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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, 02 Feb 2011 17:02:28 +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/2011/Feb/02/t12966660447xzgwsbbmlh8yer.htm/, Retrieved Sun, 19 May 2024 18:46:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=118029, Retrieved Sun, 19 May 2024 18:46:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact252

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] [] [2011-02-02 17:02:28] [ff423994c38282a6d306f7d0147a5924] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5393
5147
4846
3995
4491
4676
5461
4758
5302
5066
3491
4944
5148
5351
5178
4025
4449
4594
4603
4911
5236
4652
3479
4556
4815
4949
4499
3865
3657
4814
4614
4539
4492
4779
3193
3894
4531
4008
3764
3290
3644
3438
3833
3922
3524
3493
2814
3899
3653
3969
3427
3067
3301
3211
3382
3613
3783
3971
2842
4161

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118029&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118029&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 time0 seconds
R Server'Gwilym Jenkins' @ www.wessa.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14797.5582.2091938938661970
24681.83333333333542.2174728637841872
34342.5554.6111660024031756
43680425.3336658115921717
53531.66666666667398.3813461618111319

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4797.5 & 582.209193893866 & 1970 \tabularnewline
2 & 4681.83333333333 & 542.217472863784 & 1872 \tabularnewline
3 & 4342.5 & 554.611166002403 & 1756 \tabularnewline
4 & 3680 & 425.333665811592 & 1717 \tabularnewline
5 & 3531.66666666667 & 398.381346161811 & 1319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118029&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]4797.5[/C][C]582.209193893866[/C][C]1970[/C][/ROW]
[ROW][C]2[/C][C]4681.83333333333[/C][C]542.217472863784[/C][C]1872[/C][/ROW]
[ROW][C]3[/C][C]4342.5[/C][C]554.611166002403[/C][C]1756[/C][/ROW]
[ROW][C]4[/C][C]3680[/C][C]425.333665811592[/C][C]1717[/C][/ROW]
[ROW][C]5[/C][C]3531.66666666667[/C][C]398.381346161811[/C][C]1319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118029&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
14797.5582.2091938938661970
24681.83333333333542.2174728637841872
34342.5554.6111660024031756
43680425.3336658115921717
53531.66666666667398.3813461618111319






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-82.938864187969
beta0.138704788345891
S.D.0.0218855425284616
T-STAT6.3377358895951
p-value0.00794423168126013

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -82.938864187969 \tabularnewline
beta & 0.138704788345891 \tabularnewline
S.D. & 0.0218855425284616 \tabularnewline
T-STAT & 6.3377358895951 \tabularnewline
p-value & 0.00794423168126013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118029&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-82.938864187969[/C][/ROW]
[ROW][C]beta[/C][C]0.138704788345891[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0218855425284616[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.3377358895951[/C][/ROW]
[ROW][C]p-value[/C][C]0.00794423168126013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118029&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-82.938864187969
beta0.138704788345891
S.D.0.0218855425284616
T-STAT6.3377358895951
p-value0.00794423168126013






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.73994396917359
beta1.19281097711619
S.D.0.17127226311737
T-STAT6.96441417545102
p-value0.00607416526839947
Lambda-0.192810977116192

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.73994396917359 \tabularnewline
beta & 1.19281097711619 \tabularnewline
S.D. & 0.17127226311737 \tabularnewline
T-STAT & 6.96441417545102 \tabularnewline
p-value & 0.00607416526839947 \tabularnewline
Lambda & -0.192810977116192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118029&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.73994396917359[/C][/ROW]
[ROW][C]beta[/C][C]1.19281097711619[/C][/ROW]
[ROW][C]S.D.[/C][C]0.17127226311737[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.96441417545102[/C][/ROW]
[ROW][C]p-value[/C][C]0.00607416526839947[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.192810977116192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118029&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118029&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-3.73994396917359
beta1.19281097711619
S.D.0.17127226311737
T-STAT6.96441417545102
p-value0.00607416526839947
Lambda-0.192810977116192


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par4 = 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')