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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 computationThu, 29 Nov 2007 01:38:24 -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/2007/Nov/29/t11963249181dxo1r0b02l9hox.htm/, Retrieved Fri, 03 May 2024 05:09:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7284, Retrieved Fri, 03 May 2024 05:09:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237

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] [Inducing Stationa...] [2007-11-29 08:38:24] [031886dbad66702fa31ca1c4d15fdd0f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,25
5,02
4,73
4,57
4,52
4,37
4,77
4,57
4,41
4,26
4,01
3,81
3,38
3,68
3,85
4,09
4
4,38
4,21
4,39
4,09
3,84
3,57
3,24
3,35
3,29
2,84
2,7
2,46
2,57
2,6
2,3
2,21
2,36
2,61
2,37
2,73
2,89
2,62
2,56
2,24
2,31
2,61
2,66
2,79
2,69
2,49
2,64
2,47
2,42
2,49
2,4
2,47
2,56
2,32
2,21
2,04
2,21
2,21
2,41
2,67
2,79
2,85
2,98
3,05
3,33
3,45
3,38
3,57
3,53
3,53
3,56
3,7
3,66
3,87
3,98
3,88
4,02
4,16
4,39
4,46
4,33
4,12
4,17
4,02

Tables (Output of Computation)





Summary of compuational 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 compuational 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=7284&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7284&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 compuational 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
14.524166666666670.4000785907642132.78
23.893333333333330.3714427236731081.97
32.638333333333330.3645378976017160.86
42.60250.1854294769153250.49
52.350833333333330.1535316569863350.32
63.224166666666670.3345949609285651.26
74.061666666666670.2582399635762812.14

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.52416666666667 & 0.400078590764213 & 2.78 \tabularnewline
2 & 3.89333333333333 & 0.371442723673108 & 1.97 \tabularnewline
3 & 2.63833333333333 & 0.364537897601716 & 0.86 \tabularnewline
4 & 2.6025 & 0.185429476915325 & 0.49 \tabularnewline
5 & 2.35083333333333 & 0.153531656986335 & 0.32 \tabularnewline
6 & 3.22416666666667 & 0.334594960928565 & 1.26 \tabularnewline
7 & 4.06166666666667 & 0.258239963576281 & 2.14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7284&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]4.52416666666667[/C][C]0.400078590764213[/C][C]2.78[/C][/ROW]
[ROW][C]2[/C][C]3.89333333333333[/C][C]0.371442723673108[/C][C]1.97[/C][/ROW]
[ROW][C]3[/C][C]2.63833333333333[/C][C]0.364537897601716[/C][C]0.86[/C][/ROW]
[ROW][C]4[/C][C]2.6025[/C][C]0.185429476915325[/C][C]0.49[/C][/ROW]
[ROW][C]5[/C][C]2.35083333333333[/C][C]0.153531656986335[/C][C]0.32[/C][/ROW]
[ROW][C]6[/C][C]3.22416666666667[/C][C]0.334594960928565[/C][C]1.26[/C][/ROW]
[ROW][C]7[/C][C]4.06166666666667[/C][C]0.258239963576281[/C][C]2.14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7284&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
14.524166666666670.4000785907642132.78
23.893333333333330.3714427236731081.97
32.638333333333330.3645378976017160.86
42.60250.1854294769153250.49
52.350833333333330.1535316569863350.32
63.224166666666670.3345949609285651.26
74.061666666666670.2582399635762812.14






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0549062015037229
beta0.0722692363133497
S.D.0.0402207662808623
T-STAT1.79681400917855
p-value0.132299139703184

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0549062015037229 \tabularnewline
beta & 0.0722692363133497 \tabularnewline
S.D. & 0.0402207662808623 \tabularnewline
T-STAT & 1.79681400917855 \tabularnewline
p-value & 0.132299139703184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7284&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0549062015037229[/C][/ROW]
[ROW][C]beta[/C][C]0.0722692363133497[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0402207662808623[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.79681400917855[/C][/ROW]
[ROW][C]p-value[/C][C]0.132299139703184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7284&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)
alpha0.0549062015037229
beta0.0722692363133497
S.D.0.0402207662808623
T-STAT1.79681400917855
p-value0.132299139703184






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.42318584584142
beta0.977711347348327
S.D.0.493247325634440
T-STAT1.98219290107807
p-value0.104285347231333
Lambda0.0222886526516727

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.42318584584142 \tabularnewline
beta & 0.977711347348327 \tabularnewline
S.D. & 0.493247325634440 \tabularnewline
T-STAT & 1.98219290107807 \tabularnewline
p-value & 0.104285347231333 \tabularnewline
Lambda & 0.0222886526516727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7284&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.42318584584142[/C][/ROW]
[ROW][C]beta[/C][C]0.977711347348327[/C][/ROW]
[ROW][C]S.D.[/C][C]0.493247325634440[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.98219290107807[/C][/ROW]
[ROW][C]p-value[/C][C]0.104285347231333[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0222886526516727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7284&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-2.42318584584142
beta0.977711347348327
S.D.0.493247325634440
T-STAT1.98219290107807
p-value0.104285347231333
Lambda0.0222886526516727


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')