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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 computationWed, 04 Dec 2013 05:33:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/04/t1386153309t925izh2mzr0m6b.htm/, Retrieved Fri, 19 Apr 2024 18:54:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230491, Retrieved Fri, 19 Apr 2024 18:54:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56

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] [] [2013-12-04 10:33:21] [72063bd14069f8db0ee4c827c297f3d1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.84
9.87
9.9
9.9
9.87
9.87
9.88
9.76
9.76
9.76
9.77
9.77
9.77
9.83
9.85
9.85
9.89
9.9
9.92
9.91
9.92
9.92
9.96
9.97
9.98
10.06
10.07
10.12
10.1
10.1
10.1
10.19
10.21
10.2
10.39
10.39
10.39
10.45
10.49
10.48
10.49
10.49
10.5
10.51
10.51
10.53
10.54
10.54
10.55
10.58
10.59
10.56
10.57
10.59
10.63
10.63
10.66
10.69
10.72
10.72
10.73
10.75
10.78
10.79
10.83
10.83
10.85
10.88
10.97
10.98
11
11.04
11.08
11.16
11.19
11.2
11.22
11.26
11.29
11.31
11.39
11.37
11.39
11.39

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'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230491&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230491&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.829166666666670.05961365513695580.140000000000001
29.890833333333330.05696224161404640.200000000000001
310.15916666666670.1256588696238810.41
410.49333333333330.04163331998932230.149999999999999
510.62416666666670.06097068346692730.17
610.86916666666670.1044864787540680.309999999999999
711.27083333333330.1032612162812290.31

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.82916666666667 & 0.0596136551369558 & 0.140000000000001 \tabularnewline
2 & 9.89083333333333 & 0.0569622416140464 & 0.200000000000001 \tabularnewline
3 & 10.1591666666667 & 0.125658869623881 & 0.41 \tabularnewline
4 & 10.4933333333333 & 0.0416333199893223 & 0.149999999999999 \tabularnewline
5 & 10.6241666666667 & 0.0609706834669273 & 0.17 \tabularnewline
6 & 10.8691666666667 & 0.104486478754068 & 0.309999999999999 \tabularnewline
7 & 11.2708333333333 & 0.103261216281229 & 0.31 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230491&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]9.82916666666667[/C][C]0.0596136551369558[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]2[/C][C]9.89083333333333[/C][C]0.0569622416140464[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]3[/C][C]10.1591666666667[/C][C]0.125658869623881[/C][C]0.41[/C][/ROW]
[ROW][C]4[/C][C]10.4933333333333[/C][C]0.0416333199893223[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]5[/C][C]10.6241666666667[/C][C]0.0609706834669273[/C][C]0.17[/C][/ROW]
[ROW][C]6[/C][C]10.8691666666667[/C][C]0.104486478754068[/C][C]0.309999999999999[/C][/ROW]
[ROW][C]7[/C][C]11.2708333333333[/C][C]0.103261216281229[/C][C]0.31[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230491&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
19.829166666666670.05961365513695580.140000000000001
29.890833333333330.05696224161404640.200000000000001
310.15916666666670.1256588696238810.41
410.49333333333330.04163331998932230.149999999999999
510.62416666666670.06097068346692730.17
610.86916666666670.1044864787540680.309999999999999
711.27083333333330.1032612162812290.31






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.150982571708751
beta0.0220062595163532
S.D.0.0249782401764029
T-STAT0.881017211818737
p-value0.41863784842737

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.150982571708751 \tabularnewline
beta & 0.0220062595163532 \tabularnewline
S.D. & 0.0249782401764029 \tabularnewline
T-STAT & 0.881017211818737 \tabularnewline
p-value & 0.41863784842737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230491&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.150982571708751[/C][/ROW]
[ROW][C]beta[/C][C]0.0220062595163532[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0249782401764029[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.881017211818737[/C][/ROW]
[ROW][C]p-value[/C][C]0.41863784842737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230491&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230491&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-0.150982571708751
beta0.0220062595163532
S.D.0.0249782401764029
T-STAT0.881017211818737
p-value0.41863784842737






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.71819452482046
beta3.0310924717227
S.D.3.36312591172883
T-STAT0.901272373166829
p-value0.408755877394267
Lambda-2.0310924717227

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.71819452482046 \tabularnewline
beta & 3.0310924717227 \tabularnewline
S.D. & 3.36312591172883 \tabularnewline
T-STAT & 0.901272373166829 \tabularnewline
p-value & 0.408755877394267 \tabularnewline
Lambda & -2.0310924717227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230491&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.71819452482046[/C][/ROW]
[ROW][C]beta[/C][C]3.0310924717227[/C][/ROW]
[ROW][C]S.D.[/C][C]3.36312591172883[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.901272373166829[/C][/ROW]
[ROW][C]p-value[/C][C]0.408755877394267[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.0310924717227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230491&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230491&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-9.71819452482046
beta3.0310924717227
S.D.3.36312591172883
T-STAT0.901272373166829
p-value0.408755877394267
Lambda-2.0310924717227


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')