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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 computationTue, 10 Mar 2015 14:06:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/10/t1425996438966xt2igawozfrw.htm/, Retrieved Sun, 19 May 2024 11:10:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278139, Retrieved Sun, 19 May 2024 11:10:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148

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] [] [2015-03-10 14:06:22] [3b0947f879d0db9a6034293524e1b6d0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
6,7
-0,6
5,8
16,4
1,5
5,1
14,7
4,3
1,5
9,1
4,3
5,7
13
14,5
9,7
-4,7
7,3
5,2
-2,5
11,5
4,9
-2,4
-0,3
4,4
7,9
-9,7
-4,1
16,4
-4,9
3,5
3,8
-0,2
3,1
0,7
-2,8
5,9
-5,3
-2,9
6,6
-8,1
1,3
6,9
-7,2
-1,9
4
-5,7
3,9
-7,6
-0,9
7,3
-3,7
-2,5
9,3
1,3
9,5
11,3
-1,7
8
-4,8
1,6
1,9
-0,9
5,5
1,7
-5,4
1,9
0,2
-13,3
-8,2
0,2
5,7
-1,2
-2,8
5,5
-17,3
1,4
-2,2
-8,6
-5
4,1
0,7
-4,2
-2,3
-3,4
-4,2
-14,2
1,6
-4,9
-1,8
-0,5
-2,3
-5,3
-0,2
5,1
-1,5

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278139&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278139&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
16.233333333333335.0810402180035617
25.158333333333336.4477562458626319.2
31.508333333333336.7622559889881526.1
4-0.2083333333333335.6279268479663615
52.1256.5620292038916818.9
6-0.7583333333333335.5815374769019219
7-2.658333333333336.0302959875092122.8
8-2.633333333333334.664826477009219.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.23333333333333 & 5.08104021800356 & 17 \tabularnewline
2 & 5.15833333333333 & 6.44775624586263 & 19.2 \tabularnewline
3 & 1.50833333333333 & 6.76225598898815 & 26.1 \tabularnewline
4 & -0.208333333333333 & 5.62792684796636 & 15 \tabularnewline
5 & 2.125 & 6.56202920389168 & 18.9 \tabularnewline
6 & -0.758333333333333 & 5.58153747690192 & 19 \tabularnewline
7 & -2.65833333333333 & 6.03029598750921 & 22.8 \tabularnewline
8 & -2.63333333333333 & 4.6648264770092 & 19.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278139&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]6.23333333333333[/C][C]5.08104021800356[/C][C]17[/C][/ROW]
[ROW][C]2[/C][C]5.15833333333333[/C][C]6.44775624586263[/C][C]19.2[/C][/ROW]
[ROW][C]3[/C][C]1.50833333333333[/C][C]6.76225598898815[/C][C]26.1[/C][/ROW]
[ROW][C]4[/C][C]-0.208333333333333[/C][C]5.62792684796636[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]2.125[/C][C]6.56202920389168[/C][C]18.9[/C][/ROW]
[ROW][C]6[/C][C]-0.758333333333333[/C][C]5.58153747690192[/C][C]19[/C][/ROW]
[ROW][C]7[/C][C]-2.65833333333333[/C][C]6.03029598750921[/C][C]22.8[/C][/ROW]
[ROW][C]8[/C][C]-2.63333333333333[/C][C]4.6648264770092[/C][C]19.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278139&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
16.233333333333335.0810402180035617
25.158333333333336.4477562458626319.2
31.508333333333336.7622559889881526.1
4-0.2083333333333335.6279268479663615
52.1256.5620292038916818.9
6-0.7583333333333335.5815374769019219
7-2.658333333333336.0302959875092122.8
8-2.633333333333334.664826477009219.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.7863162294998
beta0.053285773019119
S.D.0.088447698875675
T-STAT0.602455164989869
p-value0.568924889529766

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.7863162294998 \tabularnewline
beta & 0.053285773019119 \tabularnewline
S.D. & 0.088447698875675 \tabularnewline
T-STAT & 0.602455164989869 \tabularnewline
p-value & 0.568924889529766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278139&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.7863162294998[/C][/ROW]
[ROW][C]beta[/C][C]0.053285773019119[/C][/ROW]
[ROW][C]S.D.[/C][C]0.088447698875675[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.602455164989869[/C][/ROW]
[ROW][C]p-value[/C][C]0.568924889529766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278139&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278139&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)
alpha5.7863162294998
beta0.053285773019119
S.D.0.088447698875675
T-STAT0.602455164989869
p-value0.568924889529766






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.98748022952558
beta-0.144114943089645
S.D.0.0897405729139731
T-STAT-1.60590620730487
p-value0.24952202775628
Lambda1.14411494308965

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.98748022952558 \tabularnewline
beta & -0.144114943089645 \tabularnewline
S.D. & 0.0897405729139731 \tabularnewline
T-STAT & -1.60590620730487 \tabularnewline
p-value & 0.24952202775628 \tabularnewline
Lambda & 1.14411494308965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278139&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.98748022952558[/C][/ROW]
[ROW][C]beta[/C][C]-0.144114943089645[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0897405729139731[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.60590620730487[/C][/ROW]
[ROW][C]p-value[/C][C]0.24952202775628[/C][/ROW]
[ROW][C]Lambda[/C][C]1.14411494308965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278139&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278139&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)
alpha1.98748022952558
beta-0.144114943089645
S.D.0.0897405729139731
T-STAT-1.60590620730487
p-value0.24952202775628
Lambda1.14411494308965


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')