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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 computationTue, 21 Dec 2010 12:07:57 +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/21/t1292933135028um8gczyqtoq9.htm/, Retrieved Fri, 17 May 2024 04:18:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113341, Retrieved Fri, 17 May 2024 04:18:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
F RMP   [(Partial) Autocorrelation Function] [WS 9] [2010-12-07 20:24:41] [9b13650c94c5192ca5135ec8a1fa39f7]
-    D    [(Partial) Autocorrelation Function] [ACF Paper] [2010-12-19 13:35:17] [9b13650c94c5192ca5135ec8a1fa39f7]
-   P       [(Partial) Autocorrelation Function] [] [2010-12-21 10:32:09] [9b13650c94c5192ca5135ec8a1fa39f7]
-             [(Partial) Autocorrelation Function] [] [2010-12-21 10:39:04] [9b13650c94c5192ca5135ec8a1fa39f7]
-   P           [(Partial) Autocorrelation Function] [] [2010-12-21 10:40:43] [9b13650c94c5192ca5135ec8a1fa39f7]
-   P             [(Partial) Autocorrelation Function] [] [2010-12-21 10:50:06] [9b13650c94c5192ca5135ec8a1fa39f7]
- RMP               [Spectral Analysis] [] [2010-12-21 11:01:31] [9b13650c94c5192ca5135ec8a1fa39f7]
-   P                 [Spectral Analysis] [] [2010-12-21 11:12:16] [9b13650c94c5192ca5135ec8a1fa39f7]
-   P                   [Spectral Analysis] [] [2010-12-21 11:21:27] [9b13650c94c5192ca5135ec8a1fa39f7]
- RMP                     [Variance Reduction Matrix] [] [2010-12-21 11:45:42] [9b13650c94c5192ca5135ec8a1fa39f7]
- RM                          [Standard Deviation-Mean Plot] [] [2010-12-21 12:07:57] [5fd8c857995b7937a45335fd5ccccdde] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380

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=113341&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=113341&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113341&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
1229575540.3157606108320000
223857.33333333336419.0612218374220890
322401.33333333335078.3907675442615936
423027.08333333337085.4461520953223808
523212.55938.8196944878221757
623802.756535.3521310846519196
7212964503.8044725845616277
825059.41666666675626.2067708881720132

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22957 & 5540.31576061083 & 20000 \tabularnewline
2 & 23857.3333333333 & 6419.06122183742 & 20890 \tabularnewline
3 & 22401.3333333333 & 5078.39076754426 & 15936 \tabularnewline
4 & 23027.0833333333 & 7085.44615209532 & 23808 \tabularnewline
5 & 23212.5 & 5938.81969448782 & 21757 \tabularnewline
6 & 23802.75 & 6535.35213108465 & 19196 \tabularnewline
7 & 21296 & 4503.80447258456 & 16277 \tabularnewline
8 & 25059.4166666667 & 5626.20677088817 & 20132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113341&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]22957[/C][C]5540.31576061083[/C][C]20000[/C][/ROW]
[ROW][C]2[/C][C]23857.3333333333[/C][C]6419.06122183742[/C][C]20890[/C][/ROW]
[ROW][C]3[/C][C]22401.3333333333[/C][C]5078.39076754426[/C][C]15936[/C][/ROW]
[ROW][C]4[/C][C]23027.0833333333[/C][C]7085.44615209532[/C][C]23808[/C][/ROW]
[ROW][C]5[/C][C]23212.5[/C][C]5938.81969448782[/C][C]21757[/C][/ROW]
[ROW][C]6[/C][C]23802.75[/C][C]6535.35213108465[/C][C]19196[/C][/ROW]
[ROW][C]7[/C][C]21296[/C][C]4503.80447258456[/C][C]16277[/C][/ROW]
[ROW][C]8[/C][C]25059.4166666667[/C][C]5626.20677088817[/C][C]20132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113341&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113341&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
1229575540.3157606108320000
223857.33333333336419.0612218374220890
322401.33333333335078.3907675442615936
423027.08333333337085.4461520953223808
523212.55938.8196944878221757
623802.756535.3521310846519196
7212964503.8044725845616277
825059.41666666675626.2067708881720132






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3362.38385019558
beta0.396665656475251
S.D.0.261358978661922
T-STAT1.51770434100278
p-value0.179884777682195

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3362.38385019558 \tabularnewline
beta & 0.396665656475251 \tabularnewline
S.D. & 0.261358978661922 \tabularnewline
T-STAT & 1.51770434100278 \tabularnewline
p-value & 0.179884777682195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113341&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3362.38385019558[/C][/ROW]
[ROW][C]beta[/C][C]0.396665656475251[/C][/ROW]
[ROW][C]S.D.[/C][C]0.261358978661922[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.51770434100278[/C][/ROW]
[ROW][C]p-value[/C][C]0.179884777682195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113341&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113341&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-3362.38385019558
beta0.396665656475251
S.D.0.261358978661922
T-STAT1.51770434100278
p-value0.179884777682195






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.34072442232515
beta1.79128487758922
S.D.1.00770744535945
T-STAT1.77758424415557
p-value0.125796591118193
Lambda-0.79128487758922

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.34072442232515 \tabularnewline
beta & 1.79128487758922 \tabularnewline
S.D. & 1.00770744535945 \tabularnewline
T-STAT & 1.77758424415557 \tabularnewline
p-value & 0.125796591118193 \tabularnewline
Lambda & -0.79128487758922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113341&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.34072442232515[/C][/ROW]
[ROW][C]beta[/C][C]1.79128487758922[/C][/ROW]
[ROW][C]S.D.[/C][C]1.00770744535945[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.77758424415557[/C][/ROW]
[ROW][C]p-value[/C][C]0.125796591118193[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.79128487758922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113341&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113341&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-9.34072442232515
beta1.79128487758922
S.D.1.00770744535945
T-STAT1.77758424415557
p-value0.125796591118193
Lambda-0.79128487758922


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')