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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 computationSun, 14 Dec 2008 07:15:18 -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/14/t1229264334z6olwwr6g3arx3u.htm/, Retrieved Wed, 15 May 2024 12:17:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33388, Retrieved Wed, 15 May 2024 12:17:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [standard deviatio...] [2008-12-14 14:15:18] [d300b7a0882cee7d84584ad37a3d4ede] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,02
100,67
100,47
100,38
100,33
100,34
100,37
100,39
100,21
100,21
100,22
100,28
100,25
100,25
100,21
100,16
100,18
100,1
99,96
99,88
99,88
99,86
99,84
99,8
99,82
99,81
99,92
100,03
99,99
100,02
100,01
100,13
100,33
100,13
99,96
100,05
99,83
99,8
100,01
100,1
100,13
100,16
100,41
101,34
101,65
101,85
102,07
102,12
102,14
102,21
102,28
102,19
102,33
102,54
102,44
102,78
102,9
103,08
102,77
102,65
102,71
103,29
102,86
103,45
103,72
103,65
103,83
104,45
105,14
105,07
105,31
105,19
105,3
105,02
105,17
105,28
105,45
105,38
105,8
105,96
105,08
105,11
105,61
105,5

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33388&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33388&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1100.40750.2316786567640620.810000000000002
2100.0308333333330.1761434504928170.450000000000003
3100.0166666666670.141378494785730.519999999999996
4100.7891666666670.9310840049331892.32000000000001
5102.5258333333330.3096173102200190.939999999999998
6104.0558333333330.941077316245332.60000000000001
7105.3883333333330.2918851995168120.939999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.4075 & 0.231678656764062 & 0.810000000000002 \tabularnewline
2 & 100.030833333333 & 0.176143450492817 & 0.450000000000003 \tabularnewline
3 & 100.016666666667 & 0.14137849478573 & 0.519999999999996 \tabularnewline
4 & 100.789166666667 & 0.931084004933189 & 2.32000000000001 \tabularnewline
5 & 102.525833333333 & 0.309617310220019 & 0.939999999999998 \tabularnewline
6 & 104.055833333333 & 0.94107731624533 & 2.60000000000001 \tabularnewline
7 & 105.388333333333 & 0.291885199516812 & 0.939999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33388&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]100.4075[/C][C]0.231678656764062[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]2[/C][C]100.030833333333[/C][C]0.176143450492817[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]3[/C][C]100.016666666667[/C][C]0.14137849478573[/C][C]0.519999999999996[/C][/ROW]
[ROW][C]4[/C][C]100.789166666667[/C][C]0.931084004933189[/C][C]2.32000000000001[/C][/ROW]
[ROW][C]5[/C][C]102.525833333333[/C][C]0.309617310220019[/C][C]0.939999999999998[/C][/ROW]
[ROW][C]6[/C][C]104.055833333333[/C][C]0.94107731624533[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]7[/C][C]105.388333333333[/C][C]0.291885199516812[/C][C]0.939999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33388&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
1100.40750.2316786567640620.810000000000002
2100.0308333333330.1761434504928170.450000000000003
3100.0166666666670.141378494785730.519999999999996
4100.7891666666670.9310840049331892.32000000000001
5102.5258333333330.3096173102200190.939999999999998
6104.0558333333330.941077316245332.60000000000001
7105.3883333333330.2918851995168120.939999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.35670111114123
beta0.0469981862076677
S.D.0.0696295075360184
T-STAT0.674975134404853
p-value0.529638379587051

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.35670111114123 \tabularnewline
beta & 0.0469981862076677 \tabularnewline
S.D. & 0.0696295075360184 \tabularnewline
T-STAT & 0.674975134404853 \tabularnewline
p-value & 0.529638379587051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33388&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.35670111114123[/C][/ROW]
[ROW][C]beta[/C][C]0.0469981862076677[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0696295075360184[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.674975134404853[/C][/ROW]
[ROW][C]p-value[/C][C]0.529638379587051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33388&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33388&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-4.35670111114123
beta0.0469981862076677
S.D.0.0696295075360184
T-STAT0.674975134404853
p-value0.529638379587051






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-69.0052560165646
beta14.6866754264023
S.D.14.7326651062435
T-STAT0.996878386937494
p-value0.364591119701246
Lambda-13.6866754264023

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -69.0052560165646 \tabularnewline
beta & 14.6866754264023 \tabularnewline
S.D. & 14.7326651062435 \tabularnewline
T-STAT & 0.996878386937494 \tabularnewline
p-value & 0.364591119701246 \tabularnewline
Lambda & -13.6866754264023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33388&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-69.0052560165646[/C][/ROW]
[ROW][C]beta[/C][C]14.6866754264023[/C][/ROW]
[ROW][C]S.D.[/C][C]14.7326651062435[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.996878386937494[/C][/ROW]
[ROW][C]p-value[/C][C]0.364591119701246[/C][/ROW]
[ROW][C]Lambda[/C][C]-13.6866754264023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33388&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33388&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-69.0052560165646
beta14.6866754264023
S.D.14.7326651062435
T-STAT0.996878386937494
p-value0.364591119701246
Lambda-13.6866754264023


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')