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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 03 Dec 2009 02:34:00 -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/2009/Dec/03/t1259833360w10kbagxxa2dzmc.htm/, Retrieved Fri, 19 Apr 2024 08:31:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62647, Retrieved Fri, 19 Apr 2024 08:31:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
- R  D      [Standard Deviation-Mean Plot] [] [2009-12-03 09:34:00] [2ecea65fec1cd5f6b1ab182881aa2a91] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
19
25
21
23
23
19
18
19
19
22
23
20
14
14
14
15
11
17
16
20
24
23
20
21
19
23
23
23
23
27
26
17
24
26
24
27
27
26
24
23
23
24
17
21
19
22
22
18
16
14
12
14
16
8
3
0
5
1
1
3

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62647&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62647&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1212.215646837627997
217.33333333333334.0301891075263813
3232.8919952219248810
422.91666666666673.0289011909011510
596.7419986246324218

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 21 & 2.21564683762799 & 7 \tabularnewline
2 & 17.3333333333333 & 4.03018910752638 & 13 \tabularnewline
3 & 23 & 2.89199522192488 & 10 \tabularnewline
4 & 22.9166666666667 & 3.02890119090115 & 10 \tabularnewline
5 & 9 & 6.74199862463242 & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62647&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]21[/C][C]2.21564683762799[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]17.3333333333333[/C][C]4.03018910752638[/C][C]13[/C][/ROW]
[ROW][C]3[/C][C]23[/C][C]2.89199522192488[/C][C]10[/C][/ROW]
[ROW][C]4[/C][C]22.9166666666667[/C][C]3.02890119090115[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]6.74199862463242[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62647&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
1212.215646837627997
217.33333333333334.0301891075263813
3232.8919952219248810
422.91666666666673.0289011909011510
596.7419986246324218






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.1603843778644
beta-0.288398830098758
S.D.0.053913470123068
T-STAT-5.34929080692508
p-value0.0127783366164524

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.1603843778644 \tabularnewline
beta & -0.288398830098758 \tabularnewline
S.D. & 0.053913470123068 \tabularnewline
T-STAT & -5.34929080692508 \tabularnewline
p-value & 0.0127783366164524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62647&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.1603843778644[/C][/ROW]
[ROW][C]beta[/C][C]-0.288398830098758[/C][/ROW]
[ROW][C]S.D.[/C][C]0.053913470123068[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.34929080692508[/C][/ROW]
[ROW][C]p-value[/C][C]0.0127783366164524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62647&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)
alpha9.1603843778644
beta-0.288398830098758
S.D.0.053913470123068
T-STAT-5.34929080692508
p-value0.0127783366164524






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha4.07708938559989
beta-0.982999908643526
S.D.0.247754145712586
T-STAT-3.96764262336051
p-value0.0286096289810565
Lambda1.98299990864353

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.07708938559989 \tabularnewline
beta & -0.982999908643526 \tabularnewline
S.D. & 0.247754145712586 \tabularnewline
T-STAT & -3.96764262336051 \tabularnewline
p-value & 0.0286096289810565 \tabularnewline
Lambda & 1.98299990864353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62647&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.07708938559989[/C][/ROW]
[ROW][C]beta[/C][C]-0.982999908643526[/C][/ROW]
[ROW][C]S.D.[/C][C]0.247754145712586[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.96764262336051[/C][/ROW]
[ROW][C]p-value[/C][C]0.0286096289810565[/C][/ROW]
[ROW][C]Lambda[/C][C]1.98299990864353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62647&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62647&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)
alpha4.07708938559989
beta-0.982999908643526
S.D.0.247754145712586
T-STAT-3.96764262336051
p-value0.0286096289810565
Lambda1.98299990864353


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')