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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 computationSat, 23 Apr 2016 19:44:49 +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/Apr/23/t1461437119o96eogxebs3omqt.htm/, Retrieved Sun, 12 May 2024 19:34:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294613, Retrieved Sun, 12 May 2024 19:34:57 +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)
-       [Standard Deviation-Mean Plot] [] [2016-04-23 18:44:49] [1b498ae19017f51f703ef2d779b672b0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.9
9.2
12.8
11.1
11.2
13.1
12.6
10
12.3
12.5
11.4
11.5
10.4
11
15
12.7
11.6
13.9
12.6
11.2
15.8
15.3
14
14.6
11.5
12.8
16.2
12.8
13.5
12.5
13.2
12
14.2
17.5
13.8
13.9
11.3
12.1
16.2
11.6
12.5
15.6
12.3
12
12.1
13.9
12.3
10.5
14.2
13.2
13.7
14.2
15.3
16.3
15.1
13.4
14
15.5
12.5
12.9
12.9
13.4
15
14.4
14
15.2
15
12.4
18.7
20.6
17.3
11.4

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'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294613&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294613&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111.38333333333331.397942210623324.2
213.1751.842490902900945.4
313.65833333333331.706915523996616
412.71.697056274847715.7
514.19166666666671.153223413924743.8
615.0252.670078310053519.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11.3833333333333 & 1.39794221062332 & 4.2 \tabularnewline
2 & 13.175 & 1.84249090290094 & 5.4 \tabularnewline
3 & 13.6583333333333 & 1.70691552399661 & 6 \tabularnewline
4 & 12.7 & 1.69705627484771 & 5.7 \tabularnewline
5 & 14.1916666666667 & 1.15322341392474 & 3.8 \tabularnewline
6 & 15.025 & 2.67007831005351 & 9.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294613&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]11.3833333333333[/C][C]1.39794221062332[/C][C]4.2[/C][/ROW]
[ROW][C]2[/C][C]13.175[/C][C]1.84249090290094[/C][C]5.4[/C][/ROW]
[ROW][C]3[/C][C]13.6583333333333[/C][C]1.70691552399661[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]12.7[/C][C]1.69705627484771[/C][C]5.7[/C][/ROW]
[ROW][C]5[/C][C]14.1916666666667[/C][C]1.15322341392474[/C][C]3.8[/C][/ROW]
[ROW][C]6[/C][C]15.025[/C][C]2.67007831005351[/C][C]9.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294613&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
111.38333333333331.397942210623324.2
213.1751.842490902900945.4
313.65833333333331.706915523996616
412.71.697056274847715.7
514.19166666666671.153223413924743.8
615.0252.670078310053519.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.17977331200285
beta0.218964390703377
S.D.0.173922133011101
T-STAT1.25897944621804
p-value0.276501354848163

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.17977331200285 \tabularnewline
beta & 0.218964390703377 \tabularnewline
S.D. & 0.173922133011101 \tabularnewline
T-STAT & 1.25897944621804 \tabularnewline
p-value & 0.276501354848163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294613&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.17977331200285[/C][/ROW]
[ROW][C]beta[/C][C]0.218964390703377[/C][/ROW]
[ROW][C]S.D.[/C][C]0.173922133011101[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.25897944621804[/C][/ROW]
[ROW][C]p-value[/C][C]0.276501354848163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294613&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294613&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)
alpha-1.17977331200285
beta0.218964390703377
S.D.0.173922133011101
T-STAT1.25897944621804
p-value0.276501354848163






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.82385227100931
beta1.29291983002034
S.D.1.31867268009724
T-STAT0.980470627422868
p-value0.382367495464395
Lambda-0.292919830020339

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.82385227100931 \tabularnewline
beta & 1.29291983002034 \tabularnewline
S.D. & 1.31867268009724 \tabularnewline
T-STAT & 0.980470627422868 \tabularnewline
p-value & 0.382367495464395 \tabularnewline
Lambda & -0.292919830020339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294613&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.82385227100931[/C][/ROW]
[ROW][C]beta[/C][C]1.29291983002034[/C][/ROW]
[ROW][C]S.D.[/C][C]1.31867268009724[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.980470627422868[/C][/ROW]
[ROW][C]p-value[/C][C]0.382367495464395[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.292919830020339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294613&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294613&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-2.82385227100931
beta1.29291983002034
S.D.1.31867268009724
T-STAT0.980470627422868
p-value0.382367495464395
Lambda-0.292919830020339


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')