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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 19 Dec 2008 05:57:19 -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/19/t12296914566qjnq6xlmpuua40.htm/, Retrieved Thu, 16 May 2024 03:11:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35093, Retrieved Thu, 16 May 2024 03:11:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact228

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] [Paper2] [2008-12-19 12:57:19] [acca1d0ee7cc95ffc080d0867a313954] [Current]
-    D    [Standard Deviation-Mean Plot] [Paper3] [2008-12-19 12:59:40] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [Standard Deviation-Mean Plot] [Paper 3] [2008-12-24 11:46:26] [74be16979710d4c4e7c6647856088456]
- RM D    [Variance Reduction Matrix] [Paper4] [2008-12-19 13:02:50] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [Variance Reduction Matrix] [Paper 4] [2008-12-24 11:49:13] [74be16979710d4c4e7c6647856088456]
- RM      [Variance Reduction Matrix] [Paper5] [2008-12-19 13:05:07] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [Variance Reduction Matrix] [Paper 5] [2008-12-24 11:50:12] [74be16979710d4c4e7c6647856088456]
- RM D    [Variance Reduction Matrix] [Paper6] [2008-12-19 13:06:38] [8ac58ef7b35dc5a117bc162cf16850e9]
-    D      [Variance Reduction Matrix] [Paper 6] [2008-12-24 11:52:11] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Paper7] [2008-12-19 13:10:38] [8ac58ef7b35dc5a117bc162cf16850e9]
- RMPD    [(Partial) Autocorrelation Function] [Paper7] [2008-12-19 13:10:38] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [(Partial) Autocorrelation Function] [Paper 7] [2008-12-24 11:55:02] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Paper8] [2008-12-19 13:14:16] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [(Partial) Autocorrelation Function] [Paper 8] [2008-12-24 11:57:58] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Paper9] [2008-12-19 13:17:11] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [(Partial) Autocorrelation Function] [Paper 9] [2008-12-24 11:59:02] [74be16979710d4c4e7c6647856088456]
- RMP     [(Partial) Autocorrelation Function] [Paper10] [2008-12-19 13:21:38] [8ac58ef7b35dc5a117bc162cf16850e9]
-           [(Partial) Autocorrelation Function] [Paper 10] [2008-12-24 12:00:06] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Paper11] [2008-12-19 13:24:37] [8ac58ef7b35dc5a117bc162cf16850e9]
-   PD      [(Partial) Autocorrelation Function] [Paper12] [2008-12-19 13:29:09] [74be16979710d4c4e7c6647856088456]
-             [(Partial) Autocorrelation Function] [Paper 12] [2008-12-24 12:02:27] [74be16979710d4c4e7c6647856088456]
-    D      [(Partial) Autocorrelation Function] [Paper 11] [2008-12-24 12:01:22] [74be16979710d4c4e7c6647856088456]
-         [Standard Deviation-Mean Plot] [Paper 2] [2008-12-24 11:44:45] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.256
5.008
4.181
4.666
4.476
4.912
4.340
3.830
4.285
5.537
3.813
4.610
4.207
5.099
4.112
4.199
5.110
4.218
4.736
4.624
4.145
5.299
5.011
4.730
4.619
5.578
5.369
4.902
6.102
5.024
5.731
5.732
4.491
4.755
5.208
4.962
4.163
5.592
5.754
4.929
5.219
4.429
4.143
4.308
3.996
4.634
4.138
3.759
3.922
5.560
4.004
3.937
5.250
3.908
4.814
4.407
3.243
3.740
3.949
3.711

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=35093&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=35093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35093&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
14.492833333333330.4951385175030841.724
24.624166666666670.4371321483848051.187
35.206083333333330.501302387121121.611
44.588666666666670.6471378008842731.995
54.203750.679001958090632.317

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.49283333333333 & 0.495138517503084 & 1.724 \tabularnewline
2 & 4.62416666666667 & 0.437132148384805 & 1.187 \tabularnewline
3 & 5.20608333333333 & 0.50130238712112 & 1.611 \tabularnewline
4 & 4.58866666666667 & 0.647137800884273 & 1.995 \tabularnewline
5 & 4.20375 & 0.67900195809063 & 2.317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35093&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]4.49283333333333[/C][C]0.495138517503084[/C][C]1.724[/C][/ROW]
[ROW][C]2[/C][C]4.62416666666667[/C][C]0.437132148384805[/C][C]1.187[/C][/ROW]
[ROW][C]3[/C][C]5.20608333333333[/C][C]0.50130238712112[/C][C]1.611[/C][/ROW]
[ROW][C]4[/C][C]4.58866666666667[/C][C]0.647137800884273[/C][C]1.995[/C][/ROW]
[ROW][C]5[/C][C]4.20375[/C][C]0.67900195809063[/C][C]2.317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35093&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
14.492833333333330.4951385175030841.724
24.624166666666670.4371321483848051.187
35.206083333333330.501302387121121.611
44.588666666666670.6471378008842731.995
54.203750.679001958090632.317






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.23435282637352
beta-0.147608804476809
S.D.0.142550585346519
T-STAT-1.03548367842892
p-value0.3765885717841

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.23435282637352 \tabularnewline
beta & -0.147608804476809 \tabularnewline
S.D. & 0.142550585346519 \tabularnewline
T-STAT & -1.03548367842892 \tabularnewline
p-value & 0.3765885717841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35093&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.23435282637352[/C][/ROW]
[ROW][C]beta[/C][C]-0.147608804476809[/C][/ROW]
[ROW][C]S.D.[/C][C]0.142550585346519[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.03548367842892[/C][/ROW]
[ROW][C]p-value[/C][C]0.3765885717841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35093&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)
alpha1.23435282637352
beta-0.147608804476809
S.D.0.142550585346519
T-STAT-1.03548367842892
p-value0.3765885717841






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.26746655386439
beta-1.22732300778225
S.D.1.21657518174028
T-STAT-1.00883449391643
p-value0.387365297563189
Lambda2.22732300778225

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.26746655386439 \tabularnewline
beta & -1.22732300778225 \tabularnewline
S.D. & 1.21657518174028 \tabularnewline
T-STAT & -1.00883449391643 \tabularnewline
p-value & 0.387365297563189 \tabularnewline
Lambda & 2.22732300778225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35093&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.26746655386439[/C][/ROW]
[ROW][C]beta[/C][C]-1.22732300778225[/C][/ROW]
[ROW][C]S.D.[/C][C]1.21657518174028[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.00883449391643[/C][/ROW]
[ROW][C]p-value[/C][C]0.387365297563189[/C][/ROW]
[ROW][C]Lambda[/C][C]2.22732300778225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35093&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35093&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)
alpha1.26746655386439
beta-1.22732300778225
S.D.1.21657518174028
T-STAT-1.00883449391643
p-value0.387365297563189
Lambda2.22732300778225


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')