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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 computationThu, 22 Dec 2011 20:51:43 -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/22/t1324605115roejggnezu7klhs.htm/, Retrieved Fri, 03 May 2024 11:28:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160152, Retrieved Fri, 03 May 2024 11:28:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Spectral Analysis] [Births] [2010-11-29 09:38:20] [b98453cac15ba1066b407e146608df68]
- R  D          [Spectral Analysis] [WS9 3.2 CP d=0, D=0] [2010-12-07 10:39:32] [afe9379cca749d06b3d6872e02cc47ed]
- RMPD              [Standard Deviation-Mean Plot] [PAPER: werklooshe...] [2011-12-23 01:51:43] [6baf48ba14bcb50d9e72b77bece8a45b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,072
0,073
0,073
0,073
0,074
0,073
0,074
0,074
0,076
0,076
0,077
0,077
0,078
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0,080
0,081
0,081
0,082
0,081
0,081
0,081
0,080
0,082
0,084
0,084
0,085
0,086
0,085
0,083
0,078
0,078
0,080
0,086
0,089
0,089
0,086
0,083
0,083
0,083
0,084
0,085
0,084
0,086
0,085
0,085
0,085
0,085
0,085
0,085
0,085
0,085
0,086
0,086
0,086
0,086
0,084
0,080
0,079
0,080
0,080
0,080
0,080
0,079
0,079
0,079
0,080
0,079
0,075
0,072
0,070
0,069
0,071
0,071
0,072
0,071
0,069
0,068
0,067
0,067
0,069
0,073
0,074
0,073
0,071
0,070
0,071
0,075
0,077
0,078
0,077
0,077
0,078
0,080
0,081
0,081
0,080
0,081
0,082
0,083
0,084
0,085
0,085
0,085
0,085
0,085
0,083
0,082
0,081
0,079
0,076
0,073
0,071
0,070
0,070
0,070
0,070
0,069
0,068
0,067
0,066

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160152&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160152&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.07433333333333330.001723280873710660.005
20.080750.00165831239517770.00600000000000001
30.08408333333333330.003728473568568660.011
40.08441666666666670.0009962049198956210.00299999999999999
50.08350.002844452335847640.00699999999999999
60.07608333333333330.004378840305862090.011
70.07041666666666670.002391588796113780.00699999999999999
80.07708333333333330.003579190699111470.011
90.08341666666666670.001621353717973930.004
100.070750.003695820735518820.013

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.0743333333333333 & 0.00172328087371066 & 0.005 \tabularnewline
2 & 0.08075 & 0.0016583123951777 & 0.00600000000000001 \tabularnewline
3 & 0.0840833333333333 & 0.00372847356856866 & 0.011 \tabularnewline
4 & 0.0844166666666667 & 0.000996204919895621 & 0.00299999999999999 \tabularnewline
5 & 0.0835 & 0.00284445233584764 & 0.00699999999999999 \tabularnewline
6 & 0.0760833333333333 & 0.00437884030586209 & 0.011 \tabularnewline
7 & 0.0704166666666667 & 0.00239158879611378 & 0.00699999999999999 \tabularnewline
8 & 0.0770833333333333 & 0.00357919069911147 & 0.011 \tabularnewline
9 & 0.0834166666666667 & 0.00162135371797393 & 0.004 \tabularnewline
10 & 0.07075 & 0.00369582073551882 & 0.013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160152&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]0.0743333333333333[/C][C]0.00172328087371066[/C][C]0.005[/C][/ROW]
[ROW][C]2[/C][C]0.08075[/C][C]0.0016583123951777[/C][C]0.00600000000000001[/C][/ROW]
[ROW][C]3[/C][C]0.0840833333333333[/C][C]0.00372847356856866[/C][C]0.011[/C][/ROW]
[ROW][C]4[/C][C]0.0844166666666667[/C][C]0.000996204919895621[/C][C]0.00299999999999999[/C][/ROW]
[ROW][C]5[/C][C]0.0835[/C][C]0.00284445233584764[/C][C]0.00699999999999999[/C][/ROW]
[ROW][C]6[/C][C]0.0760833333333333[/C][C]0.00437884030586209[/C][C]0.011[/C][/ROW]
[ROW][C]7[/C][C]0.0704166666666667[/C][C]0.00239158879611378[/C][C]0.00699999999999999[/C][/ROW]
[ROW][C]8[/C][C]0.0770833333333333[/C][C]0.00357919069911147[/C][C]0.011[/C][/ROW]
[ROW][C]9[/C][C]0.0834166666666667[/C][C]0.00162135371797393[/C][C]0.004[/C][/ROW]
[ROW][C]10[/C][C]0.07075[/C][C]0.00369582073551882[/C][C]0.013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160152&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
10.07433333333333330.001723280873710660.005
20.080750.00165831239517770.00600000000000001
30.08408333333333330.003728473568568660.011
40.08441666666666670.0009962049198956210.00299999999999999
50.08350.002844452335847640.00699999999999999
60.07608333333333330.004378840305862090.011
70.07041666666666670.002391588796113780.00699999999999999
80.07708333333333330.003579190699111470.011
90.08341666666666670.001621353717973930.004
100.070750.003695820735518820.013






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.00779524837534031
beta-0.065408747596886
S.D.0.070210634852635
T-STAT-0.93160740868064
p-value0.378796078753345

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.00779524837534031 \tabularnewline
beta & -0.065408747596886 \tabularnewline
S.D. & 0.070210634852635 \tabularnewline
T-STAT & -0.93160740868064 \tabularnewline
p-value & 0.378796078753345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160152&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.00779524837534031[/C][/ROW]
[ROW][C]beta[/C][C]-0.065408747596886[/C][/ROW]
[ROW][C]S.D.[/C][C]0.070210634852635[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.93160740868064[/C][/ROW]
[ROW][C]p-value[/C][C]0.378796078753345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160152&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160152&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)
alpha0.00779524837534031
beta-0.065408747596886
S.D.0.070210634852635
T-STAT-0.93160740868064
p-value0.378796078753345






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-12.2184553165292
beta-2.43134442982395
S.D.2.2552035700831
T-STAT-1.07810419515004
p-value0.312418429313637
Lambda3.43134442982395

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -12.2184553165292 \tabularnewline
beta & -2.43134442982395 \tabularnewline
S.D. & 2.2552035700831 \tabularnewline
T-STAT & -1.07810419515004 \tabularnewline
p-value & 0.312418429313637 \tabularnewline
Lambda & 3.43134442982395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160152&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.2184553165292[/C][/ROW]
[ROW][C]beta[/C][C]-2.43134442982395[/C][/ROW]
[ROW][C]S.D.[/C][C]2.2552035700831[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.07810419515004[/C][/ROW]
[ROW][C]p-value[/C][C]0.312418429313637[/C][/ROW]
[ROW][C]Lambda[/C][C]3.43134442982395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160152&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160152&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-12.2184553165292
beta-2.43134442982395
S.D.2.2552035700831
T-STAT-1.07810419515004
p-value0.312418429313637
Lambda3.43134442982395


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = multiplicative ; par2 = 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')