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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, 27 May 2015 07:34:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/27/t143270854851kgwmqs9qf53y3.htm/, Retrieved Sat, 04 May 2024 15:12:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279455, Retrieved Sat, 04 May 2024 15:12:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [] [2015-04-02 21:31:50] [693750cd301bd4fecbcaa8326eb70b61]
- R PD    [Standard Deviation-Mean Plot] [] [2015-05-27 06:34:59] [567f06ca3de45fa0ce67a0a89b883c29] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94,67
94,6
93,9
93,41
93,37
93,35
93,08
93,05
92,61
92,37
92,24
91,95
92,63
92,7
92,47
92,58
92,55
92,56
89,92
89,96
90,03
90,31
90,8
90,36
90,31
93,8
93,95
93,99
94,44
94,15
91,91
91,86
93,12
93,47
93,57
94,57
95,85
96,62
95,69
95,39
95,14
95,07
94,21
95,4
95,1
94,89
95,43
94,88
96,03
96,37
96,04
95,72
95,74
95,78
93,66
95,29
94,33
95,66
95,2
94,61
96,21
96,27
95,12
95,55
93,51
92,86
92,45
93,34
92,01
91,77
92,19
91,97

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'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279455&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279455&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'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
193.21666666666670.8666060584868192.72
291.40583333333331.249672381308822.78
393.26166666666671.273719202202984.25999999999999
495.30583333333330.5941144415825732.41000000000001
595.36916666666670.7985607318321162.71000000000001
693.60416666666671.719447365412574.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 93.2166666666667 & 0.866606058486819 & 2.72 \tabularnewline
2 & 91.4058333333333 & 1.24967238130882 & 2.78 \tabularnewline
3 & 93.2616666666667 & 1.27371920220298 & 4.25999999999999 \tabularnewline
4 & 95.3058333333333 & 0.594114441582573 & 2.41000000000001 \tabularnewline
5 & 95.3691666666667 & 0.798560731832116 & 2.71000000000001 \tabularnewline
6 & 93.6041666666667 & 1.71944736541257 & 4.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279455&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]93.2166666666667[/C][C]0.866606058486819[/C][C]2.72[/C][/ROW]
[ROW][C]2[/C][C]91.4058333333333[/C][C]1.24967238130882[/C][C]2.78[/C][/ROW]
[ROW][C]3[/C][C]93.2616666666667[/C][C]1.27371920220298[/C][C]4.25999999999999[/C][/ROW]
[ROW][C]4[/C][C]95.3058333333333[/C][C]0.594114441582573[/C][C]2.41000000000001[/C][/ROW]
[ROW][C]5[/C][C]95.3691666666667[/C][C]0.798560731832116[/C][C]2.71000000000001[/C][/ROW]
[ROW][C]6[/C][C]93.6041666666667[/C][C]1.71944736541257[/C][C]4.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279455&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
193.21666666666670.8666060584868192.72
291.40583333333331.249672381308822.78
393.26166666666671.273719202202984.25999999999999
495.30583333333330.5941144415825732.41000000000001
595.36916666666670.7985607318321162.71000000000001
693.60416666666671.719447365412574.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha15.3307562384045
beta-0.152059752354775
S.D.0.1145022124506
T-STAT-1.3280071109576
p-value0.254886146546347

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.3307562384045 \tabularnewline
beta & -0.152059752354775 \tabularnewline
S.D. & 0.1145022124506 \tabularnewline
T-STAT & -1.3280071109576 \tabularnewline
p-value & 0.254886146546347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279455&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.3307562384045[/C][/ROW]
[ROW][C]beta[/C][C]-0.152059752354775[/C][/ROW]
[ROW][C]S.D.[/C][C]0.1145022124506[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.3280071109576[/C][/ROW]
[ROW][C]p-value[/C][C]0.254886146546347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279455&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)
alpha15.3307562384045
beta-0.152059752354775
S.D.0.1145022124506
T-STAT-1.3280071109576
p-value0.254886146546347






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha69.209559574566
beta-15.2403062041839
S.D.9.41225308566745
T-STAT-1.61919851341345
p-value0.180717331246747
Lambda16.2403062041839

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 69.209559574566 \tabularnewline
beta & -15.2403062041839 \tabularnewline
S.D. & 9.41225308566745 \tabularnewline
T-STAT & -1.61919851341345 \tabularnewline
p-value & 0.180717331246747 \tabularnewline
Lambda & 16.2403062041839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279455&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]69.209559574566[/C][/ROW]
[ROW][C]beta[/C][C]-15.2403062041839[/C][/ROW]
[ROW][C]S.D.[/C][C]9.41225308566745[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.61919851341345[/C][/ROW]
[ROW][C]p-value[/C][C]0.180717331246747[/C][/ROW]
[ROW][C]Lambda[/C][C]16.2403062041839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279455&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)
alpha69.209559574566
beta-15.2403062041839
S.D.9.41225308566745
T-STAT-1.61919851341345
p-value0.180717331246747
Lambda16.2403062041839


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0,1 ; par2 = 0,9 ;
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')