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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 computationWed, 29 Dec 2010 14:12:45 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293631874w4eh69sykth7ad0.htm/, Retrieved Fri, 03 May 2024 14:06:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116857, Retrieved Fri, 03 May 2024 14:06:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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] [Paper] [2010-12-29 14:12:45] [d5e0edb7e0239841e94676417b2a1e2e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26548
26752
26967
27034
27056
27476
28497
29085
28720
29067
29249
29672
29761
30066
30315
30571
30757
30742
31310
31381
31470
31226
31081
31061
31114
30828
30418
30195
29877
29192
29876
29409
28458
28340
28164
28438
28053
27599
27226
27119
26625
26541
27023
26631
26154
26029
26008
26632
27010
27041
27244
26976
26715
27017
27714
27655
27103
27088
26968
27770
27616
27481
27279
26918
26503
26547
27467
27305
26259
26048
25743

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116857&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116857&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116857&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128010.251138.867549566033124
230811.75546.4445617726551709
329525.751018.783867256362950
426803.3333333333627.7488399516212045
527191.75337.5430275602591055

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28010.25 & 1138.86754956603 & 3124 \tabularnewline
2 & 30811.75 & 546.444561772655 & 1709 \tabularnewline
3 & 29525.75 & 1018.78386725636 & 2950 \tabularnewline
4 & 26803.3333333333 & 627.748839951621 & 2045 \tabularnewline
5 & 27191.75 & 337.543027560259 & 1055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116857&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]28010.25[/C][C]1138.86754956603[/C][C]3124[/C][/ROW]
[ROW][C]2[/C][C]30811.75[/C][C]546.444561772655[/C][C]1709[/C][/ROW]
[ROW][C]3[/C][C]29525.75[/C][C]1018.78386725636[/C][C]2950[/C][/ROW]
[ROW][C]4[/C][C]26803.3333333333[/C][C]627.748839951621[/C][C]2045[/C][/ROW]
[ROW][C]5[/C][C]27191.75[/C][C]337.543027560259[/C][C]1055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116857&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116857&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
128010.251138.867549566033124
230811.75546.4445617726551709
329525.751018.783867256362950
426803.3333333333627.7488399516212045
527191.75337.5430275602591055






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-177.328408222929
beta0.0320074413339267
S.D.0.113956413761211
T-STAT0.280874417485588
p-value0.797063888769519

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -177.328408222929 \tabularnewline
beta & 0.0320074413339267 \tabularnewline
S.D. & 0.113956413761211 \tabularnewline
T-STAT & 0.280874417485588 \tabularnewline
p-value & 0.797063888769519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116857&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-177.328408222929[/C][/ROW]
[ROW][C]beta[/C][C]0.0320074413339267[/C][/ROW]
[ROW][C]S.D.[/C][C]0.113956413761211[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.280874417485588[/C][/ROW]
[ROW][C]p-value[/C][C]0.797063888769519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116857&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116857&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-177.328408222929
beta0.0320074413339267
S.D.0.113956413761211
T-STAT0.280874417485588
p-value0.797063888769519






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-13.0747817104773
beta1.90938124827522
S.D.4.7611288998371
T-STAT0.401035403250803
p-value0.715249328778978
Lambda-0.909381248275222

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.0747817104773 \tabularnewline
beta & 1.90938124827522 \tabularnewline
S.D. & 4.7611288998371 \tabularnewline
T-STAT & 0.401035403250803 \tabularnewline
p-value & 0.715249328778978 \tabularnewline
Lambda & -0.909381248275222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116857&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.0747817104773[/C][/ROW]
[ROW][C]beta[/C][C]1.90938124827522[/C][/ROW]
[ROW][C]S.D.[/C][C]4.7611288998371[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.401035403250803[/C][/ROW]
[ROW][C]p-value[/C][C]0.715249328778978[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.909381248275222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116857&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116857&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-13.0747817104773
beta1.90938124827522
S.D.4.7611288998371
T-STAT0.401035403250803
p-value0.715249328778978
Lambda-0.909381248275222


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')