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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 computationFri, 24 Dec 2010 15:09:59 +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/24/t1293203260hbei80v2fnf15p6.htm/, Retrieved Tue, 30 Apr 2024 01:18:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115075, Retrieved Tue, 30 Apr 2024 01:18:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114

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] [smp%_paper_voet] [2010-12-17 15:00:53] [7e261c986c934df955dd3ac53e9d45c6]
-         [Standard Deviation-Mean Plot] [Kristof Nagels] [2010-12-24 15:09:59] [fff0a1ca5ad3b1801f382406d5a383a7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,7
6,7
6,5
6,3
6,3
6,3
6,5
6,6
6,5
6,3
6,3
6,5
7
7,1
7,3
7,3
7,4
7,4
7,3
7,4
7,5
7,7
7,7
7,7
7,7
7,7
7,8
8
8,1
8,1
8,2
8,2
8,2
8,1
8,1
8,2
8,3
8,3
8,4
8,5
8,5
8,4
8
7,9
8,1
8,5
8,8
8,8
8,6
8,3
8,3
8,3
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,4
8,2
8
8
8
8
7,9
7,9
7,8
7,8
8
7,8
7,4
7,2
7
7
7,2
7,2
7,2
7
6,9
6,8
6,8
6,8
6,9
7,2
7,2
7,2
7,1
7,2
7,3
7,5
7,6
7,7
7,7
7,7
7,8
8
8,1
8,1
8
8,1
8,2
8,3
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,5
8,5

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=115075&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=115075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115075&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
16.458333333333330.1564279289951030.4
27.40.2256304299271070.7
38.033333333333330.1922750555056400.499999999999999
48.3750.2800162332956630.9
58.483333333333330.1337115846843040.299999999999999
68.3750.2050498830661810.6
77.650.3896385271224881
87.033333333333330.1825741858350550.4
97.650.331662479035541
108.3750.1912875037500070.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.45833333333333 & 0.156427928995103 & 0.4 \tabularnewline
2 & 7.4 & 0.225630429927107 & 0.7 \tabularnewline
3 & 8.03333333333333 & 0.192275055505640 & 0.499999999999999 \tabularnewline
4 & 8.375 & 0.280016233295663 & 0.9 \tabularnewline
5 & 8.48333333333333 & 0.133711584684304 & 0.299999999999999 \tabularnewline
6 & 8.375 & 0.205049883066181 & 0.6 \tabularnewline
7 & 7.65 & 0.389638527122488 & 1 \tabularnewline
8 & 7.03333333333333 & 0.182574185835055 & 0.4 \tabularnewline
9 & 7.65 & 0.33166247903554 & 1 \tabularnewline
10 & 8.375 & 0.191287503750007 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115075&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]6.45833333333333[/C][C]0.156427928995103[/C][C]0.4[/C][/ROW]
[ROW][C]2[/C][C]7.4[/C][C]0.225630429927107[/C][C]0.7[/C][/ROW]
[ROW][C]3[/C][C]8.03333333333333[/C][C]0.192275055505640[/C][C]0.499999999999999[/C][/ROW]
[ROW][C]4[/C][C]8.375[/C][C]0.280016233295663[/C][C]0.9[/C][/ROW]
[ROW][C]5[/C][C]8.48333333333333[/C][C]0.133711584684304[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]6[/C][C]8.375[/C][C]0.205049883066181[/C][C]0.6[/C][/ROW]
[ROW][C]7[/C][C]7.65[/C][C]0.389638527122488[/C][C]1[/C][/ROW]
[ROW][C]8[/C][C]7.03333333333333[/C][C]0.182574185835055[/C][C]0.4[/C][/ROW]
[ROW][C]9[/C][C]7.65[/C][C]0.33166247903554[/C][C]1[/C][/ROW]
[ROW][C]10[/C][C]8.375[/C][C]0.191287503750007[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115075&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
16.458333333333330.1564279289951030.4
27.40.2256304299271070.7
38.033333333333330.1922750555056400.499999999999999
48.3750.2800162332956630.9
58.483333333333330.1337115846843040.299999999999999
68.3750.2050498830661810.6
77.650.3896385271224881
87.033333333333330.1825741858350550.4
97.650.331662479035541
108.3750.1912875037500070.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.200412863871137
beta0.00365068744118689
S.D.0.042304833934986
T-STAT0.0862948060923076
p-value0.933352810658711

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.200412863871137 \tabularnewline
beta & 0.00365068744118689 \tabularnewline
S.D. & 0.042304833934986 \tabularnewline
T-STAT & 0.0862948060923076 \tabularnewline
p-value & 0.933352810658711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115075&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.200412863871137[/C][/ROW]
[ROW][C]beta[/C][C]0.00365068744118689[/C][/ROW]
[ROW][C]S.D.[/C][C]0.042304833934986[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0862948060923076[/C][/ROW]
[ROW][C]p-value[/C][C]0.933352810658711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115075&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115075&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)
alpha0.200412863871137
beta0.00365068744118689
S.D.0.042304833934986
T-STAT0.0862948060923076
p-value0.933352810658711






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.06180810469049
beta0.261419016910635
S.D.1.30480709444659
T-STAT0.200350701665606
p-value0.84620578954471
Lambda0.738580983089365

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.06180810469049 \tabularnewline
beta & 0.261419016910635 \tabularnewline
S.D. & 1.30480709444659 \tabularnewline
T-STAT & 0.200350701665606 \tabularnewline
p-value & 0.84620578954471 \tabularnewline
Lambda & 0.738580983089365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115075&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.06180810469049[/C][/ROW]
[ROW][C]beta[/C][C]0.261419016910635[/C][/ROW]
[ROW][C]S.D.[/C][C]1.30480709444659[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.200350701665606[/C][/ROW]
[ROW][C]p-value[/C][C]0.84620578954471[/C][/ROW]
[ROW][C]Lambda[/C][C]0.738580983089365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115075&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115075&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-2.06180810469049
beta0.261419016910635
S.D.1.30480709444659
T-STAT0.200350701665606
p-value0.84620578954471
Lambda0.738580983089365


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')