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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 computationTue, 21 Dec 2010 17:50:58 +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/21/t1292953730lee5t04h50yahiu.htm/, Retrieved Sun, 19 May 2024 21:02:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113784, Retrieved Sun, 19 May 2024 21:02:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
-   PD          [Standard Deviation-Mean Plot] [] [2010-12-20 14:28:14] [94f4aa1c01e87d8321fffb341ed4df07]
-    D              [Standard Deviation-Mean Plot] [] [2010-12-21 17:50:58] [d1991ab4912b5ede0ff54c26afa5d84c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
77,33
75,28
77,43
73,25
68,41
72,87
65,61
69,04
57,84
51,07
47,48
44,01
45,29
43,8
55,48
75,73
101,42
116,07
135,81
132,69
124,05
109,65
102,79
94,09
92,23
90,6
92,6
81,71
76,36
71,44
75,26
70,3
67,68
67,65
61,92
58,34
55,04
62,5
59,44
60,03
64,24
74,33
74,41
69,75
72,03
68,18
63,01
61,71
63,52

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=113784&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=113784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113784&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
164.968333333333311.921570849311433.42
294.739166666666732.635816481654792.01
375.507511.618378955149234.26
465.38916666666676.2689950743659319.37

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 64.9683333333333 & 11.9215708493114 & 33.42 \tabularnewline
2 & 94.7391666666667 & 32.6358164816547 & 92.01 \tabularnewline
3 & 75.5075 & 11.6183789551492 & 34.26 \tabularnewline
4 & 65.3891666666667 & 6.26899507436593 & 19.37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113784&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]64.9683333333333[/C][C]11.9215708493114[/C][C]33.42[/C][/ROW]
[ROW][C]2[/C][C]94.7391666666667[/C][C]32.6358164816547[/C][C]92.01[/C][/ROW]
[ROW][C]3[/C][C]75.5075[/C][C]11.6183789551492[/C][C]34.26[/C][/ROW]
[ROW][C]4[/C][C]65.3891666666667[/C][C]6.26899507436593[/C][C]19.37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113784&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
164.968333333333311.921570849311433.42
294.739166666666732.635816481654792.01
375.507511.618378955149234.26
465.38916666666676.2689950743659319.37






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-43.8110223606806
beta0.790703779787496
S.D.0.190486915396075
T-STAT4.15096112057567
p-value0.0534280660116487

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -43.8110223606806 \tabularnewline
beta & 0.790703779787496 \tabularnewline
S.D. & 0.190486915396075 \tabularnewline
T-STAT & 4.15096112057567 \tabularnewline
p-value & 0.0534280660116487 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113784&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-43.8110223606806[/C][/ROW]
[ROW][C]beta[/C][C]0.790703779787496[/C][/ROW]
[ROW][C]S.D.[/C][C]0.190486915396075[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.15096112057567[/C][/ROW]
[ROW][C]p-value[/C][C]0.0534280660116487[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113784&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-43.8110223606806
beta0.790703779787496
S.D.0.190486915396075
T-STAT4.15096112057567
p-value0.0534280660116487






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-12.4622394993411
beta3.48823339294201
S.D.1.17772609031929
T-STAT2.96183757973497
p-value0.097591133742607
Lambda-2.48823339294201

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -12.4622394993411 \tabularnewline
beta & 3.48823339294201 \tabularnewline
S.D. & 1.17772609031929 \tabularnewline
T-STAT & 2.96183757973497 \tabularnewline
p-value & 0.097591133742607 \tabularnewline
Lambda & -2.48823339294201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113784&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.4622394993411[/C][/ROW]
[ROW][C]beta[/C][C]3.48823339294201[/C][/ROW]
[ROW][C]S.D.[/C][C]1.17772609031929[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.96183757973497[/C][/ROW]
[ROW][C]p-value[/C][C]0.097591133742607[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.48823339294201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113784&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113784&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-12.4622394993411
beta3.48823339294201
S.D.1.17772609031929
T-STAT2.96183757973497
p-value0.097591133742607
Lambda-2.48823339294201


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')