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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 26 Nov 2009 03:49:12 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/26/t1259233430t5lotafi63qznao.htm/, Retrieved Mon, 05 May 2025 21:16:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59823, Retrieved Mon, 05 May 2025 21:16:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact404

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
-   PD        [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 16:54:07] [ee7c2e7343f5b1451e62c5c16ec521f1]
-   P           [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 17:23:40] [ee7c2e7343f5b1451e62c5c16ec521f1]
- RMPD            [(Partial) Autocorrelation Function] [] [2009-11-26 08:57:08] [5edbdb7a459c4059b6c3b063ba86821c]
- RMP               [Spectral Analysis] [] [2009-11-26 10:31:07] [5edbdb7a459c4059b6c3b063ba86821c]
- RM                    [Standard Deviation-Mean Plot] [] [2009-11-26 10:49:12] [24029b2c7217429de6ff94b5379eb52c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19
18
19
19
22
23
20
14
14
14
15
11
17
16
20
24
23
20
21
19
23
23
23
23
27
26
17
24
26
24
27
27
26
24
23
23
24
17
21
19
22
22
18
16
14
12
14
16
8
3
0
5
1
1
3
6
7
8
14
14
13

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=59823&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=59823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59823&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
117.33333333333333.6762958960278912
2212.628514962691088
324.52.8123105996832810
417.91666666666673.7527767497325712
55.833333333333334.6871843328054614

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 17.3333333333333 & 3.67629589602789 & 12 \tabularnewline
2 & 21 & 2.62851496269108 & 8 \tabularnewline
3 & 24.5 & 2.81231059968328 & 10 \tabularnewline
4 & 17.9166666666667 & 3.75277674973257 & 12 \tabularnewline
5 & 5.83333333333333 & 4.68718433280546 & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59823&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]17.3333333333333[/C][C]3.67629589602789[/C][C]12[/C][/ROW]
[ROW][C]2[/C][C]21[/C][C]2.62851496269108[/C][C]8[/C][/ROW]
[ROW][C]3[/C][C]24.5[/C][C]2.81231059968328[/C][C]10[/C][/ROW]
[ROW][C]4[/C][C]17.9166666666667[/C][C]3.75277674973257[/C][C]12[/C][/ROW]
[ROW][C]5[/C][C]5.83333333333333[/C][C]4.68718433280546[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59823&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
117.33333333333333.6762958960278912
2212.628514962691088
324.52.8123105996832810
417.91666666666673.7527767497325712
55.833333333333334.6871843328054614






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.40876787456541
beta-0.109567932610819
S.D.0.0248738168126461
T-STAT-4.40495053236517
p-value0.0216978325346787

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.40876787456541 \tabularnewline
beta & -0.109567932610819 \tabularnewline
S.D. & 0.0248738168126461 \tabularnewline
T-STAT & -4.40495053236517 \tabularnewline
p-value & 0.0216978325346787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59823&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.40876787456541[/C][/ROW]
[ROW][C]beta[/C][C]-0.109567932610819[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0248738168126461[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.40495053236517[/C][/ROW]
[ROW][C]p-value[/C][C]0.0216978325346787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59823&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59823&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.40876787456541
beta-0.109567932610819
S.D.0.0248738168126461
T-STAT-4.40495053236517
p-value0.0216978325346787






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.20603224545904
beta-0.353615862509044
S.D.0.123835738032300
T-STAT-2.85552351952560
p-value0.064814471540524
Lambda1.35361586250904

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.20603224545904 \tabularnewline
beta & -0.353615862509044 \tabularnewline
S.D. & 0.123835738032300 \tabularnewline
T-STAT & -2.85552351952560 \tabularnewline
p-value & 0.064814471540524 \tabularnewline
Lambda & 1.35361586250904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59823&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.20603224545904[/C][/ROW]
[ROW][C]beta[/C][C]-0.353615862509044[/C][/ROW]
[ROW][C]S.D.[/C][C]0.123835738032300[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.85552351952560[/C][/ROW]
[ROW][C]p-value[/C][C]0.064814471540524[/C][/ROW]
[ROW][C]Lambda[/C][C]1.35361586250904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59823&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59823&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.20603224545904
beta-0.353615862509044
S.D.0.123835738032300
T-STAT-2.85552351952560
p-value0.064814471540524
Lambda1.35361586250904


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;
Parameters (R input):
par1 = 12 ;
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')