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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, 07 Dec 2016 19:35:32 +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/07/t1481135778938j788beyx651w.htm/, Retrieved Tue, 07 May 2024 11:05:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298286, Retrieved Tue, 07 May 2024 11:05:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

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] [N830] [2016-12-07 18:35:32] [85f5800284aab30c091766186b093bb4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1389
1398.6
1459
1545.2
1629.6
1675.2
1797.2
1739.2
1925.4
1908.4
2256.4
2217.6
2471.2
2634.4
2729.8
2752.6
3436.8
3579.8
3559.8
3234
3872.2
3996.8
4142.8
3992.2
4846.8
4757.4
4483.2
5033.4
5403.8
5280.8
5217
5422.2
6238
6254.8
6429
5942.4

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=298286&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=298286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298286&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
11745.06666666667291.316302116424867.4
23366.86666666667593.3191588364771671.6
35442.4640.0625253548571945.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1745.06666666667 & 291.316302116424 & 867.4 \tabularnewline
2 & 3366.86666666667 & 593.319158836477 & 1671.6 \tabularnewline
3 & 5442.4 & 640.062525354857 & 1945.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298286&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]1745.06666666667[/C][C]291.316302116424[/C][C]867.4[/C][/ROW]
[ROW][C]2[/C][C]3366.86666666667[/C][C]593.319158836477[/C][C]1671.6[/C][/ROW]
[ROW][C]3[/C][C]5442.4[/C][C]640.062525354857[/C][C]1945.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298286&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
11745.06666666667291.316302116424867.4
23366.86666666667593.3191588364771671.6
35442.4640.0625253548571945.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha187.934827302623
beta0.0910425579761761
S.D.0.0463101125100075
T-STAT1.96593255860698
p-value0.299564691705307

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 187.934827302623 \tabularnewline
beta & 0.0910425579761761 \tabularnewline
S.D. & 0.0463101125100075 \tabularnewline
T-STAT & 1.96593255860698 \tabularnewline
p-value & 0.299564691705307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298286&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]187.934827302623[/C][/ROW]
[ROW][C]beta[/C][C]0.0910425579761761[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0463101125100075[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.96593255860698[/C][/ROW]
[ROW][C]p-value[/C][C]0.299564691705307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298286&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)
alpha187.934827302623
beta0.0910425579761761
S.D.0.0463101125100075
T-STAT1.96593255860698
p-value0.299564691705307






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.406998210051092
beta0.715252457817374
S.D.0.258326278627265
T-STAT2.76879480329371
p-value0.22064551453505
Lambda0.284747542182626

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.406998210051092 \tabularnewline
beta & 0.715252457817374 \tabularnewline
S.D. & 0.258326278627265 \tabularnewline
T-STAT & 2.76879480329371 \tabularnewline
p-value & 0.22064551453505 \tabularnewline
Lambda & 0.284747542182626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298286&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.406998210051092[/C][/ROW]
[ROW][C]beta[/C][C]0.715252457817374[/C][/ROW]
[ROW][C]S.D.[/C][C]0.258326278627265[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.76879480329371[/C][/ROW]
[ROW][C]p-value[/C][C]0.22064551453505[/C][/ROW]
[ROW][C]Lambda[/C][C]0.284747542182626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298286&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298286&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)
alpha0.406998210051092
beta0.715252457817374
S.D.0.258326278627265
T-STAT2.76879480329371
p-value0.22064551453505
Lambda0.284747542182626


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;
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')