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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 computationMon, 13 Dec 2010 10:21:08 +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/13/t1292235604z69zlxex1xl5o9a.htm/, Retrieved Mon, 06 May 2024 20:59:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108776, Retrieved Mon, 06 May 2024 20:59:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-12-13 08:35:23] [21eff0c210342db4afbdafe426a7c254]
-   PD  [(Partial) Autocorrelation Function] [] [2010-12-13 09:29:04] [21eff0c210342db4afbdafe426a7c254]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-13 10:05:17] [21eff0c210342db4afbdafe426a7c254]
- RM D        [Standard Deviation-Mean Plot] [] [2010-12-13 10:21:08] [81d69fb83507cea26168920232cdff1b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113
95.4
86.2
111.7
97.5
99.7
111.5
91.8
86.3
88.7
95.1
105.1
104.5
89.1
82.6
102.7
91.8
94.1
103.1
93.2
91
94.3
99.4
115.7
116.8
99.8
96
115.9
109.1
117.3
109.8
112.8
110.7
100
113.3
122.4
112.5
104.2
92.5
117.2
109.3
106.1
118.8
105.3
106
102
112.9
116.5
114.8
100.5
85.4
114.6
109.9
100.7
115.5
100.7
99
102.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108776&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]3 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=108776&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108776&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
198.59.824459272652126.8
296.79166666666678.7585239866225433.1
3110.3258.0167013166264326.4
4108.6083333333337.5113802548754926.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.5 & 9.8244592726521 & 26.8 \tabularnewline
2 & 96.7916666666667 & 8.75852398662254 & 33.1 \tabularnewline
3 & 110.325 & 8.01670131662643 & 26.4 \tabularnewline
4 & 108.608333333333 & 7.51138025487549 & 26.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108776&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]98.5[/C][C]9.8244592726521[/C][C]26.8[/C][/ROW]
[ROW][C]2[/C][C]96.7916666666667[/C][C]8.75852398662254[/C][C]33.1[/C][/ROW]
[ROW][C]3[/C][C]110.325[/C][C]8.01670131662643[/C][C]26.4[/C][/ROW]
[ROW][C]4[/C][C]108.608333333333[/C][C]7.51138025487549[/C][C]26.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108776&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108776&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
198.59.824459272652126.8
296.79166666666678.7585239866225433.1
3110.3258.0167013166264326.4
4108.6083333333337.5113802548754926.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha20.6581783001516
beta-0.117138387035620
S.D.0.0612756712344446
T-STAT-1.91166224173117
p-value0.196074357941512

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 20.6581783001516 \tabularnewline
beta & -0.117138387035620 \tabularnewline
S.D. & 0.0612756712344446 \tabularnewline
T-STAT & -1.91166224173117 \tabularnewline
p-value & 0.196074357941512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108776&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.6581783001516[/C][/ROW]
[ROW][C]beta[/C][C]-0.117138387035620[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0612756712344446[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.91166224173117[/C][/ROW]
[ROW][C]p-value[/C][C]0.196074357941512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108776&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108776&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)
alpha20.6581783001516
beta-0.117138387035620
S.D.0.0612756712344446
T-STAT-1.91166224173117
p-value0.196074357941512






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.70539091467499
beta-1.41581349011927
S.D.0.720249035237368
T-STAT-1.96572771479336
p-value0.188248283172712
Lambda2.41581349011927

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.70539091467499 \tabularnewline
beta & -1.41581349011927 \tabularnewline
S.D. & 0.720249035237368 \tabularnewline
T-STAT & -1.96572771479336 \tabularnewline
p-value & 0.188248283172712 \tabularnewline
Lambda & 2.41581349011927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108776&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.70539091467499[/C][/ROW]
[ROW][C]beta[/C][C]-1.41581349011927[/C][/ROW]
[ROW][C]S.D.[/C][C]0.720249035237368[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.96572771479336[/C][/ROW]
[ROW][C]p-value[/C][C]0.188248283172712[/C][/ROW]
[ROW][C]Lambda[/C][C]2.41581349011927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108776&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108776&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)
alpha8.70539091467499
beta-1.41581349011927
S.D.0.720249035237368
T-STAT-1.96572771479336
p-value0.188248283172712
Lambda2.41581349011927


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')