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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 computationWed, 04 Dec 2013 06:52:07 -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/2013/Dec/04/t1386158203aiwhhp9r7auvho4.htm/, Retrieved Fri, 19 Apr 2024 12:15:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230536, Retrieved Fri, 19 Apr 2024 12:15:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [] [2013-12-04 11:52:07] [548ba37af61861f215c3470847960b18] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
462.23
464.79
465.22
468.52
469.02
469.15
469.15
469.15
469.15
469.41
469.45
469.45
469.93
477.19
478.97
480.44
480.56
481.8
483.24
483.45
483.53
483.59
483.59
483.59
492.36
495.71
499.29
499.78
500
500
500.29
500.42
500.61
498.9
499.06
496.61
498.41
501.26
505.4
506.07
506.2
507.14
507.14
507.28
507.34
507.48
506.97
506.97
510.1
515.84
519
520.1
521.26
521.04
521.12
521.12
521.1
521.16
521.14
521.13
522.17
531.39
532.12
533.34
535.72
536.25
536.25
536.68
536.76
536.79
536.99
536.99
542.38
544.1
546.96
547.04
550.27
550.32
551.17
552.83
552.35
552.44
552.47
548.78

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230536&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]3 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=230536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230536&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1467.8908333333332.411643944522387.21999999999997
2480.8233333333334.0395754352369313.66
3498.5858333333332.478014081452898.25
4505.6383333333332.844713864292329.06999999999999
5519.5091666666673.3540300273316511.16
6534.28754.2989092168299514.8200000000001
7549.2591666666673.476022958218310.45

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 467.890833333333 & 2.41164394452238 & 7.21999999999997 \tabularnewline
2 & 480.823333333333 & 4.03957543523693 & 13.66 \tabularnewline
3 & 498.585833333333 & 2.47801408145289 & 8.25 \tabularnewline
4 & 505.638333333333 & 2.84471386429232 & 9.06999999999999 \tabularnewline
5 & 519.509166666667 & 3.35403002733165 & 11.16 \tabularnewline
6 & 534.2875 & 4.29890921682995 & 14.8200000000001 \tabularnewline
7 & 549.259166666667 & 3.4760229582183 & 10.45 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230536&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]467.890833333333[/C][C]2.41164394452238[/C][C]7.21999999999997[/C][/ROW]
[ROW][C]2[/C][C]480.823333333333[/C][C]4.03957543523693[/C][C]13.66[/C][/ROW]
[ROW][C]3[/C][C]498.585833333333[/C][C]2.47801408145289[/C][C]8.25[/C][/ROW]
[ROW][C]4[/C][C]505.638333333333[/C][C]2.84471386429232[/C][C]9.06999999999999[/C][/ROW]
[ROW][C]5[/C][C]519.509166666667[/C][C]3.35403002733165[/C][C]11.16[/C][/ROW]
[ROW][C]6[/C][C]534.2875[/C][C]4.29890921682995[/C][C]14.8200000000001[/C][/ROW]
[ROW][C]7[/C][C]549.259166666667[/C][C]3.4760229582183[/C][C]10.45[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230536&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
1467.8908333333332.411643944522387.21999999999997
2480.8233333333334.0395754352369313.66
3498.5858333333332.478014081452898.25
4505.6383333333332.844713864292329.06999999999999
5519.5091666666673.3540300273316511.16
6534.28754.2989092168299514.8200000000001
7549.2591666666673.476022958218310.45






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.70967119010148
beta0.0117746559460314
S.D.0.0101457338426687
T-STAT1.16055241825014
p-value0.298219176119639

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.70967119010148 \tabularnewline
beta & 0.0117746559460314 \tabularnewline
S.D. & 0.0101457338426687 \tabularnewline
T-STAT & 1.16055241825014 \tabularnewline
p-value & 0.298219176119639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230536&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.70967119010148[/C][/ROW]
[ROW][C]beta[/C][C]0.0117746559460314[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0101457338426687[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16055241825014[/C][/ROW]
[ROW][C]p-value[/C][C]0.298219176119639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230536&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-2.70967119010148
beta0.0117746559460314
S.D.0.0101457338426687
T-STAT1.16055241825014
p-value0.298219176119639






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.1697290518907
beta1.97992010288355
S.D.1.55787921922544
T-STAT1.27090731967523
p-value0.259679231981226
Lambda-0.979920102883547

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.1697290518907 \tabularnewline
beta & 1.97992010288355 \tabularnewline
S.D. & 1.55787921922544 \tabularnewline
T-STAT & 1.27090731967523 \tabularnewline
p-value & 0.259679231981226 \tabularnewline
Lambda & -0.979920102883547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230536&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.1697290518907[/C][/ROW]
[ROW][C]beta[/C][C]1.97992010288355[/C][/ROW]
[ROW][C]S.D.[/C][C]1.55787921922544[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.27090731967523[/C][/ROW]
[ROW][C]p-value[/C][C]0.259679231981226[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.979920102883547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230536&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230536&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-11.1697290518907
beta1.97992010288355
S.D.1.55787921922544
T-STAT1.27090731967523
p-value0.259679231981226
Lambda-0.979920102883547


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')