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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 computationFri, 24 Dec 2010 14:16:21 +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/24/t1293200149jw2wy44k7zankrh.htm/, Retrieved Tue, 30 Apr 2024 04:06:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114986, Retrieved Tue, 30 Apr 2024 04:06:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2010-12-24 14:16:21] [29eeba0e6ce2cd83aa315a4a7ff8c4aa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,4
7,7
9,2
8,6
7,4
8,6
6,2
6
6,6
5,1
4,7
5
3,6
1,9
-0,1
-5,7
-5,6
-6,4
-7,7
-8
-11,9
-15,4
-15,5
-13,4
-10,9
-10,8
-7,3
-6,5
-5,1
-5,3
-6,8
-8,4
-8,4
-9,7
-8,8
-9,6
-11,5
-11
-14,9
-16,2
-14,4
-17,3
-15,7
-12,6
-9,4
-8,1
-5,4
-4,6
-4,9
-4
-3,1
-1,3
0
-0,4
3
0,4
1,2
0,6
-1,3
-3,2
-1,8
-3,6
-4,2
-6,9
-8
-7,5
-8,2
-7,6
-3,7
-1,7
-0,7
0,2
0,6
2,2
3,3
5,3
5,5
6,3
7,7
6,5
5,5
6,9
5,7
6,9
6,1
4,8
3,7
5,8
6,8
8,5
7,2
5
4,7
2,3
2,4
0,1
1,9
1,7
2
-1,9
0,5
-1,3
-3,3
-2,8
-8
-13,9
-21,9
-28,8
-27,6
-31,4
-31,8
-29,4
-27,6
-23,6
-22,8
-18,2
-17,8
-14,2
-8,8
-7,9
-7
-7
-3,6
-2,4
-4,9
-7,7
-6,5
-5,1
-3,4
-2,8
0,8

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=114986&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=114986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114986&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
16.791666666666671.512047578215674.5
2-7.016666666666676.4134564972738619.1
3-8.133333333333331.961601077660495.8
4-11.75833333333334.2081000535403212.7
5-1.083333333333332.340875257184157.9
6-4.4753.067461194834948.4
75.22.113592374908837.1
84.783333333333332.364446248195568.4
9-6.3166666666666710.100570040919230.8
10-21.75833333333338.3684970230168823.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.79166666666667 & 1.51204757821567 & 4.5 \tabularnewline
2 & -7.01666666666667 & 6.41345649727386 & 19.1 \tabularnewline
3 & -8.13333333333333 & 1.96160107766049 & 5.8 \tabularnewline
4 & -11.7583333333333 & 4.20810005354032 & 12.7 \tabularnewline
5 & -1.08333333333333 & 2.34087525718415 & 7.9 \tabularnewline
6 & -4.475 & 3.06746119483494 & 8.4 \tabularnewline
7 & 5.2 & 2.11359237490883 & 7.1 \tabularnewline
8 & 4.78333333333333 & 2.36444624819556 & 8.4 \tabularnewline
9 & -6.31666666666667 & 10.1005700409192 & 30.8 \tabularnewline
10 & -21.7583333333333 & 8.36849702301688 & 23.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114986&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]6.79166666666667[/C][C]1.51204757821567[/C][C]4.5[/C][/ROW]
[ROW][C]2[/C][C]-7.01666666666667[/C][C]6.41345649727386[/C][C]19.1[/C][/ROW]
[ROW][C]3[/C][C]-8.13333333333333[/C][C]1.96160107766049[/C][C]5.8[/C][/ROW]
[ROW][C]4[/C][C]-11.7583333333333[/C][C]4.20810005354032[/C][C]12.7[/C][/ROW]
[ROW][C]5[/C][C]-1.08333333333333[/C][C]2.34087525718415[/C][C]7.9[/C][/ROW]
[ROW][C]6[/C][C]-4.475[/C][C]3.06746119483494[/C][C]8.4[/C][/ROW]
[ROW][C]7[/C][C]5.2[/C][C]2.11359237490883[/C][C]7.1[/C][/ROW]
[ROW][C]8[/C][C]4.78333333333333[/C][C]2.36444624819556[/C][C]8.4[/C][/ROW]
[ROW][C]9[/C][C]-6.31666666666667[/C][C]10.1005700409192[/C][C]30.8[/C][/ROW]
[ROW][C]10[/C][C]-21.7583333333333[/C][C]8.36849702301688[/C][C]23.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114986&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
16.791666666666671.512047578215674.5
2-7.016666666666676.4134564972738619.1
3-8.133333333333331.961601077660495.8
4-11.75833333333334.2081000535403212.7
5-1.083333333333332.340875257184157.9
6-4.4753.067461194834948.4
75.22.113592374908837.1
84.783333333333332.364446248195568.4
9-6.3166666666666710.100570040919230.8
10-21.75833333333338.3684970230168823.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.27059104112975
beta-0.222652024397237
S.D.0.0925178915489023
T-STAT-2.40658342586146
p-value0.0427354272353758

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.27059104112975 \tabularnewline
beta & -0.222652024397237 \tabularnewline
S.D. & 0.0925178915489023 \tabularnewline
T-STAT & -2.40658342586146 \tabularnewline
p-value & 0.0427354272353758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114986&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.27059104112975[/C][/ROW]
[ROW][C]beta[/C][C]-0.222652024397237[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0925178915489023[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.40658342586146[/C][/ROW]
[ROW][C]p-value[/C][C]0.0427354272353758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114986&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114986&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)
alpha3.27059104112975
beta-0.222652024397237
S.D.0.0925178915489023
T-STAT-2.40658342586146
p-value0.0427354272353758






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.8459429034218
beta-1.27019015600093
S.D.0.0170157195672399
T-STAT-74.6480424164019
p-value0.00852777479035878
Lambda2.27019015600093

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.8459429034218 \tabularnewline
beta & -1.27019015600093 \tabularnewline
S.D. & 0.0170157195672399 \tabularnewline
T-STAT & -74.6480424164019 \tabularnewline
p-value & 0.00852777479035878 \tabularnewline
Lambda & 2.27019015600093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114986&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.8459429034218[/C][/ROW]
[ROW][C]beta[/C][C]-1.27019015600093[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0170157195672399[/C][/ROW]
[ROW][C]T-STAT[/C][C]-74.6480424164019[/C][/ROW]
[ROW][C]p-value[/C][C]0.00852777479035878[/C][/ROW]
[ROW][C]Lambda[/C][C]2.27019015600093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114986&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114986&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)
alpha2.8459429034218
beta-1.27019015600093
S.D.0.0170157195672399
T-STAT-74.6480424164019
p-value0.00852777479035878
Lambda2.27019015600093


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')