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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 computationTue, 15 Dec 2009 08:35:02 -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/15/t1260891374gwxf1u92nwno3up.htm/, Retrieved Wed, 08 May 2024 16:27:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67980, Retrieved Wed, 08 May 2024 16:27:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [mean plot bel20] [2008-12-10 18:16:19] [74be16979710d4c4e7c6647856088456]
-  M D  [Standard Deviation-Mean Plot] [] [2009-12-15 12:36:38] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   PD      [Standard Deviation-Mean Plot] [] [2009-12-15 15:35:02] [5858ea01c9bd81debbf921a11363ad90] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
27
29
27
26
24
30
26
28
28
24
23
24
24
27
28
25
19
19
19
20
16
22
21
25
29
28
25
26
24
28
28
28
28
32
31
22
29
31
29
32
32
31
29
28
28
29
22
26
24
27
27
23
21
19
17
19
21
13
8
5
10
6
6
8
11
12
13
19
19
18
20

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67980&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67980&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
126.33333333333332.229281716090857
222.08333333333333.7040109300185612
327.41666666666672.8109633849474410
428.83333333333332.7906771199618910
518.66666666666676.9587529359966822

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 26.3333333333333 & 2.22928171609085 & 7 \tabularnewline
2 & 22.0833333333333 & 3.70401093001856 & 12 \tabularnewline
3 & 27.4166666666667 & 2.81096338494744 & 10 \tabularnewline
4 & 28.8333333333333 & 2.79067711996189 & 10 \tabularnewline
5 & 18.6666666666667 & 6.95875293599668 & 22 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67980&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]26.3333333333333[/C][C]2.22928171609085[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]22.0833333333333[/C][C]3.70401093001856[/C][C]12[/C][/ROW]
[ROW][C]3[/C][C]27.4166666666667[/C][C]2.81096338494744[/C][C]10[/C][/ROW]
[ROW][C]4[/C][C]28.8333333333333[/C][C]2.79067711996189[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]18.6666666666667[/C][C]6.95875293599668[/C][C]22[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67980&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
126.33333333333332.229281716090857
222.08333333333333.7040109300185612
327.41666666666672.8109633849474410
428.83333333333332.7906771199618910
518.66666666666676.9587529359966822






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha13.5996734111026
beta-0.401389305149981
S.D.0.120417500885738
T-STAT-3.33331369773944
p-value0.0446089313999942

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 13.5996734111026 \tabularnewline
beta & -0.401389305149981 \tabularnewline
S.D. & 0.120417500885738 \tabularnewline
T-STAT & -3.33331369773944 \tabularnewline
p-value & 0.0446089313999942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67980&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.5996734111026[/C][/ROW]
[ROW][C]beta[/C][C]-0.401389305149981[/C][/ROW]
[ROW][C]S.D.[/C][C]0.120417500885738[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.33331369773944[/C][/ROW]
[ROW][C]p-value[/C][C]0.0446089313999942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67980&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)
alpha13.5996734111026
beta-0.401389305149981
S.D.0.120417500885738
T-STAT-3.33331369773944
p-value0.0446089313999942






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.34650492460406
beta-2.23122051745668
S.D.0.583423354184177
T-STAT-3.82435927779525
p-value0.0314803035402711
Lambda3.23122051745668

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.34650492460406 \tabularnewline
beta & -2.23122051745668 \tabularnewline
S.D. & 0.583423354184177 \tabularnewline
T-STAT & -3.82435927779525 \tabularnewline
p-value & 0.0314803035402711 \tabularnewline
Lambda & 3.23122051745668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67980&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.34650492460406[/C][/ROW]
[ROW][C]beta[/C][C]-2.23122051745668[/C][/ROW]
[ROW][C]S.D.[/C][C]0.583423354184177[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.82435927779525[/C][/ROW]
[ROW][C]p-value[/C][C]0.0314803035402711[/C][/ROW]
[ROW][C]Lambda[/C][C]3.23122051745668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67980&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)
alpha8.34650492460406
beta-2.23122051745668
S.D.0.583423354184177
T-STAT-3.82435927779525
p-value0.0314803035402711
Lambda3.23122051745668


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')