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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 computationWed, 25 Nov 2009 15:14:53 -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/25/t12591875328tx5md564jpn0fi.htm/, Retrieved Tue, 07 May 2024 12:21:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59670, Retrieved Tue, 07 May 2024 12:21:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact218

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
- R  D          [Standard Deviation-Mean Plot] [WS08 - Heteroskel...] [2009-11-25 22:14:53] [0cc924834281808eda7297686c82928f] [Current]
-    D            [Standard Deviation-Mean Plot] [WS10 - Heteroskel...] [2009-12-09 14:29:45] [df6326eec97a6ca984a853b142930499]
-    D            [Standard Deviation-Mean Plot] [WS10 - Heterosked...] [2009-12-14 21:45:04] [df6326eec97a6ca984a853b142930499]
-    D            [Standard Deviation-Mean Plot] [CaseStatistiek - ...] [2009-12-30 23:26:05] [df6326eec97a6ca984a853b142930499]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
423.4
404.1
500
472.6
496.1
562
434.8
538.2
577.6
518.1
625.2
561.2
523.3
536.1
607.3
637.3
606.9
652.9
617.2
670.4
729.9
677.2
710
844.3
748.2
653.9
742.6
854.2
808.4
1819
1936.5
1966.1
2083.1
1620.1
1527.6
1795
1685.1
1851.8
2164.4
1981.8
1726.5
2144.6
1758.2
1672.9
1837.3
1596.1
1446
1898.4
1964.1
1755.9
2255.3
1881.2
2117.9
1656.5
1544.1
2098.9
2133.3
1963.5
1801.2
2365.4
1936.5
1667.6
1983.5
2058.6
2448.3
1858.1
1625.4
2130.6
2515.7
2230.2
2086.9
2235
2100.2
2288.6
2490
2573.7
2543.8
2004.7
2390
2338.4
2724.5
2292.5
2386
2477.9
2337
2605.1
2560.8
2839.3
2407.2
2085.2
2735.6
2798.7
3053.2
2405
2471.9
2727.3
2790.7
2385.4
3206.6
2705.6
3518.4
1954.9
2584.3
2535.8
2685.9
2866
2236.6
2934.9
2668.6
2371.2
3165.9
2887.2
3112.2
2671.2
2432.6
2812.3
3095.7
2862.9
2607.3
2862.5

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=59670&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=59670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59670&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
1509.44166666666767.4770864588099221.1
2651.06666666666786.7762989566048321
31379.55833333333566.3115035165291429.2
41813.59166666667213.099458035800718.4
51961.44166666667245.686908883989821.3
62064.7274.391939319719890.3
72384.19166666667200.34489560997719.8
82585.525263.123182783619968
92700.425418.5304900916581563.5
102795.8256.557124597658794.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 509.441666666667 & 67.4770864588099 & 221.1 \tabularnewline
2 & 651.066666666667 & 86.7762989566048 & 321 \tabularnewline
3 & 1379.55833333333 & 566.311503516529 & 1429.2 \tabularnewline
4 & 1813.59166666667 & 213.099458035800 & 718.4 \tabularnewline
5 & 1961.44166666667 & 245.686908883989 & 821.3 \tabularnewline
6 & 2064.7 & 274.391939319719 & 890.3 \tabularnewline
7 & 2384.19166666667 & 200.34489560997 & 719.8 \tabularnewline
8 & 2585.525 & 263.123182783619 & 968 \tabularnewline
9 & 2700.425 & 418.530490091658 & 1563.5 \tabularnewline
10 & 2795.8 & 256.557124597658 & 794.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59670&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]509.441666666667[/C][C]67.4770864588099[/C][C]221.1[/C][/ROW]
[ROW][C]2[/C][C]651.066666666667[/C][C]86.7762989566048[/C][C]321[/C][/ROW]
[ROW][C]3[/C][C]1379.55833333333[/C][C]566.311503516529[/C][C]1429.2[/C][/ROW]
[ROW][C]4[/C][C]1813.59166666667[/C][C]213.099458035800[/C][C]718.4[/C][/ROW]
[ROW][C]5[/C][C]1961.44166666667[/C][C]245.686908883989[/C][C]821.3[/C][/ROW]
[ROW][C]6[/C][C]2064.7[/C][C]274.391939319719[/C][C]890.3[/C][/ROW]
[ROW][C]7[/C][C]2384.19166666667[/C][C]200.34489560997[/C][C]719.8[/C][/ROW]
[ROW][C]8[/C][C]2585.525[/C][C]263.123182783619[/C][C]968[/C][/ROW]
[ROW][C]9[/C][C]2700.425[/C][C]418.530490091658[/C][C]1563.5[/C][/ROW]
[ROW][C]10[/C][C]2795.8[/C][C]256.557124597658[/C][C]794.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59670&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
1509.44166666666767.4770864588099221.1
2651.06666666666786.7762989566048321
31379.55833333333566.3115035165291429.2
41813.59166666667213.099458035800718.4
51961.44166666667245.686908883989821.3
62064.7274.391939319719890.3
72384.19166666667200.34489560997719.8
82585.525263.123182783619968
92700.425418.5304900916581563.5
102795.8256.557124597658794.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha123.893832193563
beta0.0718125394190498
S.D.0.0582664581766499
T-STAT1.23248506372794
p-value0.252758027947641

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 123.893832193563 \tabularnewline
beta & 0.0718125394190498 \tabularnewline
S.D. & 0.0582664581766499 \tabularnewline
T-STAT & 1.23248506372794 \tabularnewline
p-value & 0.252758027947641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59670&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]123.893832193563[/C][/ROW]
[ROW][C]beta[/C][C]0.0718125394190498[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0582664581766499[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.23248506372794[/C][/ROW]
[ROW][C]p-value[/C][C]0.252758027947641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59670&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)
alpha123.893832193563
beta0.0718125394190498
S.D.0.0582664581766499
T-STAT1.23248506372794
p-value0.252758027947641






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.56807579773122
beta0.804426595637681
S.D.0.249768505386317
T-STAT3.22068867086935
p-value0.0122265544057653
Lambda0.195573404362319

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.56807579773122 \tabularnewline
beta & 0.804426595637681 \tabularnewline
S.D. & 0.249768505386317 \tabularnewline
T-STAT & 3.22068867086935 \tabularnewline
p-value & 0.0122265544057653 \tabularnewline
Lambda & 0.195573404362319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59670&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.56807579773122[/C][/ROW]
[ROW][C]beta[/C][C]0.804426595637681[/C][/ROW]
[ROW][C]S.D.[/C][C]0.249768505386317[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.22068867086935[/C][/ROW]
[ROW][C]p-value[/C][C]0.0122265544057653[/C][/ROW]
[ROW][C]Lambda[/C][C]0.195573404362319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59670&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59670&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)
alpha-0.56807579773122
beta0.804426595637681
S.D.0.249768505386317
T-STAT3.22068867086935
p-value0.0122265544057653
Lambda0.195573404362319


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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')