FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 06 Dec 2011 14:20:41 -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/2011/Dec/06/t1323199255now0qk3vwhr2cli.htm/, Retrieved Sun, 28 Apr 2024 19:39:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151823, Retrieved Sun, 28 Apr 2024 19:39:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
F   PD    [Standard Deviation-Mean Plot] [stationarity in t...] [2010-12-03 10:13:26] [74deae64b71f9d77c839af86f7c687b5]
- RM          [Standard Deviation-Mean Plot] [] [2011-12-06 19:20:41] [4be1b05f688f7fa8db5b9e9e4d3a7e33] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,76
102,37
102,38
102,86
102,87
102,92
102,95
103,02
104,08
104,16
104,24
104,33
104,73
104,86
105,03
105,62
105,63
105,63
105,94
106,61
107,69
107,78
107,93
108,48
108,14
108,48
108,48
108,89
108,93
109,21
109,47
109,80
111,73
111,85
112,12
112,15
112,17
112,67
112,80
113,44
113,53
114,53
114,51
115,05
116,67
117,07
116,92
117,00
117,02
117,35
117,36
117,82
117,88
118,24
118,50
118,80
119,76
120,09

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151823&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151823&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.1616666666670.845822174877882.56999999999999
2106.32751.323220073773213.75
3109.93751.563440989379754.01000000000001
4114.6966666666671.833820320995754.89999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.161666666667 & 0.84582217487788 & 2.56999999999999 \tabularnewline
2 & 106.3275 & 1.32322007377321 & 3.75 \tabularnewline
3 & 109.9375 & 1.56344098937975 & 4.01000000000001 \tabularnewline
4 & 114.696666666667 & 1.83382032099575 & 4.89999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151823&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]103.161666666667[/C][C]0.84582217487788[/C][C]2.56999999999999[/C][/ROW]
[ROW][C]2[/C][C]106.3275[/C][C]1.32322007377321[/C][C]3.75[/C][/ROW]
[ROW][C]3[/C][C]109.9375[/C][C]1.56344098937975[/C][C]4.01000000000001[/C][/ROW]
[ROW][C]4[/C][C]114.696666666667[/C][C]1.83382032099575[/C][C]4.89999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151823&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
1103.1616666666670.845822174877882.56999999999999
2106.32751.323220073773213.75
3109.93751.563440989379754.01000000000001
4114.6966666666671.833820320995754.89999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-7.51936951554499
beta0.0821051965751819
S.D.0.0144922686066552
T-STAT5.66544816437347
p-value0.0297709887296641

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.51936951554499 \tabularnewline
beta & 0.0821051965751819 \tabularnewline
S.D. & 0.0144922686066552 \tabularnewline
T-STAT & 5.66544816437347 \tabularnewline
p-value & 0.0297709887296641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151823&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.51936951554499[/C][/ROW]
[ROW][C]beta[/C][C]0.0821051965751819[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0144922686066552[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.66544816437347[/C][/ROW]
[ROW][C]p-value[/C][C]0.0297709887296641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151823&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151823&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-7.51936951554499
beta0.0821051965751819
S.D.0.0144922686066552
T-STAT5.66544816437347
p-value0.0297709887296641






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-32.0898425760819
beta6.90984877009071
S.D.1.73717451692906
T-STAT3.97763650269623
p-value0.0577810333269001
Lambda-5.90984877009071

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -32.0898425760819 \tabularnewline
beta & 6.90984877009071 \tabularnewline
S.D. & 1.73717451692906 \tabularnewline
T-STAT & 3.97763650269623 \tabularnewline
p-value & 0.0577810333269001 \tabularnewline
Lambda & -5.90984877009071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151823&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-32.0898425760819[/C][/ROW]
[ROW][C]beta[/C][C]6.90984877009071[/C][/ROW]
[ROW][C]S.D.[/C][C]1.73717451692906[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.97763650269623[/C][/ROW]
[ROW][C]p-value[/C][C]0.0577810333269001[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.90984877009071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151823&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151823&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-32.0898425760819
beta6.90984877009071
S.D.1.73717451692906
T-STAT3.97763650269623
p-value0.0577810333269001
Lambda-5.90984877009071


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')