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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 computationMon, 17 Dec 2007 09:41:35 -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/Dec/17/t1197908696ko1y9wu49xwl6nx.htm/, Retrieved Sat, 04 May 2024 05:32:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4394, Retrieved Sat, 04 May 2024 05:32:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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] [] [2007-12-17 16:41:35] [d02236afd58a58d13a748bbf41a37c2e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3
6
4
15
3
2
5
0
3
9
5
2
4
10
2
5
2
5
8
4
9
6
4
0
6
6
15
7
3
14
7
12
8
11
23
5
11
6
22
9
11
17
19
12
3
6
17
5
3
7
7
4
19
17
10
10
9
9
3
3

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=4394&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=4394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4394&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
14.753.9571569224748912
24.916666666666672.968266507678524
39.755.5779598746886321
411.56.0976895773578218
58.416666666666675.2476545987592217

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.75 & 3.95715692247489 & 12 \tabularnewline
2 & 4.91666666666667 & 2.96826650767852 & 4 \tabularnewline
3 & 9.75 & 5.57795987468863 & 21 \tabularnewline
4 & 11.5 & 6.09768957735782 & 18 \tabularnewline
5 & 8.41666666666667 & 5.24765459875922 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4394&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]4.75[/C][C]3.95715692247489[/C][C]12[/C][/ROW]
[ROW][C]2[/C][C]4.91666666666667[/C][C]2.96826650767852[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]9.75[/C][C]5.57795987468863[/C][C]21[/C][/ROW]
[ROW][C]4[/C][C]11.5[/C][C]6.09768957735782[/C][C]18[/C][/ROW]
[ROW][C]5[/C][C]8.41666666666667[/C][C]5.24765459875922[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4394&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
14.753.9571569224748912
24.916666666666672.968266507678524
39.755.5779598746886321
411.56.0976895773578218
58.416666666666675.2476545987592217






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.56316618121955
beta0.407616014615118
S.D.0.0786310400976656
T-STAT5.18390719630351
p-value0.0139372314411746

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.56316618121955 \tabularnewline
beta & 0.407616014615118 \tabularnewline
S.D. & 0.0786310400976656 \tabularnewline
T-STAT & 5.18390719630351 \tabularnewline
p-value & 0.0139372314411746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4394&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.56316618121955[/C][/ROW]
[ROW][C]beta[/C][C]0.407616014615118[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0786310400976656[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.18390719630351[/C][/ROW]
[ROW][C]p-value[/C][C]0.0139372314411746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4394&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)
alpha1.56316618121955
beta0.407616014615118
S.D.0.0786310400976656
T-STAT5.18390719630351
p-value0.0139372314411746






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.176349354583884
beta0.676586304437201
S.D.0.160993511764909
T-STAT4.20256876826929
p-value0.0245922267695542
Lambda0.323413695562799

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.176349354583884 \tabularnewline
beta & 0.676586304437201 \tabularnewline
S.D. & 0.160993511764909 \tabularnewline
T-STAT & 4.20256876826929 \tabularnewline
p-value & 0.0245922267695542 \tabularnewline
Lambda & 0.323413695562799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4394&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.176349354583884[/C][/ROW]
[ROW][C]beta[/C][C]0.676586304437201[/C][/ROW]
[ROW][C]S.D.[/C][C]0.160993511764909[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.20256876826929[/C][/ROW]
[ROW][C]p-value[/C][C]0.0245922267695542[/C][/ROW]
[ROW][C]Lambda[/C][C]0.323413695562799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4394&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4394&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)
alpha0.176349354583884
beta0.676586304437201
S.D.0.160993511764909
T-STAT4.20256876826929
p-value0.0245922267695542
Lambda0.323413695562799


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')