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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 computationSun, 06 Jan 2008 13:30:23 -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/Jan/06/t1199651394gxvvlhj9dx0mfvm.htm/, Retrieved Sun, 05 May 2024 01:01:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7886, Retrieved Sun, 05 May 2024 01:01:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsInducing time series Q1 WL
Estimated Impact157

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [WS2 - Robustness ...] [2007-10-20 13:06:37] [5343e105a400b9e32bf6f011133bbaf4]
- RM D    [Standard Deviation-Mean Plot] [CVWS7WLQ1] [2008-01-06 20:30:23] [b523c8d839cc24a05ea912c062a47207] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,3
7,2
7,1
6,9
6,8
6,7
6,8
6,8
6,7
6,8
6,8
6,7
6,3
6,2
6,2
6,5
6,5
6,4
6,2
6,2
6,3
7,5
7,4
7,4
7,4
7,4
7,4
7,2
7,2
7,2
7,5
7,4
7,5
8,0
8,0
8,0
8,1
8,1
8,1
7,9
7,9
8,0
8,2
8,1
8,2
8,5
8,5
8,6
8,4
8,4
8,4
7,7
7,8
7,9
8,8
8,8
8,9
8,5
8,5
8,5
8,4
8,5
8,4
8,3
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,3
8,3
8,3
8,2
8,1
8,1
8,2
8,0
7,9
7,9
7,8
7,7
7,9
7,7
7,6

Tables (Output of Computation)





Summary of compuational 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

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7886&T=0

[TABLE]
[ROW][C]Summary of compuational 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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7886&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 compuational 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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
16.883333333333330.2037526724122940.6
26.591666666666670.5195423393952051.3
37.516666666666670.3099364548751990.8
48.183333333333330.2329000305762630.700
58.383333333333330.392737093030981.2
68.450.0674199862463240.199999999999999
78.241666666666670.1975225341958520.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.88333333333333 & 0.203752672412294 & 0.6 \tabularnewline
2 & 6.59166666666667 & 0.519542339395205 & 1.3 \tabularnewline
3 & 7.51666666666667 & 0.309936454875199 & 0.8 \tabularnewline
4 & 8.18333333333333 & 0.232900030576263 & 0.700 \tabularnewline
5 & 8.38333333333333 & 0.39273709303098 & 1.2 \tabularnewline
6 & 8.45 & 0.067419986246324 & 0.199999999999999 \tabularnewline
7 & 8.24166666666667 & 0.197522534195852 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7886&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]6.88333333333333[/C][C]0.203752672412294[/C][C]0.6[/C][/ROW]
[ROW][C]2[/C][C]6.59166666666667[/C][C]0.519542339395205[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]7.51666666666667[/C][C]0.309936454875199[/C][C]0.8[/C][/ROW]
[ROW][C]4[/C][C]8.18333333333333[/C][C]0.232900030576263[/C][C]0.700[/C][/ROW]
[ROW][C]5[/C][C]8.38333333333333[/C][C]0.39273709303098[/C][C]1.2[/C][/ROW]
[ROW][C]6[/C][C]8.45[/C][C]0.067419986246324[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]7[/C][C]8.24166666666667[/C][C]0.197522534195852[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7886&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
16.883333333333330.2037526724122940.6
26.591666666666670.5195423393952051.3
37.516666666666670.3099364548751990.8
48.183333333333330.2329000305762630.700
58.383333333333330.392737093030981.2
68.450.0674199862463240.199999999999999
78.241666666666670.1975225341958520.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.07206528990471
beta-0.102869049190799
S.D.0.0736777978174313
T-STAT-1.39620146418737
p-value0.221475541992503

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.07206528990471 \tabularnewline
beta & -0.102869049190799 \tabularnewline
S.D. & 0.0736777978174313 \tabularnewline
T-STAT & -1.39620146418737 \tabularnewline
p-value & 0.221475541992503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7886&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.07206528990471[/C][/ROW]
[ROW][C]beta[/C][C]-0.102869049190799[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0736777978174313[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.39620146418737[/C][/ROW]
[ROW][C]p-value[/C][C]0.221475541992503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7886&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7886&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)
alpha1.07206528990471
beta-0.102869049190799
S.D.0.0736777978174313
T-STAT-1.39620146418737
p-value0.221475541992503






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.16008216295009
beta-3.23328552939363
S.D.2.51041343126414
T-STAT-1.28794942264370
p-value0.254147022745967
Lambda4.23328552939363

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.16008216295009 \tabularnewline
beta & -3.23328552939363 \tabularnewline
S.D. & 2.51041343126414 \tabularnewline
T-STAT & -1.28794942264370 \tabularnewline
p-value & 0.254147022745967 \tabularnewline
Lambda & 4.23328552939363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7886&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.16008216295009[/C][/ROW]
[ROW][C]beta[/C][C]-3.23328552939363[/C][/ROW]
[ROW][C]S.D.[/C][C]2.51041343126414[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.28794942264370[/C][/ROW]
[ROW][C]p-value[/C][C]0.254147022745967[/C][/ROW]
[ROW][C]Lambda[/C][C]4.23328552939363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7886&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7886&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)
alpha5.16008216295009
beta-3.23328552939363
S.D.2.51041343126414
T-STAT-1.28794942264370
p-value0.254147022745967
Lambda4.23328552939363


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')