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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 computationFri, 04 Dec 2009 05:55:06 -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/Dec/04/t1259931643x10mxjlb7x5rwn8.htm/, Retrieved Sun, 28 Apr 2024 00:34:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63448, Retrieved Sun, 28 Apr 2024 00:34:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-    D      [Standard Deviation-Mean Plot] [] [2009-12-04 12:55:06] [d1856923bab8a0db5ebd860815c7444f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,2
1,9
0
0,6
0,2
0,9
2,4
4,7
9,4
12,5
15,8
18,2
16,8
17,3
19,3
17,9
20,2
18,7
20,1
18,2
18,4
18,2
18,9
19,9
21,3
20
19,5
19,6
20,9
21
19,9
19,6
20,9
21,7
22,9
21,5
21,3
23,5
21,6
24,5
22,2
23,5
20,9
20,7
18,1
17,1
14,8
13,8
15,2
16
17,6
15
15
16,3
19,4
21,3
20,5
21,1
21,6
22,6

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=63448&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=63448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63448&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
15.816666666666676.483522237646818.2
218.65833333333331.079948090783943.4
320.73333333333331.043885515608383.4
420.16666666666673.4681232371239010.7
518.46666666666672.909337110793877.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.81666666666667 & 6.4835222376468 & 18.2 \tabularnewline
2 & 18.6583333333333 & 1.07994809078394 & 3.4 \tabularnewline
3 & 20.7333333333333 & 1.04388551560838 & 3.4 \tabularnewline
4 & 20.1666666666667 & 3.46812323712390 & 10.7 \tabularnewline
5 & 18.4666666666667 & 2.90933711079387 & 7.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63448&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]5.81666666666667[/C][C]6.4835222376468[/C][C]18.2[/C][/ROW]
[ROW][C]2[/C][C]18.6583333333333[/C][C]1.07994809078394[/C][C]3.4[/C][/ROW]
[ROW][C]3[/C][C]20.7333333333333[/C][C]1.04388551560838[/C][C]3.4[/C][/ROW]
[ROW][C]4[/C][C]20.1666666666667[/C][C]3.46812323712390[/C][C]10.7[/C][/ROW]
[ROW][C]5[/C][C]18.4666666666667[/C][C]2.90933711079387[/C][C]7.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63448&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
15.816666666666676.483522237646818.2
218.65833333333331.079948090783943.4
320.73333333333331.043885515608383.4
420.16666666666673.4681232371239010.7
518.46666666666672.909337110793877.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.24557750820245
beta-0.313007510375375
S.D.0.102253393322082
T-STAT-3.06109655832595
p-value0.054945612537903

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.24557750820245 \tabularnewline
beta & -0.313007510375375 \tabularnewline
S.D. & 0.102253393322082 \tabularnewline
T-STAT & -3.06109655832595 \tabularnewline
p-value & 0.054945612537903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63448&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.24557750820245[/C][/ROW]
[ROW][C]beta[/C][C]-0.313007510375375[/C][/ROW]
[ROW][C]S.D.[/C][C]0.102253393322082[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.06109655832595[/C][/ROW]
[ROW][C]p-value[/C][C]0.054945612537903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63448&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)
alpha8.24557750820245
beta-0.313007510375375
S.D.0.102253393322082
T-STAT-3.06109655832595
p-value0.054945612537903






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.71746415070743
beta-1.04750386357070
S.D.0.58167220869758
T-STAT-1.80084908288152
p-value0.16953573058692
Lambda2.04750386357070

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.71746415070743 \tabularnewline
beta & -1.04750386357070 \tabularnewline
S.D. & 0.58167220869758 \tabularnewline
T-STAT & -1.80084908288152 \tabularnewline
p-value & 0.16953573058692 \tabularnewline
Lambda & 2.04750386357070 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63448&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.71746415070743[/C][/ROW]
[ROW][C]beta[/C][C]-1.04750386357070[/C][/ROW]
[ROW][C]S.D.[/C][C]0.58167220869758[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.80084908288152[/C][/ROW]
[ROW][C]p-value[/C][C]0.16953573058692[/C][/ROW]
[ROW][C]Lambda[/C][C]2.04750386357070[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63448&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63448&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)
alpha3.71746415070743
beta-1.04750386357070
S.D.0.58167220869758
T-STAT-1.80084908288152
p-value0.16953573058692
Lambda2.04750386357070


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')