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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, 12 Dec 2012 07:06:16 -0500
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/Dec/12/t1355313986yyynothigt2do8e.htm/, Retrieved Mon, 29 Apr 2024 09:42:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198833, Retrieved Mon, 29 Apr 2024 09:42:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2012-12-12 12:06:16] [b7ec516ed4ac617af0f7d8ff855a58b9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15,58
15,66
15,73
15,74
15,77
15,78
15,8
15,81
15,82
15,88
15,85
15,89
15,92
16,02
16,1
16,13
16,21
16,25
16,27
16,21
16,21
16,24
16,32
16,32
16,36
16,48
16,54
16,58
16,56
16,55
16,58
16,53
16,6
16,46
16,48
16,48
16,49
16,54
16,67
16,72
16,79
16,86
16,84
16,86
16,96
17,01
17,02
17,04
17,04
17,39
17,54
17,57
17,58
17,56
17,63
17,67
17,71
17,75
17,82
17,86
17,89
17,96
18
18,08
18
18,02
18,01
18,02
17,95
17,96
18
18,01

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198833&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]2 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=198833&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198833&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115.77583333333330.08959082068780910.31
216.18333333333330.120780291388450.4
316.51666666666670.06773388212614690.240000000000002
416.81666666666670.1829720959020470.550000000000001
517.59333333333330.2174368595219950.82
617.99166666666670.04706539615419680.189999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.7758333333333 & 0.0895908206878091 & 0.31 \tabularnewline
2 & 16.1833333333333 & 0.12078029138845 & 0.4 \tabularnewline
3 & 16.5166666666667 & 0.0677338821261469 & 0.240000000000002 \tabularnewline
4 & 16.8166666666667 & 0.182972095902047 & 0.550000000000001 \tabularnewline
5 & 17.5933333333333 & 0.217436859521995 & 0.82 \tabularnewline
6 & 17.9916666666667 & 0.0470653961541968 & 0.189999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198833&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]15.7758333333333[/C][C]0.0895908206878091[/C][C]0.31[/C][/ROW]
[ROW][C]2[/C][C]16.1833333333333[/C][C]0.12078029138845[/C][C]0.4[/C][/ROW]
[ROW][C]3[/C][C]16.5166666666667[/C][C]0.0677338821261469[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]4[/C][C]16.8166666666667[/C][C]0.182972095902047[/C][C]0.550000000000001[/C][/ROW]
[ROW][C]5[/C][C]17.5933333333333[/C][C]0.217436859521995[/C][C]0.82[/C][/ROW]
[ROW][C]6[/C][C]17.9916666666667[/C][C]0.0470653961541968[/C][C]0.189999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198833&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198833&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
115.77583333333330.08959082068780910.31
216.18333333333330.120780291388450.4
316.51666666666670.06773388212614690.240000000000002
416.81666666666670.1829720959020470.550000000000001
517.59333333333330.2174368595219950.82
617.99166666666670.04706539615419680.189999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0531212410101412
beta0.0103522271253896
S.D.0.0393598846835634
T-STAT0.263014671120536
p-value0.805531201440194

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0531212410101412 \tabularnewline
beta & 0.0103522271253896 \tabularnewline
S.D. & 0.0393598846835634 \tabularnewline
T-STAT & 0.263014671120536 \tabularnewline
p-value & 0.805531201440194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198833&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0531212410101412[/C][/ROW]
[ROW][C]beta[/C][C]0.0103522271253896[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0393598846835634[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.263014671120536[/C][/ROW]
[ROW][C]p-value[/C][C]0.805531201440194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198833&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198833&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-0.0531212410101412
beta0.0103522271253896
S.D.0.0393598846835634
T-STAT0.263014671120536
p-value0.805531201440194






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.29487951118986
beta-0.692970879145034
S.D.5.86041076355824
T-STAT-0.118246127635648
p-value0.911572793193421
Lambda1.69297087914503

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.29487951118986 \tabularnewline
beta & -0.692970879145034 \tabularnewline
S.D. & 5.86041076355824 \tabularnewline
T-STAT & -0.118246127635648 \tabularnewline
p-value & 0.911572793193421 \tabularnewline
Lambda & 1.69297087914503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198833&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.29487951118986[/C][/ROW]
[ROW][C]beta[/C][C]-0.692970879145034[/C][/ROW]
[ROW][C]S.D.[/C][C]5.86041076355824[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.118246127635648[/C][/ROW]
[ROW][C]p-value[/C][C]0.911572793193421[/C][/ROW]
[ROW][C]Lambda[/C][C]1.69297087914503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198833&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198833&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-0.29487951118986
beta-0.692970879145034
S.D.5.86041076355824
T-STAT-0.118246127635648
p-value0.911572793193421
Lambda1.69297087914503


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')