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Description of Statistical Computation

Author's title

Nietje van Santfoort-Standard Deviation Plot-spreidingsgrafieken verkoop ve...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 17 May 2008 09:18:04 -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/17/t12110375731fdnu22me2n4wvn.htm/, Retrieved Mon, 13 May 2024 22:50:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12677, Retrieved Mon, 13 May 2024 22:50:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

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 17:54:19] [f48bfde976615948c8f49c9cb95da62c]
-   PD    [Standard Deviation-Mean Plot] [Nietje van Santfo...] [2008-05-17 15:18:04] [d41d8cd98f00b204e9800998ecf8427e] [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 time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12677&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12677&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12677&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
171.62583333333330.1099965564199290.409999999999997
272.19833333333330.3221753710279080.930000000000007
373.25083333333330.3068448922155760.899999999999991
473.94416666666670.3606423141949341.05999999999999
574.7250.1626205846301560.429999999999993
675.3450.2245601761828510.650000000000006

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.6258333333333 & 0.109996556419929 & 0.409999999999997 \tabularnewline
2 & 72.1983333333333 & 0.322175371027908 & 0.930000000000007 \tabularnewline
3 & 73.2508333333333 & 0.306844892215576 & 0.899999999999991 \tabularnewline
4 & 73.9441666666667 & 0.360642314194934 & 1.05999999999999 \tabularnewline
5 & 74.725 & 0.162620584630156 & 0.429999999999993 \tabularnewline
6 & 75.345 & 0.224560176182851 & 0.650000000000006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12677&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]71.6258333333333[/C][C]0.109996556419929[/C][C]0.409999999999997[/C][/ROW]
[ROW][C]2[/C][C]72.1983333333333[/C][C]0.322175371027908[/C][C]0.930000000000007[/C][/ROW]
[ROW][C]3[/C][C]73.2508333333333[/C][C]0.306844892215576[/C][C]0.899999999999991[/C][/ROW]
[ROW][C]4[/C][C]73.9441666666667[/C][C]0.360642314194934[/C][C]1.05999999999999[/C][/ROW]
[ROW][C]5[/C][C]74.725[/C][C]0.162620584630156[/C][C]0.429999999999993[/C][/ROW]
[ROW][C]6[/C][C]75.345[/C][C]0.224560176182851[/C][C]0.650000000000006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12677&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12677&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
171.62583333333330.1099965564199290.409999999999997
272.19833333333330.3221753710279080.930000000000007
373.25083333333330.3068448922155760.899999999999991
473.94416666666670.3606423141949341.05999999999999
574.7250.1626205846301560.429999999999993
675.3450.2245601761828510.650000000000006






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.104120789801113
beta0.00478716049508819
S.D.0.0341240246052263
T-STAT0.140287101256954
p-value0.895213850269558

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.104120789801113 \tabularnewline
beta & 0.00478716049508819 \tabularnewline
S.D. & 0.0341240246052263 \tabularnewline
T-STAT & 0.140287101256954 \tabularnewline
p-value & 0.895213850269558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12677&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.104120789801113[/C][/ROW]
[ROW][C]beta[/C][C]0.00478716049508819[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0341240246052263[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.140287101256954[/C][/ROW]
[ROW][C]p-value[/C][C]0.895213850269558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12677&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12677&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-0.104120789801113
beta0.00478716049508819
S.D.0.0341240246052263
T-STAT0.140287101256954
p-value0.895213850269558






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-20.3441417347875
beta4.39085518738585
S.D.11.555253252664
T-STAT0.379987793549532
p-value0.72326924287541
Lambda-3.39085518738585

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -20.3441417347875 \tabularnewline
beta & 4.39085518738585 \tabularnewline
S.D. & 11.555253252664 \tabularnewline
T-STAT & 0.379987793549532 \tabularnewline
p-value & 0.72326924287541 \tabularnewline
Lambda & -3.39085518738585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12677&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.3441417347875[/C][/ROW]
[ROW][C]beta[/C][C]4.39085518738585[/C][/ROW]
[ROW][C]S.D.[/C][C]11.555253252664[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.379987793549532[/C][/ROW]
[ROW][C]p-value[/C][C]0.72326924287541[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.39085518738585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12677&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12677&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-20.3441417347875
beta4.39085518738585
S.D.11.555253252664
T-STAT0.379987793549532
p-value0.72326924287541
Lambda-3.39085518738585


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')