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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 computationTue, 16 Dec 2008 09:30:21 -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/2008/Dec/16/t1229445063cayi4bf6ivb7odc.htm/, Retrieved Wed, 15 May 2024 02:52:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34016, Retrieved Wed, 15 May 2024 02:52:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [WS7 Q1 G6 reeks 1] [2007-11-22 09:45:51] [22f18fc6a98517db16300404be421f9a]
-    D  [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-16 16:28:12] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D      [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-16 16:30:21] [e8f764b122b426f433a1e1038b457077] [Current]
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-16 16:32:56] [4ddbf81f78ea7c738951638c7e93f6ee]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,4
9,5
9,1
9
9,3
9,9
9,8
9,4
8,3
8
8,5
10,4
11,1
10,9
9,9
9,2
9,2
9,5
9,6
9,5
9,1
8,9
9
10,1
10,3
10,2
9,6
9,2
9,3
9,4
9,4
9,2
9
9
9
9,8
10
9,9
9,3
9
9
9,1
9,1
9,1
9,2
8,8
8,3
8,4
8,1
7,8
7,9
7,9
8
7,9
7,5
7,2
6,9
6,6
6,7
7,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34016&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34016&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34016&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.216666666666670.691287775010372.3
29.666666666666670.7177405625652743.3
39.450.4461960433384742.4
49.10.4990900811385752.1
57.483333333333330.5322906474223770.0999999999999996

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.21666666666667 & 0.69128777501037 & 2.3 \tabularnewline
2 & 9.66666666666667 & 0.717740562565274 & 3.3 \tabularnewline
3 & 9.45 & 0.446196043338474 & 2.4 \tabularnewline
4 & 9.1 & 0.499090081138575 & 2.1 \tabularnewline
5 & 7.48333333333333 & 0.532290647422377 & 0.0999999999999996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34016&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]9.21666666666667[/C][C]0.69128777501037[/C][C]2.3[/C][/ROW]
[ROW][C]2[/C][C]9.66666666666667[/C][C]0.717740562565274[/C][C]3.3[/C][/ROW]
[ROW][C]3[/C][C]9.45[/C][C]0.446196043338474[/C][C]2.4[/C][/ROW]
[ROW][C]4[/C][C]9.1[/C][C]0.499090081138575[/C][C]2.1[/C][/ROW]
[ROW][C]5[/C][C]7.48333333333333[/C][C]0.532290647422377[/C][C]0.0999999999999996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34016&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34016&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
19.216666666666670.691287775010372.3
29.666666666666670.7177405625652743.3
39.450.4461960433384742.4
49.10.4990900811385752.1
57.483333333333330.5322906474223770.0999999999999996






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.219000531784115
beta0.0398872530735694
S.D.0.0768988989703016
T-STAT0.518697323468493
p-value0.639804494146754

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.219000531784115 \tabularnewline
beta & 0.0398872530735694 \tabularnewline
S.D. & 0.0768988989703016 \tabularnewline
T-STAT & 0.518697323468493 \tabularnewline
p-value & 0.639804494146754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34016&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.219000531784115[/C][/ROW]
[ROW][C]beta[/C][C]0.0398872530735694[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0768988989703016[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.518697323468493[/C][/ROW]
[ROW][C]p-value[/C][C]0.639804494146754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34016&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34016&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)
alpha0.219000531784115
beta0.0398872530735694
S.D.0.0768988989703016
T-STAT0.518697323468493
p-value0.639804494146754






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.61602609425648
beta0.478864087803367
S.D.1.13619789929891
T-STAT0.421461866897349
p-value0.70179382853523
Lambda0.521135912196633

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.61602609425648 \tabularnewline
beta & 0.478864087803367 \tabularnewline
S.D. & 1.13619789929891 \tabularnewline
T-STAT & 0.421461866897349 \tabularnewline
p-value & 0.70179382853523 \tabularnewline
Lambda & 0.521135912196633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34016&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.61602609425648[/C][/ROW]
[ROW][C]beta[/C][C]0.478864087803367[/C][/ROW]
[ROW][C]S.D.[/C][C]1.13619789929891[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.421461866897349[/C][/ROW]
[ROW][C]p-value[/C][C]0.70179382853523[/C][/ROW]
[ROW][C]Lambda[/C][C]0.521135912196633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34016&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34016&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-1.61602609425648
beta0.478864087803367
S.D.1.13619789929891
T-STAT0.421461866897349
p-value0.70179382853523
Lambda0.521135912196633


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')