Estimated Impact

195

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

-       [Standard Deviation-Mean Plot] [TIJDREEKS A - STA...] [2010-07-26 17:33:51] [35611de12c9fa8a4a915f3548e0dcd01] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78128&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78128&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	696.25	1.70782512765993	4
2	703.25	12.5266382827424	26
3	690	1.41421356237310	3
4	679.25	6.34428877022476	15
5	679	16.1451747177498	35
6	649.5	7.04745817062199	14
7	625	9.76387901058454	23
8	625.75	13.3759734848222	30
9	591.25	8.18026079453868	17
10	566	13.5646599662505	30
11	559	19.4422220952236	44
12	522.5	10.1488915650922	23
13	499.5	8.10349718742881	19
14	503	20.0166597280032	45
15	464	11.9443152447793	28
16	455.5	5.91607978309962	12
17	453.5	28.6647286166583	64
18	403.5	11.7331439378654	26
19	380.75	10.1447851956888	19
20	370.5	35.7164761233057	80
21	310.5	10.0829889748361	21
22	288.5	8.81286937760152	17
23	274	40.9715348341585	92
24	222.5	10.1488915650922	23
25	205	6.58280588604383	14
26	194.5	44.8144321991625	101
27	140.75	10.3400515794974	25
28	121.5	7.72442015083764	16
29	125.25	41.4115523334572	93
30	91.5	9.53939201416946	23

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 696.25 & 1.70782512765993 & 4 \tabularnewline
2 & 703.25 & 12.5266382827424 & 26 \tabularnewline
3 & 690 & 1.41421356237310 & 3 \tabularnewline
4 & 679.25 & 6.34428877022476 & 15 \tabularnewline
5 & 679 & 16.1451747177498 & 35 \tabularnewline
6 & 649.5 & 7.04745817062199 & 14 \tabularnewline
7 & 625 & 9.76387901058454 & 23 \tabularnewline
8 & 625.75 & 13.3759734848222 & 30 \tabularnewline
9 & 591.25 & 8.18026079453868 & 17 \tabularnewline
10 & 566 & 13.5646599662505 & 30 \tabularnewline
11 & 559 & 19.4422220952236 & 44 \tabularnewline
12 & 522.5 & 10.1488915650922 & 23 \tabularnewline
13 & 499.5 & 8.10349718742881 & 19 \tabularnewline
14 & 503 & 20.0166597280032 & 45 \tabularnewline
15 & 464 & 11.9443152447793 & 28 \tabularnewline
16 & 455.5 & 5.91607978309962 & 12 \tabularnewline
17 & 453.5 & 28.6647286166583 & 64 \tabularnewline
18 & 403.5 & 11.7331439378654 & 26 \tabularnewline
19 & 380.75 & 10.1447851956888 & 19 \tabularnewline
20 & 370.5 & 35.7164761233057 & 80 \tabularnewline
21 & 310.5 & 10.0829889748361 & 21 \tabularnewline
22 & 288.5 & 8.81286937760152 & 17 \tabularnewline
23 & 274 & 40.9715348341585 & 92 \tabularnewline
24 & 222.5 & 10.1488915650922 & 23 \tabularnewline
25 & 205 & 6.58280588604383 & 14 \tabularnewline
26 & 194.5 & 44.8144321991625 & 101 \tabularnewline
27 & 140.75 & 10.3400515794974 & 25 \tabularnewline
28 & 121.5 & 7.72442015083764 & 16 \tabularnewline
29 & 125.25 & 41.4115523334572 & 93 \tabularnewline
30 & 91.5 & 9.53939201416946 & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78128&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]696.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]703.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]690[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]679.25[/C][C]6.34428877022476[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]679[/C][C]16.1451747177498[/C][C]35[/C][/ROW]
[ROW][C]6[/C][C]649.5[/C][C]7.04745817062199[/C][C]14[/C][/ROW]
[ROW][C]7[/C][C]625[/C][C]9.76387901058454[/C][C]23[/C][/ROW]
[ROW][C]8[/C][C]625.75[/C][C]13.3759734848222[/C][C]30[/C][/ROW]
[ROW][C]9[/C][C]591.25[/C][C]8.18026079453868[/C][C]17[/C][/ROW]
[ROW][C]10[/C][C]566[/C][C]13.5646599662505[/C][C]30[/C][/ROW]
[ROW][C]11[/C][C]559[/C][C]19.4422220952236[/C][C]44[/C][/ROW]
[ROW][C]12[/C][C]522.5[/C][C]10.1488915650922[/C][C]23[/C][/ROW]
[ROW][C]13[/C][C]499.5[/C][C]8.10349718742881[/C][C]19[/C][/ROW]
[ROW][C]14[/C][C]503[/C][C]20.0166597280032[/C][C]45[/C][/ROW]
[ROW][C]15[/C][C]464[/C][C]11.9443152447793[/C][C]28[/C][/ROW]
[ROW][C]16[/C][C]455.5[/C][C]5.91607978309962[/C][C]12[/C][/ROW]
[ROW][C]17[/C][C]453.5[/C][C]28.6647286166583[/C][C]64[/C][/ROW]
[ROW][C]18[/C][C]403.5[/C][C]11.7331439378654[/C][C]26[/C][/ROW]
[ROW][C]19[/C][C]380.75[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]20[/C][C]370.5[/C][C]35.7164761233057[/C][C]80[/C][/ROW]
[ROW][C]21[/C][C]310.5[/C][C]10.0829889748361[/C][C]21[/C][/ROW]
[ROW][C]22[/C][C]288.5[/C][C]8.81286937760152[/C][C]17[/C][/ROW]
[ROW][C]23[/C][C]274[/C][C]40.9715348341585[/C][C]92[/C][/ROW]
[ROW][C]24[/C][C]222.5[/C][C]10.1488915650922[/C][C]23[/C][/ROW]
[ROW][C]25[/C][C]205[/C][C]6.58280588604383[/C][C]14[/C][/ROW]
[ROW][C]26[/C][C]194.5[/C][C]44.8144321991625[/C][C]101[/C][/ROW]
[ROW][C]27[/C][C]140.75[/C][C]10.3400515794974[/C][C]25[/C][/ROW]
[ROW][C]28[/C][C]121.5[/C][C]7.72442015083764[/C][C]16[/C][/ROW]
[ROW][C]29[/C][C]125.25[/C][C]41.4115523334572[/C][C]93[/C][/ROW]
[ROW][C]30[/C][C]91.5[/C][C]9.53939201416946[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78128&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	696.25	1.70782512765993	4
2	703.25	12.5266382827424	26
3	690	1.41421356237310	3
4	679.25	6.34428877022476	15
5	679	16.1451747177498	35
6	649.5	7.04745817062199	14
7	625	9.76387901058454	23
8	625.75	13.3759734848222	30
9	591.25	8.18026079453868	17
10	566	13.5646599662505	30
11	559	19.4422220952236	44
12	522.5	10.1488915650922	23
13	499.5	8.10349718742881	19
14	503	20.0166597280032	45
15	464	11.9443152447793	28
16	455.5	5.91607978309962	12
17	453.5	28.6647286166583	64
18	403.5	11.7331439378654	26
19	380.75	10.1447851956888	19
20	370.5	35.7164761233057	80
21	310.5	10.0829889748361	21
22	288.5	8.81286937760152	17
23	274	40.9715348341585	92
24	222.5	10.1488915650922	23
25	205	6.58280588604383	14
26	194.5	44.8144321991625	101
27	140.75	10.3400515794974	25
28	121.5	7.72442015083764	16
29	125.25	41.4115523334572	93
30	91.5	9.53939201416946	23

