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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 22 Dec 2010 20:23:10 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293049244mqn3a4gp0hbs218.htm/, Retrieved Sun, 05 May 2024 23:10:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114558, Retrieved Sun, 05 May 2024 23:10:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

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] [mean plot bel20] [2008-12-10 18:16:19] [74be16979710d4c4e7c6647856088456]
-  M D  [Standard Deviation-Mean Plot] [] [2009-12-15 12:36:38] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-    D    [Standard Deviation-Mean Plot] [] [2010-12-22 19:39:34] [82643889efeee0b265cd2ff213e5137b]
-             [Standard Deviation-Mean Plot] [] [2010-12-22 20:23:10] [4afc4ea409ad669ec2851bc39795365d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,600
4603,000
179,500
0,300
169,000
25,600
440,000
6,400
423,000
2,400
1,200
25,000
3,500
5,000
17,500
81,000
115,000
1,000
325,000
4,000
5,500
655,000
0,140
0,250
13,200
3,000
8,100
0,400
0,330
6,300
10,800
15,500
115,000
11,400
180,000
12,100
1,900
50,400
179,000
12,300
21,000
175,000
1,000
2,600
12,300
2,500
58,000
3,900

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114558&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114558&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1490.1666666666671305.203957822364602.7
2101.074166666667198.227368556153654.86
331.344166666666756.2119265019498179.67
443.32565.2421381540266178

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 490.166666666667 & 1305.20395782236 & 4602.7 \tabularnewline
2 & 101.074166666667 & 198.227368556153 & 654.86 \tabularnewline
3 & 31.3441666666667 & 56.2119265019498 & 179.67 \tabularnewline
4 & 43.325 & 65.2421381540266 & 178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114558&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]490.166666666667[/C][C]1305.20395782236[/C][C]4602.7[/C][/ROW]
[ROW][C]2[/C][C]101.074166666667[/C][C]198.227368556153[/C][C]654.86[/C][/ROW]
[ROW][C]3[/C][C]31.3441666666667[/C][C]56.2119265019498[/C][C]179.67[/C][/ROW]
[ROW][C]4[/C][C]43.325[/C][C]65.2421381540266[/C][C]178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114558&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
1490.1666666666671305.203957822364602.7
2101.074166666667198.227368556153654.86
331.344166666666756.2119265019498179.67
443.32565.2421381540266178






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-54.0049146603385
beta2.76449527665276
S.D.0.0678523836524992
T-STAT40.742787914584
p-value0.000601874979037145

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -54.0049146603385 \tabularnewline
beta & 2.76449527665276 \tabularnewline
S.D. & 0.0678523836524992 \tabularnewline
T-STAT & 40.742787914584 \tabularnewline
p-value & 0.000601874979037145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114558&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-54.0049146603385[/C][/ROW]
[ROW][C]beta[/C][C]2.76449527665276[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0678523836524992[/C][/ROW]
[ROW][C]T-STAT[/C][C]40.742787914584[/C][/ROW]
[ROW][C]p-value[/C][C]0.000601874979037145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114558&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114558&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-54.0049146603385
beta2.76449527665276
S.D.0.0678523836524992
T-STAT40.742787914584
p-value0.000601874979037145






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.139712032390855
beta1.17782901678136
S.D.0.0549650037968935
T-STAT21.4287080036175
p-value0.00217066184763719
Lambda-0.17782901678136

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.139712032390855 \tabularnewline
beta & 1.17782901678136 \tabularnewline
S.D. & 0.0549650037968935 \tabularnewline
T-STAT & 21.4287080036175 \tabularnewline
p-value & 0.00217066184763719 \tabularnewline
Lambda & -0.17782901678136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114558&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.139712032390855[/C][/ROW]
[ROW][C]beta[/C][C]1.17782901678136[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0549650037968935[/C][/ROW]
[ROW][C]T-STAT[/C][C]21.4287080036175[/C][/ROW]
[ROW][C]p-value[/C][C]0.00217066184763719[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.17782901678136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114558&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114558&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-0.139712032390855
beta1.17782901678136
S.D.0.0549650037968935
T-STAT21.4287080036175
p-value0.00217066184763719
Lambda-0.17782901678136


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')