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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, 08 Jan 2009 14:59:47 -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/Jan/08/t1231452029ttq58rtvpo6va4i.htm/, Retrieved Wed, 08 May 2024 09:59:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36835, Retrieved Wed, 08 May 2024 09:59:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

213

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

-       [Standard Deviation-Mean Plot] [standard deviatio...] [2009-01-08 21:59:47] [9e20205489828c19845a9d736cd20362] [Current]
- RMPD    [Classical Decomposition] [verbetering klass...] [2009-01-26 21:18:05] [65364f12da24daf6c8f7985fc762862c] 

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36835&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36835&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36835&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	92.6425	1.25138256873481	2.82000000000001
2	90.715	0.147082743152738	0.330000000000013
3	89.5575	0.394324316605843	0.86
4	88.435	0.816108652896989	1.79000000000001
5	86.98	0.0999999999999943	0.199999999999989
6	86.2325	0.513898498408655	1.10000000000001
7	85.02	0.99421660953067	2.23999999999999
8	83.34	0.048304589153965	0.109999999999999
9	82.0375	0.5439592509248	1.21000000000001
10	81.69	0.183121089264273	0.370000000000005
11	82.09	0.594250227878237	1.21000000000001
12	82.8925	0.159452187191018	0.329999999999998
13	82.3325	0.657235371334604	1.34000000000000
14	81.2625	0.0921502396451986	0.190000000000012
15	80.65	0.240970260959040	0.510000000000005
16	80.5625	0.153704261489393	0.359999999999999
17	79.5825	0.318995820244300	0.75
18	78.51	0.297993288515029	0.680000000000007
19	77.0275	1.47685194473470	3.16000000000000
20	75.055	0.0525991127935293	0.0999999999999943
21	73.005	0.665357047005594	1.45000000000000
22	71.79	0.764765759345088	1.56000000000000
23	69.75	0.450851047095013	0.980000000000004
24	67.0175	0.841125238395965	1.79000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.6425 & 1.25138256873481 & 2.82000000000001 \tabularnewline
2 & 90.715 & 0.147082743152738 & 0.330000000000013 \tabularnewline
3 & 89.5575 & 0.394324316605843 & 0.86 \tabularnewline
4 & 88.435 & 0.816108652896989 & 1.79000000000001 \tabularnewline
5 & 86.98 & 0.0999999999999943 & 0.199999999999989 \tabularnewline
6 & 86.2325 & 0.513898498408655 & 1.10000000000001 \tabularnewline
7 & 85.02 & 0.99421660953067 & 2.23999999999999 \tabularnewline
8 & 83.34 & 0.048304589153965 & 0.109999999999999 \tabularnewline
9 & 82.0375 & 0.5439592509248 & 1.21000000000001 \tabularnewline
10 & 81.69 & 0.183121089264273 & 0.370000000000005 \tabularnewline
11 & 82.09 & 0.594250227878237 & 1.21000000000001 \tabularnewline
12 & 82.8925 & 0.159452187191018 & 0.329999999999998 \tabularnewline
13 & 82.3325 & 0.657235371334604 & 1.34000000000000 \tabularnewline
14 & 81.2625 & 0.0921502396451986 & 0.190000000000012 \tabularnewline
15 & 80.65 & 0.240970260959040 & 0.510000000000005 \tabularnewline
16 & 80.5625 & 0.153704261489393 & 0.359999999999999 \tabularnewline
17 & 79.5825 & 0.318995820244300 & 0.75 \tabularnewline
18 & 78.51 & 0.297993288515029 & 0.680000000000007 \tabularnewline
19 & 77.0275 & 1.47685194473470 & 3.16000000000000 \tabularnewline
20 & 75.055 & 0.0525991127935293 & 0.0999999999999943 \tabularnewline
21 & 73.005 & 0.665357047005594 & 1.45000000000000 \tabularnewline
22 & 71.79 & 0.764765759345088 & 1.56000000000000 \tabularnewline
23 & 69.75 & 0.450851047095013 & 0.980000000000004 \tabularnewline
24 & 67.0175 & 0.841125238395965 & 1.79000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36835&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]92.6425[/C][C]1.25138256873481[/C][C]2.82000000000001[/C][/ROW]
[ROW][C]2[/C][C]90.715[/C][C]0.147082743152738[/C][C]0.330000000000013[/C][/ROW]
[ROW][C]3[/C][C]89.5575[/C][C]0.394324316605843[/C][C]0.86[/C][/ROW]
[ROW][C]4[/C][C]88.435[/C][C]0.816108652896989[/C][C]1.79000000000001[/C][/ROW]
[ROW][C]5[/C][C]86.98[/C][C]0.0999999999999943[/C][C]0.199999999999989[/C][/ROW]
[ROW][C]6[/C][C]86.2325[/C][C]0.513898498408655[/C][C]1.10000000000001[/C][/ROW]
[ROW][C]7[/C][C]85.02[/C][C]0.99421660953067[/C][C]2.23999999999999[/C][/ROW]
[ROW][C]8[/C][C]83.34[/C][C]0.048304589153965[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]9[/C][C]82.0375[/C][C]0.5439592509248[/C][C]1.21000000000001[/C][/ROW]
[ROW][C]10[/C][C]81.69[/C][C]0.183121089264273[/C][C]0.370000000000005[/C][/ROW]
[ROW][C]11[/C][C]82.09[/C][C]0.594250227878237[/C][C]1.21000000000001[/C][/ROW]
[ROW][C]12[/C][C]82.8925[/C][C]0.159452187191018[/C][C]0.329999999999998[/C][/ROW]
[ROW][C]13[/C][C]82.3325[/C][C]0.657235371334604[/C][C]1.34000000000000[/C][/ROW]
[ROW][C]14[/C][C]81.2625[/C][C]0.0921502396451986[/C][C]0.190000000000012[/C][/ROW]
[ROW][C]15[/C][C]80.65[/C][C]0.240970260959040[/C][C]0.510000000000005[/C][/ROW]
[ROW][C]16[/C][C]80.5625[/C][C]0.153704261489393[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]17[/C][C]79.5825[/C][C]0.318995820244300[/C][C]0.75[/C][/ROW]
[ROW][C]18[/C][C]78.51[/C][C]0.297993288515029[/C][C]0.680000000000007[/C][/ROW]
[ROW][C]19[/C][C]77.0275[/C][C]1.47685194473470[/C][C]3.16000000000000[/C][/ROW]
[ROW][C]20[/C][C]75.055[/C][C]0.0525991127935293[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]21[/C][C]73.005[/C][C]0.665357047005594[/C][C]1.45000000000000[/C][/ROW]
[ROW][C]22[/C][C]71.79[/C][C]0.764765759345088[/C][C]1.56000000000000[/C][/ROW]
[ROW][C]23[/C][C]69.75[/C][C]0.450851047095013[/C][C]0.980000000000004[/C][/ROW]
[ROW][C]24[/C][C]67.0175[/C][C]0.841125238395965[/C][C]1.79000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36835&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36835&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	92.6425	1.25138256873481	2.82000000000001
2	90.715	0.147082743152738	0.330000000000013
3	89.5575	0.394324316605843	0.86
4	88.435	0.816108652896989	1.79000000000001
5	86.98	0.0999999999999943	0.199999999999989
6	86.2325	0.513898498408655	1.10000000000001
7	85.02	0.99421660953067	2.23999999999999
8	83.34	0.048304589153965	0.109999999999999
9	82.0375	0.5439592509248	1.21000000000001
10	81.69	0.183121089264273	0.370000000000005
11	82.09	0.594250227878237	1.21000000000001
12	82.8925	0.159452187191018	0.329999999999998
13	82.3325	0.657235371334604	1.34000000000000
14	81.2625	0.0921502396451986	0.190000000000012
15	80.65	0.240970260959040	0.510000000000005
16	80.5625	0.153704261489393	0.359999999999999
17	79.5825	0.318995820244300	0.75
18	78.51	0.297993288515029	0.680000000000007
19	77.0275	1.47685194473470	3.16000000000000
20	75.055	0.0525991127935293	0.0999999999999943
21	73.005	0.665357047005594	1.45000000000000
22	71.79	0.764765759345088	1.56000000000000
23	69.75	0.450851047095013	0.980000000000004
24	67.0175	0.841125238395965	1.79000000000001