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	23.9703262287886
beta	-0.0211427451366656
S.D.	0.0103841142092862
T-STAT	-2.03606631346161
p-value	0.0513032360208188

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 23.9703262287886 \tabularnewline
beta & -0.0211427451366656 \tabularnewline
S.D. & 0.0103841142092862 \tabularnewline
T-STAT & -2.03606631346161 \tabularnewline
p-value & 0.0513032360208188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78128&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.9703262287886[/C][/ROW]
[ROW][C]beta[/C][C]-0.0211427451366656[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0103841142092862[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.03606631346161[/C][/ROW]
[ROW][C]p-value[/C][C]0.0513032360208188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78128&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	23.9703262287886
beta	-0.0211427451366656
S.D.	0.0103841142092862
T-STAT	-2.03606631346161
p-value	0.0513032360208188

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.73370622739984
beta	-0.390377442782828
S.D.	0.238127496653785
T-STAT	-1.63936314902097
p-value	0.112326791283919
Lambda	1.39037744278283

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.73370622739984 \tabularnewline
beta & -0.390377442782828 \tabularnewline
S.D. & 0.238127496653785 \tabularnewline
T-STAT & -1.63936314902097 \tabularnewline
p-value & 0.112326791283919 \tabularnewline
Lambda & 1.39037744278283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78128&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.73370622739984[/C][/ROW]
[ROW][C]beta[/C][C]-0.390377442782828[/C][/ROW]
[ROW][C]S.D.[/C][C]0.238127496653785[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.63936314902097[/C][/ROW]
[ROW][C]p-value[/C][C]0.112326791283919[/C][/ROW]
[ROW][C]Lambda[/C][C]1.39037744278283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78128&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78128&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	4.73370622739984
beta	-0.390377442782828
S.D.	0.238127496653785
T-STAT	-1.63936314902097
p-value	0.112326791283919
Lambda	1.39037744278283

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