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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, 15 Dec 2008 12:50:53 -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/15/t1229370987i2atuo5g1dilfn6.htm/, Retrieved Wed, 15 May 2024 02:20:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33798, Retrieved Wed, 15 May 2024 02:20:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [Q1 ] [2008-12-07 13:13:15] [74be16979710d4c4e7c6647856088456]
-    D      [Standard Deviation-Mean Plot] [SMP eigen tijdreeks] [2008-12-15 19:50:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RM D        [Variance Reduction Matrix] [paper] [2008-12-23 14:13:27] [5262baed313b307078ce11eb68e9efe6]
- RMPD        [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:27:57] [5262baed313b307078ce11eb68e9efe6]
-   P           [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:38:06] [5262baed313b307078ce11eb68e9efe6]
-   P             [(Partial) Autocorrelation Function] [Paper] [2008-12-23 15:13:44] [5262baed313b307078ce11eb68e9efe6]
-   P               [(Partial) Autocorrelation Function] [paper] [2008-12-23 15:16:02] [5262baed313b307078ce11eb68e9efe6]
- RMP           [Spectral Analysis] [paper] [2008-12-23 14:54:12] [5262baed313b307078ce11eb68e9efe6]
-   P           [(Partial) Autocorrelation Function] [Paper] [2008-12-23 15:11:14] [5262baed313b307078ce11eb68e9efe6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1091075
1514814
1748997
2424406
2747942
2377332
5210706
3882821
2197469
2271155
1618917
1391579
1143249
1445785
1870242
2597788
2436231
2684184
4705109
4331347
2369192
2283947
1749607
1598601
1221234
1497778
1823567
2489908
2532837
2456065
4627018
4276894
2314950
2238987
1652753
1561968
1115878
1596714
1910242
2286450
2772441
2394538
4715128
4402420
2325392
2306683
1725282
1541370
1168142
1457835
1816380
2446552
2575774
2537852
4728097
4372685
2302672
2346402
1689915
1576183

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33798&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33798&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33798&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12373101.083333331160626.165819474119631
22434606.833333331087144.390744673561860
32391163.251059153.986025143405784
42424378.166666671097719.644076663599250
52418207.416666671099612.012474023559955

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2373101.08333333 & 1160626.16581947 & 4119631 \tabularnewline
2 & 2434606.83333333 & 1087144.39074467 & 3561860 \tabularnewline
3 & 2391163.25 & 1059153.98602514 & 3405784 \tabularnewline
4 & 2424378.16666667 & 1097719.64407666 & 3599250 \tabularnewline
5 & 2418207.41666667 & 1099612.01247402 & 3559955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33798&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]2373101.08333333[/C][C]1160626.16581947[/C][C]4119631[/C][/ROW]
[ROW][C]2[/C][C]2434606.83333333[/C][C]1087144.39074467[/C][C]3561860[/C][/ROW]
[ROW][C]3[/C][C]2391163.25[/C][C]1059153.98602514[/C][C]3405784[/C][/ROW]
[ROW][C]4[/C][C]2424378.16666667[/C][C]1097719.64407666[/C][C]3599250[/C][/ROW]
[ROW][C]5[/C][C]2418207.41666667[/C][C]1099612.01247402[/C][C]3559955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33798&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33798&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
12373101.083333331160626.165819474119631
22434606.833333331087144.390744673561860
32391163.251059153.986025143405784
42424378.166666671097719.644076663599250
52418207.416666671099612.012474023559955






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2791998.34477203
beta-0.702218651802257
S.D.0.739773019672912
T-STAT-0.94923528315853
p-value0.412530391791139

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2791998.34477203 \tabularnewline
beta & -0.702218651802257 \tabularnewline
S.D. & 0.739773019672912 \tabularnewline
T-STAT & -0.94923528315853 \tabularnewline
p-value & 0.412530391791139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33798&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2791998.34477203[/C][/ROW]
[ROW][C]beta[/C][C]-0.702218651802257[/C][/ROW]
[ROW][C]S.D.[/C][C]0.739773019672912[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.94923528315853[/C][/ROW]
[ROW][C]p-value[/C][C]0.412530391791139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33798&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33798&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)
alpha2791998.34477203
beta-0.702218651802257
S.D.0.739773019672912
T-STAT-0.94923528315853
p-value0.412530391791139






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha35.6961263031705
beta-1.48253789944175
S.D.1.60871779898099
T-STAT-0.921564926042862
p-value0.424722376160858
Lambda2.48253789944175

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 35.6961263031705 \tabularnewline
beta & -1.48253789944175 \tabularnewline
S.D. & 1.60871779898099 \tabularnewline
T-STAT & -0.921564926042862 \tabularnewline
p-value & 0.424722376160858 \tabularnewline
Lambda & 2.48253789944175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33798&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]35.6961263031705[/C][/ROW]
[ROW][C]beta[/C][C]-1.48253789944175[/C][/ROW]
[ROW][C]S.D.[/C][C]1.60871779898099[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.921564926042862[/C][/ROW]
[ROW][C]p-value[/C][C]0.424722376160858[/C][/ROW]
[ROW][C]Lambda[/C][C]2.48253789944175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33798&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33798&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)
alpha35.6961263031705
beta-1.48253789944175
S.D.1.60871779898099
T-STAT-0.921564926042862
p-value0.424722376160858
Lambda2.48253789944175


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')