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Description of Statistical Computation

Author's title

Nietje van Santfoort-Standard Deviation Mean Plot-spreidings-gemiddeldegraf...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 11 May 2008 14:18:35 -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/11/t1210537188xkcdxyhn03csqvj.htm/, Retrieved Sun, 19 May 2024 19:49:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12283, Retrieved Sun, 19 May 2024 19:49:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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] [Nietje van Santfo...] [2008-05-11 20:18:35] [934a640f32b984cc814aae4d8bf2ca79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
71.42
71.47
71.64
71.55
71.62
71.65
71.65
71.65
71.6
71.7
71.73
71.83
71.83
71.87
71.91
71.99
72.1
72.12
72.12
72.12
72.25
72.59
72.72
72.76
72.76
72.91
73
73.16
73.16
73.11
73.11
73.33
73.51
73.66
73.65
73.65
73.65
73.65
73.71
73.73
73.85
73.77
73.77
73.78
73.88
74.3
74.53
74.71
74.71
74.78
74.9
74.65
74.65
74.53
74.53
74.53
74.65
74.85
74.96
74.96
74.96
75.19
74.98
75.54
75.61
75.59
75.58
75.44
75.37
75.22
75.33
75.33

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12283&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12283&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
171.520.09626352718795720.219999999999999
271.64250.01500000000000060.0300000000000011
371.7150.09469248474228030.230000000000004
471.90.06831300510639480.159999999999997
572.1150.01000000000000510.0200000000000102
672.580.2316606713852550.510000000000005
772.95750.1674066904278290.399999999999991
873.17750.1043631480296880.219999999999999
973.61750.07182153808804930.149999999999991
1073.6850.04123105625617360.0799999999999983
1173.79250.03862210075418680.0799999999999983
1274.3550.3583759664560860.829999999999998
1374.760.1073933579572480.25
1474.560.06000000000000230.120000000000005
1574.8550.1461734129951990.309999999999988
1675.16750.2692427653005160.580000000000013
1775.5550.07767453465154160.170000000000002
1875.31250.06448514040717860.150000000000006

