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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 computationFri, 16 Dec 2011 11:27:53 -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/16/t1324052945xdnnj6r85hbvm10.htm/, Retrieved Sun, 05 May 2024 18:25:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156078, Retrieved Sun, 05 May 2024 18:25:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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...] [2011-12-16 16:27:53] [274a40ad31da88f12aea425a159a1f93] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9911.00
8915.00
9452.00
9112.00
8472.00
8230.00
8384.00
8625.00
8221.00
8649.00
8625.00
10443.00
10357.00
8586.00
8892.00
8329.00
8101.00
7922.00
8120.00
7838.00
7735.00
8406.00
8209.00
9451.00
10041.00
9411.00
10405.00
8467.00
8464.00
8102.00
7627.00
7513.00
7510.00
8291.00
8064.00
9383.00
9706.00
8579.00
9474.00
8318.00
8213.00
8059.00
9111.00
7708.00
7680.00
8014.00
8007.00
8718.00
9486.00
9113.00
9025.00
8476.00
7952.00
7759.00
7835.00
7600.00
7651.00
8319.00
8812.00
8630.00

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=156078&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=156078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156078&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
18919.91666666667695.5517702885352222
28495.5756.6420433852342622
38606.5981.1020241637372895
48465.58333333333667.7551889908772026
58388.16666666667635.574304837521886

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8919.91666666667 & 695.551770288535 & 2222 \tabularnewline
2 & 8495.5 & 756.642043385234 & 2622 \tabularnewline
3 & 8606.5 & 981.102024163737 & 2895 \tabularnewline
4 & 8465.58333333333 & 667.755188990877 & 2026 \tabularnewline
5 & 8388.16666666667 & 635.57430483752 & 1886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156078&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]8919.91666666667[/C][C]695.551770288535[/C][C]2222[/C][/ROW]
[ROW][C]2[/C][C]8495.5[/C][C]756.642043385234[/C][C]2622[/C][/ROW]
[ROW][C]3[/C][C]8606.5[/C][C]981.102024163737[/C][C]2895[/C][/ROW]
[ROW][C]4[/C][C]8465.58333333333[/C][C]667.755188990877[/C][C]2026[/C][/ROW]
[ROW][C]5[/C][C]8388.16666666667[/C][C]635.57430483752[/C][C]1886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156078&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
18919.91666666667695.5517702885352222
28495.5756.6420433852342622
38606.5981.1020241637372895
48465.58333333333667.7551889908772026
58388.16666666667635.574304837521886






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-161.442275108863
beta0.105977050865142
S.D.0.378175624424751
T-STAT0.280232368298051
p-value0.797512038015854

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -161.442275108863 \tabularnewline
beta & 0.105977050865142 \tabularnewline
S.D. & 0.378175624424751 \tabularnewline
T-STAT & 0.280232368298051 \tabularnewline
p-value & 0.797512038015854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156078&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-161.442275108863[/C][/ROW]
[ROW][C]beta[/C][C]0.105977050865142[/C][/ROW]
[ROW][C]S.D.[/C][C]0.378175624424751[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.280232368298051[/C][/ROW]
[ROW][C]p-value[/C][C]0.797512038015854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156078&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-161.442275108863
beta0.105977050865142
S.D.0.378175624424751
T-STAT0.280232368298051
p-value0.797512038015854






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.3845067017362
beta1.32377820819755
S.D.4.05095975309568
T-STAT0.326781377471337
p-value0.765305123998826
Lambda-0.323778208197552

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.3845067017362 \tabularnewline
beta & 1.32377820819755 \tabularnewline
S.D. & 4.05095975309568 \tabularnewline
T-STAT & 0.326781377471337 \tabularnewline
p-value & 0.765305123998826 \tabularnewline
Lambda & -0.323778208197552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156078&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.3845067017362[/C][/ROW]
[ROW][C]beta[/C][C]1.32377820819755[/C][/ROW]
[ROW][C]S.D.[/C][C]4.05095975309568[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.326781377471337[/C][/ROW]
[ROW][C]p-value[/C][C]0.765305123998826[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.323778208197552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156078&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-5.3845067017362
beta1.32377820819755
S.D.4.05095975309568
T-STAT0.326781377471337
p-value0.765305123998826
Lambda-0.323778208197552


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')