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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Module--
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 21 Dec 2012 15:20:31 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356121263jp9iofqwbqk7bjf.htm/, Retrieved Sat, 20 Apr 2024 08:08:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204222, Retrieved Sat, 20 Apr 2024 08:08:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

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] [] [2011-12-05 21:56:19] [bdca8f3e7c3554be8c1291e54f61d441]
- RM      [Standard Deviation-Mean Plot] [] [2012-12-21 20:20:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9007
8106
8928
9137
10017
10826
11317
10744
9713
9938
9161
8927
7750
6981
8038
8422
8714
9512
10120
9823
8743
9129
8710
8680
8162
7306
8124
7870
9387
9556
10093
9620
8285
8433
8160
8034
7717
7461
7776
7925
8634
8945
10078
9179
8037
8488
7874
8647
7792
6957
7726
8106
8890
9299
10625
9302
8314
8850
8265
8796
7836
6892
7791
8129
9115
9434
10484
9827
9110
9070
8633
9240

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' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204222&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204222&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' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19651.75949.8303317387323211
28718.5878.6529462762873139
38585.83333333333856.3756432922662787
48396.75751.6399192311562617
58576.83333333333944.5947503687723668
68796.75991.7940699927213592

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9651.75 & 949.830331738732 & 3211 \tabularnewline
2 & 8718.5 & 878.652946276287 & 3139 \tabularnewline
3 & 8585.83333333333 & 856.375643292266 & 2787 \tabularnewline
4 & 8396.75 & 751.639919231156 & 2617 \tabularnewline
5 & 8576.83333333333 & 944.594750368772 & 3668 \tabularnewline
6 & 8796.75 & 991.794069992721 & 3592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204222&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]9651.75[/C][C]949.830331738732[/C][C]3211[/C][/ROW]
[ROW][C]2[/C][C]8718.5[/C][C]878.652946276287[/C][C]3139[/C][/ROW]
[ROW][C]3[/C][C]8585.83333333333[/C][C]856.375643292266[/C][C]2787[/C][/ROW]
[ROW][C]4[/C][C]8396.75[/C][C]751.639919231156[/C][C]2617[/C][/ROW]
[ROW][C]5[/C][C]8576.83333333333[/C][C]944.594750368772[/C][C]3668[/C][/ROW]
[ROW][C]6[/C][C]8796.75[/C][C]991.794069992721[/C][C]3592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204222&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
19651.75949.8303317387323211
28718.5878.6529462762873139
38585.83333333333856.3756432922662787
48396.75751.6399192311562617
58576.83333333333944.5947503687723668
68796.75991.7940699927213592






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-17.1994837743824
beta0.103858462412982
S.D.0.0817803411812195
T-STAT1.26996856350647
p-value0.272945694342843

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -17.1994837743824 \tabularnewline
beta & 0.103858462412982 \tabularnewline
S.D. & 0.0817803411812195 \tabularnewline
T-STAT & 1.26996856350647 \tabularnewline
p-value & 0.272945694342843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204222&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-17.1994837743824[/C][/ROW]
[ROW][C]beta[/C][C]0.103858462412982[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0817803411812195[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.26996856350647[/C][/ROW]
[ROW][C]p-value[/C][C]0.272945694342843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204222&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)
alpha-17.1994837743824
beta0.103858462412982
S.D.0.0817803411812195
T-STAT1.26996856350647
p-value0.272945694342843






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.35023743160565
beta1.11712098223417
S.D.0.8475040811184
T-STAT1.31813050476403
p-value0.257875344012024
Lambda-0.117120982234171

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.35023743160565 \tabularnewline
beta & 1.11712098223417 \tabularnewline
S.D. & 0.8475040811184 \tabularnewline
T-STAT & 1.31813050476403 \tabularnewline
p-value & 0.257875344012024 \tabularnewline
Lambda & -0.117120982234171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204222&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.35023743160565[/C][/ROW]
[ROW][C]beta[/C][C]1.11712098223417[/C][/ROW]
[ROW][C]S.D.[/C][C]0.8475040811184[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.31813050476403[/C][/ROW]
[ROW][C]p-value[/C][C]0.257875344012024[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.117120982234171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204222&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204222&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)
alpha-3.35023743160565
beta1.11712098223417
S.D.0.8475040811184
T-STAT1.31813050476403
p-value0.257875344012024
Lambda-0.117120982234171


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')