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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, 25 Apr 2012 17:54:46 -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/Apr/25/t1335390942bhb1hf1ih195fcm.htm/, Retrieved Mon, 06 May 2024 11:53:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164869, Retrieved Mon, 06 May 2024 11:53:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W81
Estimated Impact74

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] [sportvesten] [2012-04-25 21:54:46] [f6a7b86b75cb82ac7a5a766dce297b13] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
162.32
162.76
163.39
162.58
162.66
162.66
162.66
162.89
163.03
162.38
162.44
162.51
162.51
162.42
162.07
161.45
162.22
162.21
162.21
162.21
162.41
163.96
163.79
163.86
163.86
164.39
164.74
164.27
165.2
165.42
165.42
165.5
165.71
165.74
165.29
164.88
164.88
164.57
164.53
165.03
165.92
165.92
165.92
165.92
166.12
166.34
165.48
165.61
165.61
165.94
165.88
166.23
166.32
166.43
166.43
166.2
166.21
168.02
168.68
168.65

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R Server'AstonUniversity' @ aston.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 & 11 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164869&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]11 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164869&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 time11 seconds
R Server'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1162.690.3004844573200211.06999999999999
2162.610.8052554648286282.51000000000002
3165.0350.6068173306088661.88
4165.520.6189727560460731.81
5166.7166666666671.082978496666683.06999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 162.69 & 0.300484457320021 & 1.06999999999999 \tabularnewline
2 & 162.61 & 0.805255464828628 & 2.51000000000002 \tabularnewline
3 & 165.035 & 0.606817330608866 & 1.88 \tabularnewline
4 & 165.52 & 0.618972756046073 & 1.81 \tabularnewline
5 & 166.716666666667 & 1.08297849666668 & 3.06999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164869&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]162.69[/C][C]0.300484457320021[/C][C]1.06999999999999[/C][/ROW]
[ROW][C]2[/C][C]162.61[/C][C]0.805255464828628[/C][C]2.51000000000002[/C][/ROW]
[ROW][C]3[/C][C]165.035[/C][C]0.606817330608866[/C][C]1.88[/C][/ROW]
[ROW][C]4[/C][C]165.52[/C][C]0.618972756046073[/C][C]1.81[/C][/ROW]
[ROW][C]5[/C][C]166.716666666667[/C][C]1.08297849666668[/C][C]3.06999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164869&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
1162.690.3004844573200211.06999999999999
2162.610.8052554648286282.51000000000002
3165.0350.6068173306088661.88
4165.520.6189727560460731.81
5166.7166666666671.082978496666683.06999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-14.9276949828816
beta0.0948889763443652
S.D.0.0737090499243367
T-STAT1.28734499280306
p-value0.288300663002148

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -14.9276949828816 \tabularnewline
beta & 0.0948889763443652 \tabularnewline
S.D. & 0.0737090499243367 \tabularnewline
T-STAT & 1.28734499280306 \tabularnewline
p-value & 0.288300663002148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164869&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.9276949828816[/C][/ROW]
[ROW][C]beta[/C][C]0.0948889763443652[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0737090499243367[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.28734499280306[/C][/ROW]
[ROW][C]p-value[/C][C]0.288300663002148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164869&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)
alpha-14.9276949828816
beta0.0948889763443652
S.D.0.0737090499243367
T-STAT1.28734499280306
p-value0.288300663002148






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-130.980342912814
beta25.576709149761
S.D.20.1092246579225
T-STAT1.2718893734018
p-value0.29305543502788
Lambda-24.576709149761

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -130.980342912814 \tabularnewline
beta & 25.576709149761 \tabularnewline
S.D. & 20.1092246579225 \tabularnewline
T-STAT & 1.2718893734018 \tabularnewline
p-value & 0.29305543502788 \tabularnewline
Lambda & -24.576709149761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164869&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-130.980342912814[/C][/ROW]
[ROW][C]beta[/C][C]25.576709149761[/C][/ROW]
[ROW][C]S.D.[/C][C]20.1092246579225[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.2718893734018[/C][/ROW]
[ROW][C]p-value[/C][C]0.29305543502788[/C][/ROW]
[ROW][C]Lambda[/C][C]-24.576709149761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164869&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-130.980342912814
beta25.576709149761
S.D.20.1092246579225
T-STAT1.2718893734018
p-value0.29305543502788
Lambda-24.576709149761


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')