FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 28 Nov 2013 12:33:52 -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/Nov/28/t1385660044c5sdh7rm5jksiic.htm/, Retrieved Fri, 03 May 2024 06:54:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229380, Retrieved Fri, 03 May 2024 06:54:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2013-11-28 17:33:52] [d7aee701571668449ffc3c4d70a8a545] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
2
0
0
3
-2
0
1
-1
-2
-1
-1
1
-2
-5
-5
-6
-4
-3
-3
-1
-2
-3
-3
-3
-5
-5

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229380&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229380&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'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14.916666666666671.083624669450833
23.166666666666672.124888588879787
3-2.752.094364733365147
40.08333333333333332.108783937953277
511.128152149635534
6-0.752.005673770264568
7-3.583333333333331.443375672974065

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.91666666666667 & 1.08362466945083 & 3 \tabularnewline
2 & 3.16666666666667 & 2.12488858887978 & 7 \tabularnewline
3 & -2.75 & 2.09436473336514 & 7 \tabularnewline
4 & 0.0833333333333333 & 2.10878393795327 & 7 \tabularnewline
5 & 1 & 1.12815214963553 & 4 \tabularnewline
6 & -0.75 & 2.00567377026456 & 8 \tabularnewline
7 & -3.58333333333333 & 1.44337567297406 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229380&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]4.91666666666667[/C][C]1.08362466945083[/C][C]3[/C][/ROW]
[ROW][C]2[/C][C]3.16666666666667[/C][C]2.12488858887978[/C][C]7[/C][/ROW]
[ROW][C]3[/C][C]-2.75[/C][C]2.09436473336514[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]0.0833333333333333[/C][C]2.10878393795327[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]1.12815214963553[/C][C]4[/C][/ROW]
[ROW][C]6[/C][C]-0.75[/C][C]2.00567377026456[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]-3.58333333333333[/C][C]1.44337567297406[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229380&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
14.916666666666671.083624669450833
23.166666666666672.124888588879787
3-2.752.094364733365147
40.08333333333333332.108783937953277
511.128152149635534
6-0.752.005673770264568
7-3.583333333333331.443375672974065






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.72685663050926
beta-0.0475837876999925
S.D.0.0668807626338787
T-STAT-0.71147196631829
p-value0.508598337284008

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.72685663050926 \tabularnewline
beta & -0.0475837876999925 \tabularnewline
S.D. & 0.0668807626338787 \tabularnewline
T-STAT & -0.71147196631829 \tabularnewline
p-value & 0.508598337284008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229380&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.72685663050926[/C][/ROW]
[ROW][C]beta[/C][C]-0.0475837876999925[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0668807626338787[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.71147196631829[/C][/ROW]
[ROW][C]p-value[/C][C]0.508598337284008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229380&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)
alpha1.72685663050926
beta-0.0475837876999925
S.D.0.0668807626338787
T-STAT-0.71147196631829
p-value0.508598337284008






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.431468409819687
beta-0.0965815664691844
S.D.0.128140948121222
T-STAT-0.753713530961374
p-value0.529671071063137
Lambda1.09658156646918

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.431468409819687 \tabularnewline
beta & -0.0965815664691844 \tabularnewline
S.D. & 0.128140948121222 \tabularnewline
T-STAT & -0.753713530961374 \tabularnewline
p-value & 0.529671071063137 \tabularnewline
Lambda & 1.09658156646918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229380&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.431468409819687[/C][/ROW]
[ROW][C]beta[/C][C]-0.0965815664691844[/C][/ROW]
[ROW][C]S.D.[/C][C]0.128140948121222[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.753713530961374[/C][/ROW]
[ROW][C]p-value[/C][C]0.529671071063137[/C][/ROW]
[ROW][C]Lambda[/C][C]1.09658156646918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229380&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)
alpha0.431468409819687
beta-0.0965815664691844
S.D.0.128140948121222
T-STAT-0.753713530961374
p-value0.529671071063137
Lambda1.09658156646918


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')