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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 computationFri, 29 May 2009 12:37:55 -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/29/t1243622324pjuu69tpw78f2sw.htm/, Retrieved Sat, 27 Apr 2024 18:40:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40785, Retrieved Sat, 27 Apr 2024 18:40:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

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] [maandelijkse gem ...] [2009-05-29 18:37:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40785&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40785&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13.490833333333330.0431610795495060.1
23.619166666666670.0608213977498250.17
33.750833333333330.05401318581998510.110000000000000
44.096666666666670.1320697703580360.39
54.420.0628128533459080.220000000000000
64.52250.09964710459689950.230000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.49083333333333 & 0.043161079549506 & 0.1 \tabularnewline
2 & 3.61916666666667 & 0.060821397749825 & 0.17 \tabularnewline
3 & 3.75083333333333 & 0.0540131858199851 & 0.110000000000000 \tabularnewline
4 & 4.09666666666667 & 0.132069770358036 & 0.39 \tabularnewline
5 & 4.42 & 0.062812853345908 & 0.220000000000000 \tabularnewline
6 & 4.5225 & 0.0996471045968995 & 0.230000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40785&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]3.49083333333333[/C][C]0.043161079549506[/C][C]0.1[/C][/ROW]
[ROW][C]2[/C][C]3.61916666666667[/C][C]0.060821397749825[/C][C]0.17[/C][/ROW]
[ROW][C]3[/C][C]3.75083333333333[/C][C]0.0540131858199851[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]4[/C][C]4.09666666666667[/C][C]0.132069770358036[/C][C]0.39[/C][/ROW]
[ROW][C]5[/C][C]4.42[/C][C]0.062812853345908[/C][C]0.220000000000000[/C][/ROW]
[ROW][C]6[/C][C]4.5225[/C][C]0.0996471045968995[/C][C]0.230000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40785&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
13.490833333333330.0431610795495060.1
23.619166666666670.0608213977498250.17
33.750833333333330.05401318581998510.110000000000000
44.096666666666670.1320697703580360.39
54.420.0628128533459080.220000000000000
64.52250.09964710459689950.230000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0978039133276897
beta0.0434874004764141
S.D.0.0325795313055631
T-STAT1.33480743073147
p-value0.252847677020277

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0978039133276897 \tabularnewline
beta & 0.0434874004764141 \tabularnewline
S.D. & 0.0325795313055631 \tabularnewline
T-STAT & 1.33480743073147 \tabularnewline
p-value & 0.252847677020277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40785&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0978039133276897[/C][/ROW]
[ROW][C]beta[/C][C]0.0434874004764141[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0325795313055631[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.33480743073147[/C][/ROW]
[ROW][C]p-value[/C][C]0.252847677020277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40785&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-0.0978039133276897
beta0.0434874004764141
S.D.0.0325795313055631
T-STAT1.33480743073147
p-value0.252847677020277






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.09630889001864
beta2.49506328525115
S.D.1.47100660764982
T-STAT1.69616048784270
p-value0.165096197020729
Lambda-1.49506328525115

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.09630889001864 \tabularnewline
beta & 2.49506328525115 \tabularnewline
S.D. & 1.47100660764982 \tabularnewline
T-STAT & 1.69616048784270 \tabularnewline
p-value & 0.165096197020729 \tabularnewline
Lambda & -1.49506328525115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40785&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.09630889001864[/C][/ROW]
[ROW][C]beta[/C][C]2.49506328525115[/C][/ROW]
[ROW][C]S.D.[/C][C]1.47100660764982[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.69616048784270[/C][/ROW]
[ROW][C]p-value[/C][C]0.165096197020729[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.49506328525115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40785&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40785&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-6.09630889001864
beta2.49506328525115
S.D.1.47100660764982
T-STAT1.69616048784270
p-value0.165096197020729
Lambda-1.49506328525115


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')