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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 computationSat, 06 Jun 2009 05:53:00 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t12442896915qg7sdfj7yq4et3.htm/, Retrieved Sun, 28 Apr 2024 23:00:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41976, Retrieved Sun, 28 Apr 2024 23:00:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [Jurgen Leemans - ...] [2009-06-06 11:53:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
163.40
162.89
162.29
161.26
161.43
161.44
161.44
161.44
161.92
162.23
161.89
161.40
161.40
159.55
158.93
158.59
158.29
158.03
158.03
163.94
164.36
164.39
163.22
163.22
163.56
162.82
162.80
162.44
161.98
161.53
161.53
161.52
162.07
161.84
161.54
161.47
161.47
161.54
161.57
160.75
160.31
160.57
160.57
159.65
158.76
158.95
159.25
158.72
158.72
158.72
158.53
157.92
157.89
157.81
157.81
157.88
157.52
156.11
155.61
155.31
155.31
155.31
153.09
151.94
151.73
151.65
151.65
151.09
149.94
149.47
149.15
149.22

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41976&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41976&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1161.9191666666670.674367829672332.14000000000001
2160.9958333333332.673494336948746.35999999999999
3162.0916666666670.6765128949027492.09000000000000
4160.1758333333331.082853623393752.84999999999999
5157.4858333333331.167790908536543.41000000000000
6151.6291666666672.112626363443186.16

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 161.919166666667 & 0.67436782967233 & 2.14000000000001 \tabularnewline
2 & 160.995833333333 & 2.67349433694874 & 6.35999999999999 \tabularnewline
3 & 162.091666666667 & 0.676512894902749 & 2.09000000000000 \tabularnewline
4 & 160.175833333333 & 1.08285362339375 & 2.84999999999999 \tabularnewline
5 & 157.485833333333 & 1.16779090853654 & 3.41000000000000 \tabularnewline
6 & 151.629166666667 & 2.11262636344318 & 6.16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41976&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]161.919166666667[/C][C]0.67436782967233[/C][C]2.14000000000001[/C][/ROW]
[ROW][C]2[/C][C]160.995833333333[/C][C]2.67349433694874[/C][C]6.35999999999999[/C][/ROW]
[ROW][C]3[/C][C]162.091666666667[/C][C]0.676512894902749[/C][C]2.09000000000000[/C][/ROW]
[ROW][C]4[/C][C]160.175833333333[/C][C]1.08285362339375[/C][C]2.84999999999999[/C][/ROW]
[ROW][C]5[/C][C]157.485833333333[/C][C]1.16779090853654[/C][C]3.41000000000000[/C][/ROW]
[ROW][C]6[/C][C]151.629166666667[/C][C]2.11262636344318[/C][C]6.16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41976&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
1161.9191666666670.674367829672332.14000000000001
2160.9958333333332.673494336948746.35999999999999
3162.0916666666670.6765128949027492.09000000000000
4160.1758333333331.082853623393752.84999999999999
5157.4858333333331.167790908536543.41000000000000
6151.6291666666672.112626363443186.16






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha15.4777916312169
beta-0.0885249136987199
S.D.0.0919398043398911
T-STAT-0.962857320986384
p-value0.390144800763027

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.4777916312169 \tabularnewline
beta & -0.0885249136987199 \tabularnewline
S.D. & 0.0919398043398911 \tabularnewline
T-STAT & -0.962857320986384 \tabularnewline
p-value & 0.390144800763027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41976&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.4777916312169[/C][/ROW]
[ROW][C]beta[/C][C]-0.0885249136987199[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0919398043398911[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.962857320986384[/C][/ROW]
[ROW][C]p-value[/C][C]0.390144800763027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41976&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)
alpha15.4777916312169
beta-0.0885249136987199
S.D.0.0919398043398911
T-STAT-0.962857320986384
p-value0.390144800763027






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha60.7139183713061
beta-11.9387796103984
S.D.9.46986147998208
T-STAT-1.26071322538722
p-value0.275937435441056
Lambda12.9387796103984

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 60.7139183713061 \tabularnewline
beta & -11.9387796103984 \tabularnewline
S.D. & 9.46986147998208 \tabularnewline
T-STAT & -1.26071322538722 \tabularnewline
p-value & 0.275937435441056 \tabularnewline
Lambda & 12.9387796103984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41976&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]60.7139183713061[/C][/ROW]
[ROW][C]beta[/C][C]-11.9387796103984[/C][/ROW]
[ROW][C]S.D.[/C][C]9.46986147998208[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.26071322538722[/C][/ROW]
[ROW][C]p-value[/C][C]0.275937435441056[/C][/ROW]
[ROW][C]Lambda[/C][C]12.9387796103984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41976&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)
alpha60.7139183713061
beta-11.9387796103984
S.D.9.46986147998208
T-STAT-1.26071322538722
p-value0.275937435441056
Lambda12.9387796103984


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')