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 computationSat, 20 Dec 2008 11:56:50 -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/20/t122979943805c6qxrppngw4ho.htm/, Retrieved Sun, 19 May 2024 10:06:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35432, Retrieved Sun, 19 May 2024 10:06:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158

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] [juyt] [2008-12-20 18:56:50] [7a2afff08a618fdf6611a1bb6e1c3da4] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
130.3
130.9
104.7
115.2
124.5
112.3
127.5
120.6
117.5
117.7
120.4
125
131.6
121.1
114.2
112.1
127
116.8
112
129.7
113.6
115.7
119.5
125.8
129.6
128
112.8
101.6
123.9
118.8
109.1
130.6
112.4
111
116.2
119.8
117.2
127.3
107.7
97.5
120.1
110.6
111.3
119.8
105.5
108.7
128.7
119.5
121.1
128.4
108.8
107.5
125.6
102.9
107.5
120.4
104.3
100.6
121.9
112.7
124.9
123.9
102.2
104.9
109.8
98.9
107.3
112.6
104
110.6
100.8
103.8
117
108.4
95.5
96.9
103.9
101.1
100.6
104.3
98
99.5
97.4
105.6
117.5
107.4
97.8
91.5
107.7
100.1
96.6
106.8
98
98.6

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35432&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35432&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1120.557.6944490026606526.2
2119.9257.0221888584426719.6
3117.8166666666678.9970533896920829
4114.4916666666679.2074533379049531.2
5113.4759.546453410941327.8
6108.6416666666678.4027547791654626
7102.356.0361788033038421.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 120.55 & 7.69444900266065 & 26.2 \tabularnewline
2 & 119.925 & 7.02218885844267 & 19.6 \tabularnewline
3 & 117.816666666667 & 8.99705338969208 & 29 \tabularnewline
4 & 114.491666666667 & 9.20745333790495 & 31.2 \tabularnewline
5 & 113.475 & 9.5464534109413 & 27.8 \tabularnewline
6 & 108.641666666667 & 8.40275477916546 & 26 \tabularnewline
7 & 102.35 & 6.03617880330384 & 21.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35432&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]120.55[/C][C]7.69444900266065[/C][C]26.2[/C][/ROW]
[ROW][C]2[/C][C]119.925[/C][C]7.02218885844267[/C][C]19.6[/C][/ROW]
[ROW][C]3[/C][C]117.816666666667[/C][C]8.99705338969208[/C][C]29[/C][/ROW]
[ROW][C]4[/C][C]114.491666666667[/C][C]9.20745333790495[/C][C]31.2[/C][/ROW]
[ROW][C]5[/C][C]113.475[/C][C]9.5464534109413[/C][C]27.8[/C][/ROW]
[ROW][C]6[/C][C]108.641666666667[/C][C]8.40275477916546[/C][C]26[/C][/ROW]
[ROW][C]7[/C][C]102.35[/C][C]6.03617880330384[/C][C]21.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35432&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
1120.557.6944490026606526.2
2119.9257.0221888584426719.6
3117.8166666666678.9970533896920829
4114.4916666666679.2074533379049531.2
5113.4759.546453410941327.8
6108.6416666666678.4027547791654626
7102.356.0361788033038421.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.781393079785024
beta0.0645177548116849
S.D.0.0823190421514214
T-STAT0.783752496694604
p-value0.468667998516728

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.781393079785024 \tabularnewline
beta & 0.0645177548116849 \tabularnewline
S.D. & 0.0823190421514214 \tabularnewline
T-STAT & 0.783752496694604 \tabularnewline
p-value & 0.468667998516728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35432&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.781393079785024[/C][/ROW]
[ROW][C]beta[/C][C]0.0645177548116849[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0823190421514214[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.783752496694604[/C][/ROW]
[ROW][C]p-value[/C][C]0.468667998516728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35432&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)
alpha0.781393079785024
beta0.0645177548116849
S.D.0.0823190421514214
T-STAT0.783752496694604
p-value0.468667998516728






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.16244579618775
beta1.10832453959533
S.D.1.16046958901718
T-STAT0.955065561462918
p-value0.383405479248701
Lambda-0.108324539595330

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.16244579618775 \tabularnewline
beta & 1.10832453959533 \tabularnewline
S.D. & 1.16046958901718 \tabularnewline
T-STAT & 0.955065561462918 \tabularnewline
p-value & 0.383405479248701 \tabularnewline
Lambda & -0.108324539595330 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35432&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.16244579618775[/C][/ROW]
[ROW][C]beta[/C][C]1.10832453959533[/C][/ROW]
[ROW][C]S.D.[/C][C]1.16046958901718[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.955065561462918[/C][/ROW]
[ROW][C]p-value[/C][C]0.383405479248701[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.108324539595330[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35432&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35432&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-3.16244579618775
beta1.10832453959533
S.D.1.16046958901718
T-STAT0.955065561462918
p-value0.383405479248701
Lambda-0.108324539595330


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')