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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 computationThu, 22 Dec 2016 22:50:02 +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/22/t1482443737nodj8l1au65iyqw.htm/, Retrieved Fri, 16 May 2025 04:32:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302704, Retrieved Fri, 16 May 2025 04:32:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

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...] [2016-12-22 21:50:02] [d4ebbcc95b180bc93fc42d05f31a3dde] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5500
3860
4880
4420
4900
4230
3970
4690
4190
4960
5590
5000
6030
4690
4090
5070
5050
4520
5070
4290
4400
5080
4180
5230
5200
3800
5010
4420
4810
4690
5390
4730
4770
4690
4450
5400
5590
4360
5370
4660
4450
4980
4590
4580
4290
4840
5100
6170
5990
4950
5310

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=302704&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=302704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302704&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
14682.5560.5537035337961730
24808.33333333333554.5486835474791940
34780447.6605857119881600
44915562.4217117236691880

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4682.5 & 560.553703533796 & 1730 \tabularnewline
2 & 4808.33333333333 & 554.548683547479 & 1940 \tabularnewline
3 & 4780 & 447.660585711988 & 1600 \tabularnewline
4 & 4915 & 562.421711723669 & 1880 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302704&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]4682.5[/C][C]560.553703533796[/C][C]1730[/C][/ROW]
[ROW][C]2[/C][C]4808.33333333333[/C][C]554.548683547479[/C][C]1940[/C][/ROW]
[ROW][C]3[/C][C]4780[/C][C]447.660585711988[/C][C]1600[/C][/ROW]
[ROW][C]4[/C][C]4915[/C][C]562.421711723669[/C][C]1880[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302704&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
14682.5560.5537035337961730
24808.33333333333554.5486835474791940
34780447.6605857119881600
44915562.4217117236691880






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180.408308026284
beta0.0731556158143663
S.D.0.409658216099866
T-STAT0.178577196646613
p-value0.874721678993091

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 180.408308026284 \tabularnewline
beta & 0.0731556158143663 \tabularnewline
S.D. & 0.409658216099866 \tabularnewline
T-STAT & 0.178577196646613 \tabularnewline
p-value & 0.874721678993091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302704&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]180.408308026284[/C][/ROW]
[ROW][C]beta[/C][C]0.0731556158143663[/C][/ROW]
[ROW][C]S.D.[/C][C]0.409658216099866[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.178577196646613[/C][/ROW]
[ROW][C]p-value[/C][C]0.874721678993091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302704&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302704&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)
alpha180.408308026284
beta0.0731556158143663
S.D.0.409658216099866
T-STAT0.178577196646613
p-value0.874721678993091






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.632985822053177
beta0.665195744854839
S.D.3.92238070924641
T-STAT0.16958979613752
p-value0.880934947844985
Lambda0.334804255145161

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.632985822053177 \tabularnewline
beta & 0.665195744854839 \tabularnewline
S.D. & 3.92238070924641 \tabularnewline
T-STAT & 0.16958979613752 \tabularnewline
p-value & 0.880934947844985 \tabularnewline
Lambda & 0.334804255145161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302704&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.632985822053177[/C][/ROW]
[ROW][C]beta[/C][C]0.665195744854839[/C][/ROW]
[ROW][C]S.D.[/C][C]3.92238070924641[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.16958979613752[/C][/ROW]
[ROW][C]p-value[/C][C]0.880934947844985[/C][/ROW]
[ROW][C]Lambda[/C][C]0.334804255145161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302704&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302704&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)
alpha0.632985822053177
beta0.665195744854839
S.D.3.92238070924641
T-STAT0.16958979613752
p-value0.880934947844985
Lambda0.334804255145161


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 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')