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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 computationMon, 08 Dec 2008 11:31:34 -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/Dec/08/t12287612682ttt6p12q7c2huj.htm/, Retrieved Thu, 16 May 2024 12:24:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30660, Retrieved Thu, 16 May 2024 12:24:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

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]
- RMPD    [Standard Deviation-Mean Plot] [S1 - SDM] [2008-12-08 18:31:34] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15645
14568
12520
14803
15873
14755
12875
14291
14205
15859
15259
15499
15107
15024
12083
15761
16943
15070
13660
14769
14725
15998
15371
14957
15470
15102
11704
16284
16727
14969
14861
14583
15306
17904
16379
15420
17871
15913
13867
17823
17872
17420
16704
15991
16584
19124
17839
17209
18587
16258
15142
19202
17747
19090
18040
17516
17752
21072
17170
19440
19795
17575
16165
19465
19932
19961
17343
18924
18574
21351
18595
19823
20844
19640
17735
19814
22239
20682
17819
21872
22117
21866
23451
20954
22497

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30660&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30660&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114679.33333333331090.637039310123353
214955.66666666671202.900988393804860
315392.41666666671497.794709706326200
417018.08333333331345.153553812105257
518084.66666666671556.664051649225930
618958.58333333331413.863723556095186
720752.751751.096234570585716

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14679.3333333333 & 1090.63703931012 & 3353 \tabularnewline
2 & 14955.6666666667 & 1202.90098839380 & 4860 \tabularnewline
3 & 15392.4166666667 & 1497.79470970632 & 6200 \tabularnewline
4 & 17018.0833333333 & 1345.15355381210 & 5257 \tabularnewline
5 & 18084.6666666667 & 1556.66405164922 & 5930 \tabularnewline
6 & 18958.5833333333 & 1413.86372355609 & 5186 \tabularnewline
7 & 20752.75 & 1751.09623457058 & 5716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30660&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]14679.3333333333[/C][C]1090.63703931012[/C][C]3353[/C][/ROW]
[ROW][C]2[/C][C]14955.6666666667[/C][C]1202.90098839380[/C][C]4860[/C][/ROW]
[ROW][C]3[/C][C]15392.4166666667[/C][C]1497.79470970632[/C][C]6200[/C][/ROW]
[ROW][C]4[/C][C]17018.0833333333[/C][C]1345.15355381210[/C][C]5257[/C][/ROW]
[ROW][C]5[/C][C]18084.6666666667[/C][C]1556.66405164922[/C][C]5930[/C][/ROW]
[ROW][C]6[/C][C]18958.5833333333[/C][C]1413.86372355609[/C][C]5186[/C][/ROW]
[ROW][C]7[/C][C]20752.75[/C][C]1751.09623457058[/C][C]5716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30660&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
114679.33333333331090.637039310123353
214955.66666666671202.900988393804860
315392.41666666671497.794709706326200
417018.08333333331345.153553812105257
518084.66666666671556.664051649225930
618958.58333333331413.863723556095186
720752.751751.096234570585716






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha50.33032941174
beta0.0793197514643597
S.D.0.0251761587503574
T-STAT3.15058989939177
p-value0.0253621065165561

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 50.33032941174 \tabularnewline
beta & 0.0793197514643597 \tabularnewline
S.D. & 0.0251761587503574 \tabularnewline
T-STAT & 3.15058989939177 \tabularnewline
p-value & 0.0253621065165561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30660&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]50.33032941174[/C][/ROW]
[ROW][C]beta[/C][C]0.0793197514643597[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0251761587503574[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.15058989939177[/C][/ROW]
[ROW][C]p-value[/C][C]0.0253621065165561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30660&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)
alpha50.33032941174
beta0.0793197514643597
S.D.0.0251761587503574
T-STAT3.15058989939177
p-value0.0253621065165561






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.33805161784907
beta0.98324815042485
S.D.0.319970419168591
T-STAT3.07293453244745
p-value0.0276911945729756
Lambda0.0167518495751506

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.33805161784907 \tabularnewline
beta & 0.98324815042485 \tabularnewline
S.D. & 0.319970419168591 \tabularnewline
T-STAT & 3.07293453244745 \tabularnewline
p-value & 0.0276911945729756 \tabularnewline
Lambda & 0.0167518495751506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30660&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.33805161784907[/C][/ROW]
[ROW][C]beta[/C][C]0.98324815042485[/C][/ROW]
[ROW][C]S.D.[/C][C]0.319970419168591[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.07293453244745[/C][/ROW]
[ROW][C]p-value[/C][C]0.0276911945729756[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0167518495751506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30660&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-2.33805161784907
beta0.98324815042485
S.D.0.319970419168591
T-STAT3.07293453244745
p-value0.0276911945729756
Lambda0.0167518495751506


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')