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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, 30 May 2009 03:19:14 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/30/t1243675391hqyrxinosr9hv8m.htm/, Retrieved Wed, 01 May 2024 22:22:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40800, Retrieved Wed, 01 May 2024 22:22:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202

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] [Opgave 8 - Sofie ...] [2009-05-28 19:25:06] [8a3efd678ee4b71ca25331686ae4e18d]
-   P     [Standard Deviation-Mean Plot] [Opgave 8 verbeter...] [2009-05-30 09:19:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
30.06
30.46
30.46
30.49
30.49
30.5
30.5
30.5
30.51
30.51
30.61
30.88
30.95
31.09
31.28
31.31
31.32
31.34
31.34
31.34
31.34
31.36
31.36
31.36
31.72
32.07
32.13
32.19
32.26
32.27
32.28
32.28
32.28
32.29
32.61
32.68
32.69
32.74
32.86
32.86
32.9
32.95
32.95
32.96
32.99
33
33.06
33.42
33.48
33.5
33.51
33.52
33.55
33.56
33.56
33.56
33.6
33.61
33.62
33.72
33.83
33.96
34.06
34.11
34.11
34.21
34.19
34.17
34.12
34.15
34.15
34.15

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40800&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40800&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
130.49750.1792978730290110.82
231.28250.1282841306702360.41
332.2550.2431423077503830.96
432.94833333333330.1827981168260540.730000000000004
533.56583333333330.06542981435141470.240000000000002
634.10083333333330.1075730900224110.380000000000003

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 30.4975 & 0.179297873029011 & 0.82 \tabularnewline
2 & 31.2825 & 0.128284130670236 & 0.41 \tabularnewline
3 & 32.255 & 0.243142307750383 & 0.96 \tabularnewline
4 & 32.9483333333333 & 0.182798116826054 & 0.730000000000004 \tabularnewline
5 & 33.5658333333333 & 0.0654298143514147 & 0.240000000000002 \tabularnewline
6 & 34.1008333333333 & 0.107573090022411 & 0.380000000000003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40800&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]30.4975[/C][C]0.179297873029011[/C][C]0.82[/C][/ROW]
[ROW][C]2[/C][C]31.2825[/C][C]0.128284130670236[/C][C]0.41[/C][/ROW]
[ROW][C]3[/C][C]32.255[/C][C]0.243142307750383[/C][C]0.96[/C][/ROW]
[ROW][C]4[/C][C]32.9483333333333[/C][C]0.182798116826054[/C][C]0.730000000000004[/C][/ROW]
[ROW][C]5[/C][C]33.5658333333333[/C][C]0.0654298143514147[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]6[/C][C]34.1008333333333[/C][C]0.107573090022411[/C][C]0.380000000000003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40800&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
130.49750.1792978730290110.82
231.28250.1282841306702360.41
332.2550.2431423077503830.96
432.94833333333330.1827981168260540.730000000000004
533.56583333333330.06542981435141470.240000000000002
634.10083333333330.1075730900224110.380000000000003






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.832215892173678
beta-0.0209954791697537
S.D.0.0205091561667307
T-STAT-1.02371248232104
p-value0.36384091346418

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.832215892173678 \tabularnewline
beta & -0.0209954791697537 \tabularnewline
S.D. & 0.0205091561667307 \tabularnewline
T-STAT & -1.02371248232104 \tabularnewline
p-value & 0.36384091346418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40800&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.832215892173678[/C][/ROW]
[ROW][C]beta[/C][C]-0.0209954791697537[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0205091561667307[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.02371248232104[/C][/ROW]
[ROW][C]p-value[/C][C]0.36384091346418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40800&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40800&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)
alpha0.832215892173678
beta-0.0209954791697537
S.D.0.0205091561667307
T-STAT-1.02371248232104
p-value0.36384091346418






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha17.3172717817645
beta-5.54546132723001
S.D.4.73824266778902
T-STAT-1.17036245630232
p-value0.306826191051554
Lambda6.54546132723001

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 17.3172717817645 \tabularnewline
beta & -5.54546132723001 \tabularnewline
S.D. & 4.73824266778902 \tabularnewline
T-STAT & -1.17036245630232 \tabularnewline
p-value & 0.306826191051554 \tabularnewline
Lambda & 6.54546132723001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40800&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.3172717817645[/C][/ROW]
[ROW][C]beta[/C][C]-5.54546132723001[/C][/ROW]
[ROW][C]S.D.[/C][C]4.73824266778902[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.17036245630232[/C][/ROW]
[ROW][C]p-value[/C][C]0.306826191051554[/C][/ROW]
[ROW][C]Lambda[/C][C]6.54546132723001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40800&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40800&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)
alpha17.3172717817645
beta-5.54546132723001
S.D.4.73824266778902
T-STAT-1.17036245630232
p-value0.306826191051554
Lambda6.54546132723001


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')