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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 computationSun, 21 Dec 2008 03:25:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229855197nq1o13zgzohrwr2.htm/, Retrieved Sun, 19 May 2024 10:51:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35481, Retrieved Sun, 19 May 2024 10:51:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

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] [SMP Paper] [2008-12-21 10:25:16] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1995
1947
1766
1635
1833
1910
1960
1970
2061
2093
2121
2175
2197
2350
2440
2409
2473
2408
2455
2448
2498
2646
2757
2849
2921
2982
3081
3106
3119
3061
3097
3162
3257
3277
3295
3364
3494
3667
3813
3918
3896
3801
3570
3702
3862
3970
4139
4200
4291
4444
4503
4357
4591
4697
4621
4563
4203
4296
4435
4105
4117

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35481&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35481&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11955.5154.677670716176540
22494.16666666667178.089269409439652
33143.5132.489793775013443
43836210.896786474936706
54425.5180.011868295601592

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1955.5 & 154.677670716176 & 540 \tabularnewline
2 & 2494.16666666667 & 178.089269409439 & 652 \tabularnewline
3 & 3143.5 & 132.489793775013 & 443 \tabularnewline
4 & 3836 & 210.896786474936 & 706 \tabularnewline
5 & 4425.5 & 180.011868295601 & 592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35481&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]1955.5[/C][C]154.677670716176[/C][C]540[/C][/ROW]
[ROW][C]2[/C][C]2494.16666666667[/C][C]178.089269409439[/C][C]652[/C][/ROW]
[ROW][C]3[/C][C]3143.5[/C][C]132.489793775013[/C][C]443[/C][/ROW]
[ROW][C]4[/C][C]3836[/C][C]210.896786474936[/C][C]706[/C][/ROW]
[ROW][C]5[/C][C]4425.5[/C][C]180.011868295601[/C][C]592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35481&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
11955.5154.677670716176540
22494.16666666667178.089269409439652
33143.5132.489793775013443
43836210.896786474936706
54425.5180.011868295601592






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha127.959008378555
beta0.0136471079037752
S.D.0.0151914072265652
T-STAT0.898343892717886
p-value0.435206420690696

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 127.959008378555 \tabularnewline
beta & 0.0136471079037752 \tabularnewline
S.D. & 0.0151914072265652 \tabularnewline
T-STAT & 0.898343892717886 \tabularnewline
p-value & 0.435206420690696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35481&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]127.959008378555[/C][/ROW]
[ROW][C]beta[/C][C]0.0136471079037752[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0151914072265652[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.898343892717886[/C][/ROW]
[ROW][C]p-value[/C][C]0.435206420690696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35481&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)
alpha127.959008378555
beta0.0136471079037752
S.D.0.0151914072265652
T-STAT0.898343892717886
p-value0.435206420690696






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.34499873002042
beta0.222678666839035
S.D.0.280524737396555
T-STAT0.793793334968003
p-value0.485306593374255
Lambda0.777321333160965

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.34499873002042 \tabularnewline
beta & 0.222678666839035 \tabularnewline
S.D. & 0.280524737396555 \tabularnewline
T-STAT & 0.793793334968003 \tabularnewline
p-value & 0.485306593374255 \tabularnewline
Lambda & 0.777321333160965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35481&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.34499873002042[/C][/ROW]
[ROW][C]beta[/C][C]0.222678666839035[/C][/ROW]
[ROW][C]S.D.[/C][C]0.280524737396555[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.793793334968003[/C][/ROW]
[ROW][C]p-value[/C][C]0.485306593374255[/C][/ROW]
[ROW][C]Lambda[/C][C]0.777321333160965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35481&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)
alpha3.34499873002042
beta0.222678666839035
S.D.0.280524737396555
T-STAT0.793793334968003
p-value0.485306593374255
Lambda0.777321333160965


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')