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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 computationFri, 09 May 2008 06:15:28 -0600
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/May/09/t12103354092cwf2gwbei2udyy.htm/, Retrieved Tue, 14 May 2024 14:18:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12142, Retrieved Tue, 14 May 2024 14:18:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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] [gaelle.wauters-St...] [2008-05-09 12:15:28] [1a88f818bfac0ba502c6e25c4c816249] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.8
9.7
9.5
9.3
9.1
9
9.5
10
10.2
10.1
10
9.9
10
9.9
9.7
9.5
9.2
9
9.3
9.8
9.8
9.6
9.4
9.3
9.2
9.2
9
8.8
8.7
8.7
9.1
9.7
9.8
9.6
9.4
9.4
9.5
9.4
9.3
9.2
9
8.9
9.2
9.8
9.9
9.6
9.2
9.1
9.1
9.1
8.9
8.7
8.5
8.4
8.4
8.7
8.5
8.1
7.8
7.7
7.4
7.2
7
6.6
6.4
6.4
6.8
7.3
7
7
6.7
6.7
6.3
6.2
6
6.3
6.2
6.1
6.2
6.6
6.6
7.8
7.4
7.4
7.5
7.4
7.4
7
6.9
6.9
7.6
7.7
7.6
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.3
7.4
7.1
7.3
7.1
7.1

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12142&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12142&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.6750.3957156922474881.2
29.541666666666670.3088345639315461
39.216666666666670.3761849963982501.10000000000000
49.341666666666670.3088345639315461
58.491666666666670.4541892543729751.4
66.8750.3306330017076061
76.591666666666670.6022055422789761.8
87.5250.4413306326018251.3
98.1750.3360871099202491
108.383333333333330.6806859285554041.9
118.441666666666670.2466441431158120.700
128.241666666666670.2968266507678521
137.491666666666670.3476108935769041

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.675 & 0.395715692247488 & 1.2 \tabularnewline
2 & 9.54166666666667 & 0.308834563931546 & 1 \tabularnewline
3 & 9.21666666666667 & 0.376184996398250 & 1.10000000000000 \tabularnewline
4 & 9.34166666666667 & 0.308834563931546 & 1 \tabularnewline
5 & 8.49166666666667 & 0.454189254372975 & 1.4 \tabularnewline
6 & 6.875 & 0.330633001707606 & 1 \tabularnewline
7 & 6.59166666666667 & 0.602205542278976 & 1.8 \tabularnewline
8 & 7.525 & 0.441330632601825 & 1.3 \tabularnewline
9 & 8.175 & 0.336087109920249 & 1 \tabularnewline
10 & 8.38333333333333 & 0.680685928555404 & 1.9 \tabularnewline
11 & 8.44166666666667 & 0.246644143115812 & 0.700 \tabularnewline
12 & 8.24166666666667 & 0.296826650767852 & 1 \tabularnewline
13 & 7.49166666666667 & 0.347610893576904 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12142&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]9.675[/C][C]0.395715692247488[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]9.54166666666667[/C][C]0.308834563931546[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]9.21666666666667[/C][C]0.376184996398250[/C][C]1.10000000000000[/C][/ROW]
[ROW][C]4[/C][C]9.34166666666667[/C][C]0.308834563931546[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]8.49166666666667[/C][C]0.454189254372975[/C][C]1.4[/C][/ROW]
[ROW][C]6[/C][C]6.875[/C][C]0.330633001707606[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]6.59166666666667[/C][C]0.602205542278976[/C][C]1.8[/C][/ROW]
[ROW][C]8[/C][C]7.525[/C][C]0.441330632601825[/C][C]1.3[/C][/ROW]
[ROW][C]9[/C][C]8.175[/C][C]0.336087109920249[/C][C]1[/C][/ROW]
[ROW][C]10[/C][C]8.38333333333333[/C][C]0.680685928555404[/C][C]1.9[/C][/ROW]
[ROW][C]11[/C][C]8.44166666666667[/C][C]0.246644143115812[/C][C]0.700[/C][/ROW]
[ROW][C]12[/C][C]8.24166666666667[/C][C]0.296826650767852[/C][C]1[/C][/ROW]
[ROW][C]13[/C][C]7.49166666666667[/C][C]0.347610893576904[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12142&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
19.6750.3957156922474881.2
29.541666666666670.3088345639315461
39.216666666666670.3761849963982501.10000000000000
49.341666666666670.3088345639315461
58.491666666666670.4541892543729751.4
66.8750.3306330017076061
76.591666666666670.6022055422789761.8
87.5250.4413306326018251.3
98.1750.3360871099202491
108.383333333333330.6806859285554041.9
118.441666666666670.2466441431158120.700
128.241666666666670.2968266507678521
137.491666666666670.3476108935769041






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.71219932279558
beta-0.0382696957135838
S.D.0.0364174305407904
T-STAT-1.05086204999331
p-value0.315860614679618

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.71219932279558 \tabularnewline
beta & -0.0382696957135838 \tabularnewline
S.D. & 0.0364174305407904 \tabularnewline
T-STAT & -1.05086204999331 \tabularnewline
p-value & 0.315860614679618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12142&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.71219932279558[/C][/ROW]
[ROW][C]beta[/C][C]-0.0382696957135838[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0364174305407904[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.05086204999331[/C][/ROW]
[ROW][C]p-value[/C][C]0.315860614679618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12142&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)
alpha0.71219932279558
beta-0.0382696957135838
S.D.0.0364174305407904
T-STAT-1.05086204999331
p-value0.315860614679618






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.549721706056861
beta-0.720542507604331
S.D.0.676149416623525
T-STAT-1.06565574100839
p-value0.309411201114547
Lambda1.72054250760433

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.549721706056861 \tabularnewline
beta & -0.720542507604331 \tabularnewline
S.D. & 0.676149416623525 \tabularnewline
T-STAT & -1.06565574100839 \tabularnewline
p-value & 0.309411201114547 \tabularnewline
Lambda & 1.72054250760433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12142&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.549721706056861[/C][/ROW]
[ROW][C]beta[/C][C]-0.720542507604331[/C][/ROW]
[ROW][C]S.D.[/C][C]0.676149416623525[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.06565574100839[/C][/ROW]
[ROW][C]p-value[/C][C]0.309411201114547[/C][/ROW]
[ROW][C]Lambda[/C][C]1.72054250760433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12142&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12142&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)
alpha0.549721706056861
beta-0.720542507604331
S.D.0.676149416623525
T-STAT-1.06565574100839
p-value0.309411201114547
Lambda1.72054250760433


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')