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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 computationSun, 21 Dec 2008 11:31:09 -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/2008/Dec/21/t122988440373s7vqnfohxq4ue.htm/, Retrieved Sun, 19 May 2024 11:37:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35740, Retrieved Sun, 19 May 2024 11:37:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

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-oefening...] [2008-12-21 18:31:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113,9000
112,0000
113,8500
113,0800
111,7200
110,6900
113,5300
113,9900
112,7400
112,1500
115,8200
118,3800
118,8100
123,8500
117,9600
120,1600
118,7400
119,8400
124,8100
121,3300
120,2000
118,3200
129,5800
130,2000
127,1900
133,1000
129,1200
123,2800
123,3600
124,1300
126,9700
127,1400
123,7000
123,6700
130,1900
134,0100
124,9600
129,9600
128,3200
132,3800
126,2500
128,9100
131,4200
129,4400
126,8600
126,7100
131,6300
132,7800
126,6100
132,8400
123,1400
128,1300
125,4900
126,4800
130,8600
127,3200
126,5600
126,6400
129,2600
126,4700
135,4000
135,5000
132,2200
122,6200
125,1600
128,5000
133,8600
128,8700
125,0700
125,2500
132,1600
130,2400

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35740&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35740&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1113.48752.03624933729557.69
2121.9833333333334.2471323658832812.24
3127.1553.7910504660797710.73
4129.1352.585991984800917.82
5127.4833333333332.538701648600349.7
6129.5708333333334.3696816158894712.88

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 113.4875 & 2.0362493372955 & 7.69 \tabularnewline
2 & 121.983333333333 & 4.24713236588328 & 12.24 \tabularnewline
3 & 127.155 & 3.79105046607977 & 10.73 \tabularnewline
4 & 129.135 & 2.58599198480091 & 7.82 \tabularnewline
5 & 127.483333333333 & 2.53870164860034 & 9.7 \tabularnewline
6 & 129.570833333333 & 4.36968161588947 & 12.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35740&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]113.4875[/C][C]2.0362493372955[/C][C]7.69[/C][/ROW]
[ROW][C]2[/C][C]121.983333333333[/C][C]4.24713236588328[/C][C]12.24[/C][/ROW]
[ROW][C]3[/C][C]127.155[/C][C]3.79105046607977[/C][C]10.73[/C][/ROW]
[ROW][C]4[/C][C]129.135[/C][C]2.58599198480091[/C][C]7.82[/C][/ROW]
[ROW][C]5[/C][C]127.483333333333[/C][C]2.53870164860034[/C][C]9.7[/C][/ROW]
[ROW][C]6[/C][C]129.570833333333[/C][C]4.36968161588947[/C][C]12.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35740&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
1113.48752.03624933729557.69
2121.9833333333334.2471323658832812.24
3127.1553.7910504660797710.73
4129.1352.585991984800917.82
5127.4833333333332.538701648600349.7
6129.5708333333334.3696816158894712.88






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.10481387534436
beta0.0670361713782649
S.D.0.0734556462297219
T-STAT0.912607468847513
p-value0.413077496478814

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.10481387534436 \tabularnewline
beta & 0.0670361713782649 \tabularnewline
S.D. & 0.0734556462297219 \tabularnewline
T-STAT & 0.912607468847513 \tabularnewline
p-value & 0.413077496478814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35740&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.10481387534436[/C][/ROW]
[ROW][C]beta[/C][C]0.0670361713782649[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0734556462297219[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.912607468847513[/C][/ROW]
[ROW][C]p-value[/C][C]0.413077496478814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35740&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-5.10481387534436
beta0.0670361713782649
S.D.0.0734556462297219
T-STAT0.912607468847513
p-value0.413077496478814






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-13.4306631513054
beta3.01962629366694
S.D.2.7420105776152
T-STAT1.10124531185915
p-value0.332601580149664
Lambda-2.01962629366694

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.4306631513054 \tabularnewline
beta & 3.01962629366694 \tabularnewline
S.D. & 2.7420105776152 \tabularnewline
T-STAT & 1.10124531185915 \tabularnewline
p-value & 0.332601580149664 \tabularnewline
Lambda & -2.01962629366694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35740&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.4306631513054[/C][/ROW]
[ROW][C]beta[/C][C]3.01962629366694[/C][/ROW]
[ROW][C]S.D.[/C][C]2.7420105776152[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10124531185915[/C][/ROW]
[ROW][C]p-value[/C][C]0.332601580149664[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.01962629366694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35740&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-13.4306631513054
beta3.01962629366694
S.D.2.7420105776152
T-STAT1.10124531185915
p-value0.332601580149664
Lambda-2.01962629366694


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')