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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, 07 Dec 2011 11:16:15 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/07/t1323274676aik6dr6m275qw5p.htm/, Retrieved Thu, 02 May 2024 16:44:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152543, Retrieved Thu, 02 May 2024 16:44:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact75

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...] [2011-12-07 16:16:15] [b7d89a59d057204a66389ee14552eeec] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R Server'AstonUniversity' @ aston.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 & 11 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152543&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]11 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152543&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 time11 seconds
R Server'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111525.41666666671112.95368345463405
215460.9166666667695.1090768993592520
316322775.6835109056462166
419107.9166666667703.2356980200142069
5224801260.966944992474147
629740.83333333332835.123945770068661

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11525.4166666667 & 1112.9536834546 & 3405 \tabularnewline
2 & 15460.9166666667 & 695.109076899359 & 2520 \tabularnewline
3 & 16322 & 775.683510905646 & 2166 \tabularnewline
4 & 19107.9166666667 & 703.235698020014 & 2069 \tabularnewline
5 & 22480 & 1260.96694499247 & 4147 \tabularnewline
6 & 29740.8333333333 & 2835.12394577006 & 8661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152543&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]11525.4166666667[/C][C]1112.9536834546[/C][C]3405[/C][/ROW]
[ROW][C]2[/C][C]15460.9166666667[/C][C]695.109076899359[/C][C]2520[/C][/ROW]
[ROW][C]3[/C][C]16322[/C][C]775.683510905646[/C][C]2166[/C][/ROW]
[ROW][C]4[/C][C]19107.9166666667[/C][C]703.235698020014[/C][C]2069[/C][/ROW]
[ROW][C]5[/C][C]22480[/C][C]1260.96694499247[/C][C]4147[/C][/ROW]
[ROW][C]6[/C][C]29740.8333333333[/C][C]2835.12394577006[/C][C]8661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152543&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
111525.41666666671112.95368345463405
215460.9166666667695.1090768993592520
316322775.6835109056462166
419107.9166666667703.2356980200142069
5224801260.966944992474147
629740.83333333332835.123945770068661






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-772.05785534682
beta0.10481268052839
S.D.0.0373244017284204
T-STAT2.8081543353602
p-value0.0484077850820987

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -772.05785534682 \tabularnewline
beta & 0.10481268052839 \tabularnewline
S.D. & 0.0373244017284204 \tabularnewline
T-STAT & 2.8081543353602 \tabularnewline
p-value & 0.0484077850820987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152543&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-772.05785534682[/C][/ROW]
[ROW][C]beta[/C][C]0.10481268052839[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0373244017284204[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.8081543353602[/C][/ROW]
[ROW][C]p-value[/C][C]0.0484077850820987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152543&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-772.05785534682
beta0.10481268052839
S.D.0.0373244017284204
T-STAT2.8081543353602
p-value0.0484077850820987






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.65992604196524
beta1.08390594439509
S.D.0.6169161852155
T-STAT1.75697440004182
p-value0.153758888805699
Lambda-0.0839059443950911

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.65992604196524 \tabularnewline
beta & 1.08390594439509 \tabularnewline
S.D. & 0.6169161852155 \tabularnewline
T-STAT & 1.75697440004182 \tabularnewline
p-value & 0.153758888805699 \tabularnewline
Lambda & -0.0839059443950911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152543&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.65992604196524[/C][/ROW]
[ROW][C]beta[/C][C]1.08390594439509[/C][/ROW]
[ROW][C]S.D.[/C][C]0.6169161852155[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.75697440004182[/C][/ROW]
[ROW][C]p-value[/C][C]0.153758888805699[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0839059443950911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152543&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152543&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-3.65992604196524
beta1.08390594439509
S.D.0.6169161852155
T-STAT1.75697440004182
p-value0.153758888805699
Lambda-0.0839059443950911


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')