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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 computationWed, 23 Dec 2009 03:56:25 -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/23/t12615658506rzvrg3ezp3qtpy.htm/, Retrieved Mon, 29 Apr 2024 13:55:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70496, Retrieved Mon, 29 Apr 2024 13:55:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact141

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] [Opgave 8: oefenin...] [2009-12-23 10:56:25] [99dd5e7f67b5ad84b7cfa9edf27cffe4] [Current]
- RMPD    [Classical Decomposition] [Opgave 9 oef 2 de...] [2010-01-08 23:23:10] [4ef36953ac96474260c49165aa503bfa]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
5
2
3
-2
-4
0
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8

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=70496&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=70496&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70496&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
141.825741858350554
2-1.252.217355782608355
3-0.53.31662479035547
413.366501646120697
5-1.252.061552812808835
62.753.774917217635378
78.751.53
810.753.862210075418828
99.752.217355782608355
10121.825741858350554
11121.414213562373103
1211.755.123475382979811
1310.53.109126351029607
1415.53.31662479035548
1513.751.258305739211793
1614.251.53
17131.414213562373103
189.251.53

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4 & 1.82574185835055 & 4 \tabularnewline
2 & -1.25 & 2.21735578260835 & 5 \tabularnewline
3 & -0.5 & 3.3166247903554 & 7 \tabularnewline
4 & 1 & 3.36650164612069 & 7 \tabularnewline
5 & -1.25 & 2.06155281280883 & 5 \tabularnewline
6 & 2.75 & 3.77491721763537 & 8 \tabularnewline
7 & 8.75 & 1.5 & 3 \tabularnewline
8 & 10.75 & 3.86221007541882 & 8 \tabularnewline
9 & 9.75 & 2.21735578260835 & 5 \tabularnewline
10 & 12 & 1.82574185835055 & 4 \tabularnewline
11 & 12 & 1.41421356237310 & 3 \tabularnewline
12 & 11.75 & 5.1234753829798 & 11 \tabularnewline
13 & 10.5 & 3.10912635102960 & 7 \tabularnewline
14 & 15.5 & 3.3166247903554 & 8 \tabularnewline
15 & 13.75 & 1.25830573921179 & 3 \tabularnewline
16 & 14.25 & 1.5 & 3 \tabularnewline
17 & 13 & 1.41421356237310 & 3 \tabularnewline
18 & 9.25 & 1.5 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70496&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[/C][C]1.82574185835055[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]-1.25[/C][C]2.21735578260835[/C][C]5[/C][/ROW]
[ROW][C]3[/C][C]-0.5[/C][C]3.3166247903554[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]1[/C][C]3.36650164612069[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]-1.25[/C][C]2.06155281280883[/C][C]5[/C][/ROW]
[ROW][C]6[/C][C]2.75[/C][C]3.77491721763537[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]8.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]8[/C][C]10.75[/C][C]3.86221007541882[/C][C]8[/C][/ROW]
[ROW][C]9[/C][C]9.75[/C][C]2.21735578260835[/C][C]5[/C][/ROW]
[ROW][C]10[/C][C]12[/C][C]1.82574185835055[/C][C]4[/C][/ROW]
[ROW][C]11[/C][C]12[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]12[/C][C]11.75[/C][C]5.1234753829798[/C][C]11[/C][/ROW]
[ROW][C]13[/C][C]10.5[/C][C]3.10912635102960[/C][C]7[/C][/ROW]
[ROW][C]14[/C][C]15.5[/C][C]3.3166247903554[/C][C]8[/C][/ROW]
[ROW][C]15[/C][C]13.75[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]16[/C][C]14.25[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]17[/C][C]13[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]18[/C][C]9.25[/C][C]1.5[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70496&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70496&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
141.825741858350554
2-1.252.217355782608355
3-0.53.31662479035547
413.366501646120697
5-1.252.061552812808835
62.753.774917217635378
78.751.53
810.753.862210075418828
99.752.217355782608355
10121.825741858350554
11121.414213562373103
1211.755.123475382979811
1310.53.109126351029607
1415.53.31662479035548
1513.751.258305739211793
1614.251.53
17131.414213562373103
189.251.53






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.73284006683976
beta-0.0314189040447672
S.D.0.0479954903750754
T-STAT-0.654622003009754
p-value0.522011090301607

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.73284006683976 \tabularnewline
beta & -0.0314189040447672 \tabularnewline
S.D. & 0.0479954903750754 \tabularnewline
T-STAT & -0.654622003009754 \tabularnewline
p-value & 0.522011090301607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70496&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.73284006683976[/C][/ROW]
[ROW][C]beta[/C][C]-0.0314189040447672[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0479954903750754[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.654622003009754[/C][/ROW]
[ROW][C]p-value[/C][C]0.522011090301607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70496&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70496&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)
alpha2.73284006683976
beta-0.0314189040447672
S.D.0.0479954903750754
T-STAT-0.654622003009754
p-value0.522011090301607






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.21847155506834
beta-0.197308827227441
S.D.0.161700710761730
T-STAT-1.22021001823659
p-value0.244058422185337
Lambda1.19730882722744

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.21847155506834 \tabularnewline
beta & -0.197308827227441 \tabularnewline
S.D. & 0.161700710761730 \tabularnewline
T-STAT & -1.22021001823659 \tabularnewline
p-value & 0.244058422185337 \tabularnewline
Lambda & 1.19730882722744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70496&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.21847155506834[/C][/ROW]
[ROW][C]beta[/C][C]-0.197308827227441[/C][/ROW]
[ROW][C]S.D.[/C][C]0.161700710761730[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.22021001823659[/C][/ROW]
[ROW][C]p-value[/C][C]0.244058422185337[/C][/ROW]
[ROW][C]Lambda[/C][C]1.19730882722744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70496&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70496&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)
alpha1.21847155506834
beta-0.197308827227441
S.D.0.161700710761730
T-STAT-1.22021001823659
p-value0.244058422185337
Lambda1.19730882722744


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')