FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 27 May 2009 15:51:58 -0600
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/May/27/t1243461214qpar1tr4nn9455c.htm/, Retrieved Thu, 02 May 2024 17:27:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40522, Retrieved Thu, 02 May 2024 17:27:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

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] [standard deviatio...] [2009-01-08 20:44:55] [a18c43c8b63fa6800a53bb187b9ddd45]
-    D    [Standard Deviation-Mean Plot] [Maxime Jonckheere...] [2009-05-27 21:51:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66.2
66.2
66.2
66.08
66.31
66.39
66.37
66.23
66.27
66.27
66.27
66.28
66.28
66.28
66.26
66.13
65.86
65.9
65.94
65.94
65.91
65.95
65.91
66.08
66.47
66.47
66.56
66.78
67.08
67.28
67.27
67.27
67.26
67.37
67.5
67.63
67.64
67.64
67.71
67.87
67.93
68.33
68.39
68.39
68.58
68.44
68.49
68.52
68.54
68.54
68.54
68.62
68.75
68.71
68.72
68.72
68.72
68.92
68.9
69.12
69.09
69.09
69.1
69.16
68.83
68.52
68.53
68.53
68.51
68.38
68.44
68.41
68.42
68.42
68.45
68.63
68.84
68.72
68.37
68.37
68.47
68.69
68.46
68.17
68.17

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=40522&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=40522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40522&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
166.25583333333330.08317105411394220.310000000000002
266.03666666666670.1615455653893660.420000000000002
367.07833333333330.4058847425592931.16000000000000
468.16083333333330.3702936999766850.939999999999998
568.73333333333330.1754129327321590.579999999999998
668.71583333333330.3118991192774690.780000000000001
768.50083333333330.1852496268347760.670000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.2558333333333 & 0.0831710541139422 & 0.310000000000002 \tabularnewline
2 & 66.0366666666667 & 0.161545565389366 & 0.420000000000002 \tabularnewline
3 & 67.0783333333333 & 0.405884742559293 & 1.16000000000000 \tabularnewline
4 & 68.1608333333333 & 0.370293699976685 & 0.939999999999998 \tabularnewline
5 & 68.7333333333333 & 0.175412932732159 & 0.579999999999998 \tabularnewline
6 & 68.7158333333333 & 0.311899119277469 & 0.780000000000001 \tabularnewline
7 & 68.5008333333333 & 0.185249626834776 & 0.670000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40522&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]66.2558333333333[/C][C]0.0831710541139422[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]2[/C][C]66.0366666666667[/C][C]0.161545565389366[/C][C]0.420000000000002[/C][/ROW]
[ROW][C]3[/C][C]67.0783333333333[/C][C]0.405884742559293[/C][C]1.16000000000000[/C][/ROW]
[ROW][C]4[/C][C]68.1608333333333[/C][C]0.370293699976685[/C][C]0.939999999999998[/C][/ROW]
[ROW][C]5[/C][C]68.7333333333333[/C][C]0.175412932732159[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]6[/C][C]68.7158333333333[/C][C]0.311899119277469[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]7[/C][C]68.5008333333333[/C][C]0.185249626834776[/C][C]0.670000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40522&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
166.25583333333330.08317105411394220.310000000000002
266.03666666666670.1615455653893660.420000000000002
367.07833333333330.4058847425592931.16000000000000
468.16083333333330.3702936999766850.939999999999998
568.73333333333330.1754129327321590.579999999999998
668.71583333333330.3118991192774690.780000000000001
768.50083333333330.1852496268347760.670000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.05348973318266
beta0.0339356008993568
S.D.0.0437470704540172
T-STAT0.775722820914986
p-value0.472988655896573

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.05348973318266 \tabularnewline
beta & 0.0339356008993568 \tabularnewline
S.D. & 0.0437470704540172 \tabularnewline
T-STAT & 0.775722820914986 \tabularnewline
p-value & 0.472988655896573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40522&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.05348973318266[/C][/ROW]
[ROW][C]beta[/C][C]0.0339356008993568[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0437470704540172[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.775722820914986[/C][/ROW]
[ROW][C]p-value[/C][C]0.472988655896573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40522&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-2.05348973318266
beta0.0339356008993568
S.D.0.0437470704540172
T-STAT0.775722820914986
p-value0.472988655896573






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-62.7045464737371
beta14.5137806734736
S.D.12.9465657991261
T-STAT1.12105255545477
p-value0.313201168448140
Lambda-13.5137806734736

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -62.7045464737371 \tabularnewline
beta & 14.5137806734736 \tabularnewline
S.D. & 12.9465657991261 \tabularnewline
T-STAT & 1.12105255545477 \tabularnewline
p-value & 0.313201168448140 \tabularnewline
Lambda & -13.5137806734736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40522&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-62.7045464737371[/C][/ROW]
[ROW][C]beta[/C][C]14.5137806734736[/C][/ROW]
[ROW][C]S.D.[/C][C]12.9465657991261[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.12105255545477[/C][/ROW]
[ROW][C]p-value[/C][C]0.313201168448140[/C][/ROW]
[ROW][C]Lambda[/C][C]-13.5137806734736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40522&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40522&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-62.7045464737371
beta14.5137806734736
S.D.12.9465657991261
T-STAT1.12105255545477
p-value0.313201168448140
Lambda-13.5137806734736


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')