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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, 04 Dec 2009 04:43:02 -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/2009/Dec/04/t1259927049iobvmwyxtf2jr49.htm/, Retrieved Sun, 28 Apr 2024 14:56:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63304, Retrieved Sun, 28 Apr 2024 14:56:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-    D      [Standard Deviation-Mean Plot] [] [2009-12-04 11:43:02] [2f6049721194fa571920c3539d7b729e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17
14
15
16
16
15
13
12
13
13
12
10
14
14
15
16
16
15
15
13
15
15
15
13
16
16
14
16
15
14
15
15
14
13
12
13
12
9
10
8
11
8
8
8
4
6
8
10
5
6
5
9
8
6
9
11
11
8
11
11
13

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=63304&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=63304&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63304&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
113.83333333333332.037526724122947
214.66666666666670.9847319278346623
314.41666666666671.311372170551514
48.52.153221687695828
58.333333333333332.386832565759426

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 13.8333333333333 & 2.03752672412294 & 7 \tabularnewline
2 & 14.6666666666667 & 0.984731927834662 & 3 \tabularnewline
3 & 14.4166666666667 & 1.31137217055151 & 4 \tabularnewline
4 & 8.5 & 2.15322168769582 & 8 \tabularnewline
5 & 8.33333333333333 & 2.38683256575942 & 6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63304&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]13.8333333333333[/C][C]2.03752672412294[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]14.6666666666667[/C][C]0.984731927834662[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]14.4166666666667[/C][C]1.31137217055151[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]2.15322168769582[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]8.33333333333333[/C][C]2.38683256575942[/C][C]6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63304&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63304&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
113.83333333333332.037526724122947
214.66666666666670.9847319278346623
314.41666666666671.311372170551514
48.52.153221687695828
58.333333333333332.386832565759426






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.57138521360996
beta-0.150347129574652
S.D.0.0615020186805667
T-STAT-2.44458853221607
p-value0.0921225062816104

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.57138521360996 \tabularnewline
beta & -0.150347129574652 \tabularnewline
S.D. & 0.0615020186805667 \tabularnewline
T-STAT & -2.44458853221607 \tabularnewline
p-value & 0.0921225062816104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63304&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.57138521360996[/C][/ROW]
[ROW][C]beta[/C][C]-0.150347129574652[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0615020186805667[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.44458853221607[/C][/ROW]
[ROW][C]p-value[/C][C]0.0921225062816104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63304&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63304&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)
alpha3.57138521360996
beta-0.150347129574652
S.D.0.0615020186805667
T-STAT-2.44458853221607
p-value0.0921225062816104






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.96300703962408
beta-0.997492502620205
S.D.0.47658782260290
T-STAT-2.09298780898842
p-value0.127413478088393
Lambda1.99749250262020

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.96300703962408 \tabularnewline
beta & -0.997492502620205 \tabularnewline
S.D. & 0.47658782260290 \tabularnewline
T-STAT & -2.09298780898842 \tabularnewline
p-value & 0.127413478088393 \tabularnewline
Lambda & 1.99749250262020 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63304&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.96300703962408[/C][/ROW]
[ROW][C]beta[/C][C]-0.997492502620205[/C][/ROW]
[ROW][C]S.D.[/C][C]0.47658782260290[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.09298780898842[/C][/ROW]
[ROW][C]p-value[/C][C]0.127413478088393[/C][/ROW]
[ROW][C]Lambda[/C][C]1.99749250262020[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63304&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63304&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)
alpha2.96300703962408
beta-0.997492502620205
S.D.0.47658782260290
T-STAT-2.09298780898842
p-value0.127413478088393
Lambda1.99749250262020


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')