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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 computationSun, 22 Nov 2009 08:55:09 -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/22/t12589053403pk09xig6pjvtkl.htm/, Retrieved Sun, 28 Apr 2024 16:58:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58651, Retrieved Sun, 28 Apr 2024 16:58:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208

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]
-    D          [Standard Deviation-Mean Plot] [WS 8 30] [2009-11-22 15:55:09] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
-    D            [Standard Deviation-Mean Plot] [Paper heteroskeda...] [2010-12-21 11:22:29] [a9e130f95bad0a0597234e75c6380c5a]
-    D              [Standard Deviation-Mean Plot] [] [2011-12-20 19:19:22] [06f5daa9a1979410bf169cb7a41fb3eb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,63
103,64
103,66
103,77
103,88
103,91
103,91
103,92
104,05
104,23
104,30
104,31
104,31
104,34
104,55
104,65
104,73
104,75
104,75
104,76
104,94
105,29
105,38
105,43
105,43
105,42
105,52
105,69
105,72
105,74
105,74
105,74
105,95
106,17
106,34
106,37
106,37
106,36
106,44
106,29
106,23
106,23
106,23
106,23
106,34
106,44
106,44
106,48
106,50
106,57
106,40
106,37
106,25
106,21
106,21
106,24
106,19
106,08
106,13
106,09

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=58651&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=58651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58651&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
1103.9341666666670.2452256227652540.680000000000007
2104.8233333333330.3735172707053201.12000000000000
3105.8191666666670.3248064691847180.950000000000003
4106.340.09620054809898480.25
5106.270.1574801574802370.489999999999995

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.934166666667 & 0.245225622765254 & 0.680000000000007 \tabularnewline
2 & 104.823333333333 & 0.373517270705320 & 1.12000000000000 \tabularnewline
3 & 105.819166666667 & 0.324806469184718 & 0.950000000000003 \tabularnewline
4 & 106.34 & 0.0962005480989848 & 0.25 \tabularnewline
5 & 106.27 & 0.157480157480237 & 0.489999999999995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58651&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]103.934166666667[/C][C]0.245225622765254[/C][C]0.680000000000007[/C][/ROW]
[ROW][C]2[/C][C]104.823333333333[/C][C]0.373517270705320[/C][C]1.12000000000000[/C][/ROW]
[ROW][C]3[/C][C]105.819166666667[/C][C]0.324806469184718[/C][C]0.950000000000003[/C][/ROW]
[ROW][C]4[/C][C]106.34[/C][C]0.0962005480989848[/C][C]0.25[/C][/ROW]
[ROW][C]5[/C][C]106.27[/C][C]0.157480157480237[/C][C]0.489999999999995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58651&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
1103.9341666666670.2452256227652540.680000000000007
2104.8233333333330.3735172707053201.12000000000000
3105.8191666666670.3248064691847180.950000000000003
4106.340.09620054809898480.25
5106.270.1574801574802370.489999999999995






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.52981956815439
beta-0.0596598316330789
S.D.0.0538045679663539
T-STAT-1.10882465723703
p-value0.348404340005441

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.52981956815439 \tabularnewline
beta & -0.0596598316330789 \tabularnewline
S.D. & 0.0538045679663539 \tabularnewline
T-STAT & -1.10882465723703 \tabularnewline
p-value & 0.348404340005441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58651&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.52981956815439[/C][/ROW]
[ROW][C]beta[/C][C]-0.0596598316330789[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0538045679663539[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.10882465723703[/C][/ROW]
[ROW][C]p-value[/C][C]0.348404340005441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58651&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)
alpha6.52981956815439
beta-0.0596598316330789
S.D.0.0538045679663539
T-STAT-1.10882465723703
p-value0.348404340005441






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha153.70996774294
beta-33.3293903172517
S.D.26.3061247926034
T-STAT-1.26698214123211
p-value0.294582124757157
Lambda34.3293903172517

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 153.70996774294 \tabularnewline
beta & -33.3293903172517 \tabularnewline
S.D. & 26.3061247926034 \tabularnewline
T-STAT & -1.26698214123211 \tabularnewline
p-value & 0.294582124757157 \tabularnewline
Lambda & 34.3293903172517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58651&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]153.70996774294[/C][/ROW]
[ROW][C]beta[/C][C]-33.3293903172517[/C][/ROW]
[ROW][C]S.D.[/C][C]26.3061247926034[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.26698214123211[/C][/ROW]
[ROW][C]p-value[/C][C]0.294582124757157[/C][/ROW]
[ROW][C]Lambda[/C][C]34.3293903172517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58651&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58651&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)
alpha153.70996774294
beta-33.3293903172517
S.D.26.3061247926034
T-STAT-1.26698214123211
p-value0.294582124757157
Lambda34.3293903172517


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')