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.770495587319635
beta	-0.00345615015591331
S.D.	0.0126316899290788
T-STAT	-0.273609483395969
p-value	0.786937066040794

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.770495587319635 \tabularnewline
beta & -0.00345615015591331 \tabularnewline
S.D. & 0.0126316899290788 \tabularnewline
T-STAT & -0.273609483395969 \tabularnewline
p-value & 0.786937066040794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36835&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.770495587319635[/C][/ROW]
[ROW][C]beta[/C][C]-0.00345615015591331[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0126316899290788[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.273609483395969[/C][/ROW]
[ROW][C]p-value[/C][C]0.786937066040794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36835&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36835&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	0.770495587319635
beta	-0.00345615015591331
S.D.	0.0126316899290788
T-STAT	-0.273609483395969
p-value	0.786937066040794

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.51383466303698
beta	-1.27538761622301
S.D.	2.51459150864769
T-STAT	-0.507194751846154
p-value	0.61706473985287
Lambda	2.27538761622301

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.51383466303698 \tabularnewline
beta & -1.27538761622301 \tabularnewline
S.D. & 2.51459150864769 \tabularnewline
T-STAT & -0.507194751846154 \tabularnewline
p-value & 0.61706473985287 \tabularnewline
Lambda & 2.27538761622301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36835&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.51383466303698[/C][/ROW]
[ROW][C]beta[/C][C]-1.27538761622301[/C][/ROW]
[ROW][C]S.D.[/C][C]2.51459150864769[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.507194751846154[/C][/ROW]
[ROW][C]p-value[/C][C]0.61706473985287[/C][/ROW]
[ROW][C]Lambda[/C][C]2.27538761622301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36835&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36835&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	4.51383466303698
beta	-1.27538761622301
S.D.	2.51459150864769
T-STAT	-0.507194751846154
p-value	0.61706473985287
Lambda	2.27538761622301

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