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.52 & 0.0962635271879572 & 0.219999999999999 \tabularnewline
2 & 71.6425 & 0.0150000000000006 & 0.0300000000000011 \tabularnewline
3 & 71.715 & 0.0946924847422803 & 0.230000000000004 \tabularnewline
4 & 71.9 & 0.0683130051063948 & 0.159999999999997 \tabularnewline
5 & 72.115 & 0.0100000000000051 & 0.0200000000000102 \tabularnewline
6 & 72.58 & 0.231660671385255 & 0.510000000000005 \tabularnewline
7 & 72.9575 & 0.167406690427829 & 0.399999999999991 \tabularnewline
8 & 73.1775 & 0.104363148029688 & 0.219999999999999 \tabularnewline
9 & 73.6175 & 0.0718215380880493 & 0.149999999999991 \tabularnewline
10 & 73.685 & 0.0412310562561736 & 0.0799999999999983 \tabularnewline
11 & 73.7925 & 0.0386221007541868 & 0.0799999999999983 \tabularnewline
12 & 74.355 & 0.358375966456086 & 0.829999999999998 \tabularnewline
13 & 74.76 & 0.107393357957248 & 0.25 \tabularnewline
14 & 74.56 & 0.0600000000000023 & 0.120000000000005 \tabularnewline
15 & 74.855 & 0.146173412995199 & 0.309999999999988 \tabularnewline
16 & 75.1675 & 0.269242765300516 & 0.580000000000013 \tabularnewline
17 & 75.555 & 0.0776745346515416 & 0.170000000000002 \tabularnewline
18 & 75.3125 & 0.0644851404071786 & 0.150000000000006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12283&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]71.52[/C][C]0.0962635271879572[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]2[/C][C]71.6425[/C][C]0.0150000000000006[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]3[/C][C]71.715[/C][C]0.0946924847422803[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]4[/C][C]71.9[/C][C]0.0683130051063948[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]5[/C][C]72.115[/C][C]0.0100000000000051[/C][C]0.0200000000000102[/C][/ROW]
[ROW][C]6[/C][C]72.58[/C][C]0.231660671385255[/C][C]0.510000000000005[/C][/ROW]
[ROW][C]7[/C][C]72.9575[/C][C]0.167406690427829[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]8[/C][C]73.1775[/C][C]0.104363148029688[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]9[/C][C]73.6175[/C][C]0.0718215380880493[/C][C]0.149999999999991[/C][/ROW]
[ROW][C]10[/C][C]73.685[/C][C]0.0412310562561736[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]11[/C][C]73.7925[/C][C]0.0386221007541868[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]12[/C][C]74.355[/C][C]0.358375966456086[/C][C]0.829999999999998[/C][/ROW]
[ROW][C]13[/C][C]74.76[/C][C]0.107393357957248[/C][C]0.25[/C][/ROW]
[ROW][C]14[/C][C]74.56[/C][C]0.0600000000000023[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]15[/C][C]74.855[/C][C]0.146173412995199[/C][C]0.309999999999988[/C][/ROW]
[ROW][C]16[/C][C]75.1675[/C][C]0.269242765300516[/C][C]0.580000000000013[/C][/ROW]
[ROW][C]17[/C][C]75.555[/C][C]0.0776745346515416[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]18[/C][C]75.3125[/C][C]0.0644851404071786[/C][C]0.150000000000006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12283&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
171.520.09626352718795720.219999999999999
271.64250.01500000000000060.0300000000000011
371.7150.09469248474228030.230000000000004
471.90.06831300510639480.159999999999997
572.1150.01000000000000510.0200000000000102
672.580.2316606713852550.510000000000005
772.95750.1674066904278290.399999999999991
873.17750.1043631480296880.219999999999999
973.61750.07182153808804930.149999999999991
1073.6850.04123105625617360.0799999999999983
1173.79250.03862210075418680.0799999999999983
1274.3550.3583759664560860.829999999999998
1374.760.1073933579572480.25
1474.560.06000000000000230.120000000000005
1574.8550.1461734129951990.309999999999988
1675.16750.2692427653005160.580000000000013
1775.5550.07767453465154160.170000000000002
1875.31250.06448514040717860.150000000000006






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.21626948317573
beta0.0180731183203008
S.D.0.0161855248940897
T-STAT1.11662231769205
p-value0.280644523893090

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.21626948317573 \tabularnewline
beta & 0.0180731183203008 \tabularnewline
S.D. & 0.0161855248940897 \tabularnewline
T-STAT & 1.11662231769205 \tabularnewline
p-value & 0.280644523893090 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12283&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.21626948317573[/C][/ROW]
[ROW][C]beta[/C][C]0.0180731183203008[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0161855248940897[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.11662231769205[/C][/ROW]
[ROW][C]p-value[/C][C]0.280644523893090[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12283&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-1.21626948317573
beta0.0180731183203008
S.D.0.0161855248940897
T-STAT1.11662231769205
p-value0.280644523893090






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-76.6962409444604
beta17.2608462283736
S.D.11.4695360342441
T-STAT1.50492977020506
p-value0.151826478883581
Lambda-16.2608462283736

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -76.6962409444604 \tabularnewline
beta & 17.2608462283736 \tabularnewline
S.D. & 11.4695360342441 \tabularnewline
T-STAT & 1.50492977020506 \tabularnewline
p-value & 0.151826478883581 \tabularnewline
Lambda & -16.2608462283736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12283&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-76.6962409444604[/C][/ROW]
[ROW][C]beta[/C][C]17.2608462283736[/C][/ROW]
[ROW][C]S.D.[/C][C]11.4695360342441[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.50492977020506[/C][/ROW]
[ROW][C]p-value[/C][C]0.151826478883581[/C][/ROW]
[ROW][C]Lambda[/C][C]-16.2608462283736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12283&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-76.6962409444604
beta17.2608462283736
S.D.11.4695360342441
T-STAT1.50492977020506
p-value0.151826478883581
Lambda-16.2608462283736


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')