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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 computationSat, 20 Dec 2008 11:13:15 -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/20/t1229796830kxa0bnqlkwi80rn.htm/, Retrieved Sun, 19 May 2024 11:39:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35429, Retrieved Sun, 19 May 2024 11:39:19 +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)
-       [Standard Deviation-Mean Plot] [fds] [2008-12-20 18:13:15] [7a2afff08a618fdf6611a1bb6e1c3da4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,6
6,6
6,6
6,6
6,6
6,6
6,8
6,8
6,9
7
7
7
7,1
7,1
7,3
7,4
7,6
7,8
7,9
7,7
7,7
7,8
7,9
8
8,1
8,2
8,1
8,2
8,3
8,4
8,4
8,5
8,6
8,6
8,6
8,5
8,5
8,4
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,4
8,4
8,4
8,5
8,7
8,7
8,6
8,2
8
8
8,3
8,4
8,4
8,4
8,3
8,3
8,2
8,2
8,2
8,2
8,2
8,2
8,1
8,1
8,1
7,9
7,8
7,7
7,6
7,6
7,6
7,4
7,4
7,3
7,3
7,3
7,2
7,2
7,1
7,1
6,7
6,5
6,4
6,5
6,6
6,5
6,3
6,3
6,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35429&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35429&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35429&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
16.758333333333330.1781640374554420.4
27.608333333333330.3117642854737690.9
38.3750.1912875037500070.5
48.450.05222329678670920.0999999999999996
58.3750.2340357393064730.700
68.1250.1422226167923820.500000000000001
77.391666666666670.1928651593652150.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.75833333333333 & 0.178164037455442 & 0.4 \tabularnewline
2 & 7.60833333333333 & 0.311764285473769 & 0.9 \tabularnewline
3 & 8.375 & 0.191287503750007 & 0.5 \tabularnewline
4 & 8.45 & 0.0522232967867092 & 0.0999999999999996 \tabularnewline
5 & 8.375 & 0.234035739306473 & 0.700 \tabularnewline
6 & 8.125 & 0.142222616792382 & 0.500000000000001 \tabularnewline
7 & 7.39166666666667 & 0.192865159365215 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35429&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]6.75833333333333[/C][C]0.178164037455442[/C][C]0.4[/C][/ROW]
[ROW][C]2[/C][C]7.60833333333333[/C][C]0.311764285473769[/C][C]0.9[/C][/ROW]
[ROW][C]3[/C][C]8.375[/C][C]0.191287503750007[/C][C]0.5[/C][/ROW]
[ROW][C]4[/C][C]8.45[/C][C]0.0522232967867092[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]5[/C][C]8.375[/C][C]0.234035739306473[/C][C]0.700[/C][/ROW]
[ROW][C]6[/C][C]8.125[/C][C]0.142222616792382[/C][C]0.500000000000001[/C][/ROW]
[ROW][C]7[/C][C]7.39166666666667[/C][C]0.192865159365215[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35429&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35429&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
16.758333333333330.1781640374554420.4
27.608333333333330.3117642854737690.9
38.3750.1912875037500070.5
48.450.05222329678670920.0999999999999996
58.3750.2340357393064730.700
68.1250.1422226167923820.500000000000001
77.391666666666670.1928651593652150.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.473559042626671
beta-0.0365328410188811
S.D.0.0533668789434372
T-STAT-0.684560194303319
p-value0.524056339330004

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.473559042626671 \tabularnewline
beta & -0.0365328410188811 \tabularnewline
S.D. & 0.0533668789434372 \tabularnewline
T-STAT & -0.684560194303319 \tabularnewline
p-value & 0.524056339330004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35429&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.473559042626671[/C][/ROW]
[ROW][C]beta[/C][C]-0.0365328410188811[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0533668789434372[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.684560194303319[/C][/ROW]
[ROW][C]p-value[/C][C]0.524056339330004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35429&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35429&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)
alpha0.473559042626671
beta-0.0365328410188811
S.D.0.0533668789434372
T-STAT-0.684560194303319
p-value0.524056339330004






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.03273399737129
beta-2.34218696208806
S.D.2.83953502810236
T-STAT-0.82484876534639
p-value0.447008750898212
Lambda3.34218696208806

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.03273399737129 \tabularnewline
beta & -2.34218696208806 \tabularnewline
S.D. & 2.83953502810236 \tabularnewline
T-STAT & -0.82484876534639 \tabularnewline
p-value & 0.447008750898212 \tabularnewline
Lambda & 3.34218696208806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35429&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.03273399737129[/C][/ROW]
[ROW][C]beta[/C][C]-2.34218696208806[/C][/ROW]
[ROW][C]S.D.[/C][C]2.83953502810236[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.82484876534639[/C][/ROW]
[ROW][C]p-value[/C][C]0.447008750898212[/C][/ROW]
[ROW][C]Lambda[/C][C]3.34218696208806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35429&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35429&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)
alpha3.03273399737129
beta-2.34218696208806
S.D.2.83953502810236
T-STAT-0.82484876534639
p-value0.447008750898212
Lambda3.34218696208806


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')