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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 computationWed, 21 Dec 2016 15:12:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482329758tuygslusdde43zp.htm/, Retrieved Mon, 06 May 2024 21:56:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302312, Retrieved Mon, 06 May 2024 21:56:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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] [Standard Deviatio...] [2016-12-21 14:12:14] [1759881725a0396915ebed807ae3b27a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4450
4400
4650
4800
4800
4750
5200
5050
4900
5300
5500
6050
5200
5350
5450
5900
5800
5950
6750
6500
6500
7100
7100
8400
6900
7400
7650
7850
7750
8000
8950
9100
9100
10050
10450
11900
10000
11250
11250
11650
11550
11800
13050
12350
12200
13450
13450
14450
12500
13350
13600
13200
13450
13600
14450
14000
13600
14700
14450
15250
13750
14450
14300
14600
14700
14600

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302312&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302312&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14987.5469.1021404575111650
26333.33333333333920.803338329523200
38758.333333333331465.176584662215000
412204.16666666671223.344583384824450
513845.8333333333754.8203679543812750

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4987.5 & 469.102140457511 & 1650 \tabularnewline
2 & 6333.33333333333 & 920.80333832952 & 3200 \tabularnewline
3 & 8758.33333333333 & 1465.17658466221 & 5000 \tabularnewline
4 & 12204.1666666667 & 1223.34458338482 & 4450 \tabularnewline
5 & 13845.8333333333 & 754.820367954381 & 2750 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302312&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]4987.5[/C][C]469.102140457511[/C][C]1650[/C][/ROW]
[ROW][C]2[/C][C]6333.33333333333[/C][C]920.80333832952[/C][C]3200[/C][/ROW]
[ROW][C]3[/C][C]8758.33333333333[/C][C]1465.17658466221[/C][C]5000[/C][/ROW]
[ROW][C]4[/C][C]12204.1666666667[/C][C]1223.34458338482[/C][C]4450[/C][/ROW]
[ROW][C]5[/C][C]13845.8333333333[/C][C]754.820367954381[/C][C]2750[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302312&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
14987.5469.1021404575111650
26333.33333333333920.803338329523200
38758.333333333331465.176584662215000
412204.16666666671223.344583384824450
513845.8333333333754.8203679543812750






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha675.036998701015
beta0.0316082454257075
S.D.0.0569465981456117
T-STAT0.555050634366
p-value0.617561316222668

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 675.036998701015 \tabularnewline
beta & 0.0316082454257075 \tabularnewline
S.D. & 0.0569465981456117 \tabularnewline
T-STAT & 0.555050634366 \tabularnewline
p-value & 0.617561316222668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302312&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]675.036998701015[/C][/ROW]
[ROW][C]beta[/C][C]0.0316082454257075[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0569465981456117[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.555050634366[/C][/ROW]
[ROW][C]p-value[/C][C]0.617561316222668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302312&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)
alpha675.036998701015
beta0.0316082454257075
S.D.0.0569465981456117
T-STAT0.555050634366
p-value0.617561316222668






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.14247842836236
beta0.514209723687111
S.D.0.516391411226467
T-STAT0.99577512814519
p-value0.392752882358961
Lambda0.485790276312889

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.14247842836236 \tabularnewline
beta & 0.514209723687111 \tabularnewline
S.D. & 0.516391411226467 \tabularnewline
T-STAT & 0.99577512814519 \tabularnewline
p-value & 0.392752882358961 \tabularnewline
Lambda & 0.485790276312889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302312&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.14247842836236[/C][/ROW]
[ROW][C]beta[/C][C]0.514209723687111[/C][/ROW]
[ROW][C]S.D.[/C][C]0.516391411226467[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.99577512814519[/C][/ROW]
[ROW][C]p-value[/C][C]0.392752882358961[/C][/ROW]
[ROW][C]Lambda[/C][C]0.485790276312889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302312&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302312&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)
alpha2.14247842836236
beta0.514209723687111
S.D.0.516391411226467
T-STAT0.99577512814519
p-value0.392752882358961
Lambda0.485790276312889


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')