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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 02 May 2012 16:10:39 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/02/t1335989461spyqtzq0tjq6b97.htm/, Retrieved Tue, 07 May 2024 19:37:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=165998, Retrieved Tue, 07 May 2024 19:37:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [Bootstrap Plot va...] [2012-05-02 19:39:36] [562ee1d5a96d07a2dc4978b28f7ac089]
- RMPD  [Blocked Bootstrap Plot - Central Tendency] [Blocked Bootstrap...] [2012-05-02 19:52:56] [562ee1d5a96d07a2dc4978b28f7ac089]
- RMPD      [Standard Deviation-Mean Plot] [Blocked Bootstrap...] [2012-05-02 20:10:39] [1f07dfe249cf12c76d4857e2b59f088a] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92.8
90.61
88.49
88.33
87.7
87.33
87.33
87.33
85.47
86.1
86.1
86.13
83.31
83.31
83.55
84.11
84.11
77.59
77.59
76.44
72.71
72.9
72.39
72.46
72.48
72.48
72.48
72.3
72.3
72.3
71.14
71.14
68.99
68.42
68.42
69.28
65.22
70.21
70.21
71.2
68.94
68.94
68.93
68.93
68.93
68.93
59.94
61.04
60.2
60.2
60.12
60.25
58.03
62.37
62.16
62.16
62.16
62.16
62.29
64.39

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165998&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165998&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
187.812.095935460491447.33
278.37255.0373281608408211.72
370.97751.705222592774654.06
467.61833333333333.6259239156971111.26
561.37416666666671.656208475751626.36

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 87.81 & 2.09593546049144 & 7.33 \tabularnewline
2 & 78.3725 & 5.03732816084082 & 11.72 \tabularnewline
3 & 70.9775 & 1.70522259277465 & 4.06 \tabularnewline
4 & 67.6183333333333 & 3.62592391569711 & 11.26 \tabularnewline
5 & 61.3741666666667 & 1.65620847575162 & 6.36 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165998&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]87.81[/C][C]2.09593546049144[/C][C]7.33[/C][/ROW]
[ROW][C]2[/C][C]78.3725[/C][C]5.03732816084082[/C][C]11.72[/C][/ROW]
[ROW][C]3[/C][C]70.9775[/C][C]1.70522259277465[/C][C]4.06[/C][/ROW]
[ROW][C]4[/C][C]67.6183333333333[/C][C]3.62592391569711[/C][C]11.26[/C][/ROW]
[ROW][C]5[/C][C]61.3741666666667[/C][C]1.65620847575162[/C][C]6.36[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165998&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
187.812.095935460491447.33
278.37255.0373281608408211.72
370.97751.705222592774654.06
467.61833333333333.6259239156971111.26
561.37416666666671.656208475751626.36






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.601251802364093
beta0.0303544550255295
S.D.0.0815564346699228
T-STAT0.372189578276451
p-value0.734488508471349

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.601251802364093 \tabularnewline
beta & 0.0303544550255295 \tabularnewline
S.D. & 0.0815564346699228 \tabularnewline
T-STAT & 0.372189578276451 \tabularnewline
p-value & 0.734488508471349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165998&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.601251802364093[/C][/ROW]
[ROW][C]beta[/C][C]0.0303544550255295[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0815564346699228[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.372189578276451[/C][/ROW]
[ROW][C]p-value[/C][C]0.734488508471349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165998&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)
alpha0.601251802364093
beta0.0303544550255295
S.D.0.0815564346699228
T-STAT0.372189578276451
p-value0.734488508471349






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.09712490174589
beta0.941154893214327
S.D.1.99686656341895
T-STAT0.471315865794719
p-value0.66957150231742
Lambda0.0588451067856731

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.09712490174589 \tabularnewline
beta & 0.941154893214327 \tabularnewline
S.D. & 1.99686656341895 \tabularnewline
T-STAT & 0.471315865794719 \tabularnewline
p-value & 0.66957150231742 \tabularnewline
Lambda & 0.0588451067856731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165998&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.09712490174589[/C][/ROW]
[ROW][C]beta[/C][C]0.941154893214327[/C][/ROW]
[ROW][C]S.D.[/C][C]1.99686656341895[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.471315865794719[/C][/ROW]
[ROW][C]p-value[/C][C]0.66957150231742[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0588451067856731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165998&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-3.09712490174589
beta0.941154893214327
S.D.1.99686656341895
T-STAT0.471315865794719
p-value0.66957150231742
Lambda0.0588451067856731


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 750 ; par2 = 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')