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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 computationMon, 02 Dec 2013 07:09:50 -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/02/t138598632057nmur3tr4677dc.htm/, Retrieved Fri, 19 Apr 2024 21:48:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229977, Retrieved Fri, 19 Apr 2024 21:48:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

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] [] [2013-12-02 12:09:50] [629d05b8910d8b56ad89862016f2bc6c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
120.6
119.9
119.48
117.45
118.37
117.07
114.98
112.59
111.7
112.04
110.79
109.82
109.11
109.84
109.31
108.29
107.42
106.71
105.11
104.43
105.55
106.12
105.78
105.33
104.63
104.62
105.57
107.5
107.52
107.76
106.74
106.21
105.77
105.27
104.35
103.52
102.28
100.93
101.04
99.95
99.55
99.56
99.01
98.64
98.98
100.8
100.32
100.72
280.8
280.4
280.4
280.3
281
280.9
279.7
283.1
290.6
291.6
291.7
291.8
291.7
291.5
291.7
293.4
293.1
293.1
292.6
292.1
292.2
292
292.1
293.4
292.2
292.1
291.6
290.9
290.9
290.8
290.5
290
290.2
290.1
291
291.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229977&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229977&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1115.3991666666673.8752042956898810.78
2106.9166666666671.834672788925665.41
3105.7883333333331.386197108726764.24000000000001
4100.1483333333331.06217472739433.64
5284.3583333333335.288659966610112.1
6292.4083333333330.6868350779062051.89999999999998
7291.0083333333330.763316130545872.19999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 115.399166666667 & 3.87520429568988 & 10.78 \tabularnewline
2 & 106.916666666667 & 1.83467278892566 & 5.41 \tabularnewline
3 & 105.788333333333 & 1.38619710872676 & 4.24000000000001 \tabularnewline
4 & 100.148333333333 & 1.0621747273943 & 3.64 \tabularnewline
5 & 284.358333333333 & 5.2886599666101 & 12.1 \tabularnewline
6 & 292.408333333333 & 0.686835077906205 & 1.89999999999998 \tabularnewline
7 & 291.008333333333 & 0.76331613054587 & 2.19999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229977&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]115.399166666667[/C][C]3.87520429568988[/C][C]10.78[/C][/ROW]
[ROW][C]2[/C][C]106.916666666667[/C][C]1.83467278892566[/C][C]5.41[/C][/ROW]
[ROW][C]3[/C][C]105.788333333333[/C][C]1.38619710872676[/C][C]4.24000000000001[/C][/ROW]
[ROW][C]4[/C][C]100.148333333333[/C][C]1.0621747273943[/C][C]3.64[/C][/ROW]
[ROW][C]5[/C][C]284.358333333333[/C][C]5.2886599666101[/C][C]12.1[/C][/ROW]
[ROW][C]6[/C][C]292.408333333333[/C][C]0.686835077906205[/C][C]1.89999999999998[/C][/ROW]
[ROW][C]7[/C][C]291.008333333333[/C][C]0.76331613054587[/C][C]2.19999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229977&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
1115.3991666666673.8752042956898810.78
2106.9166666666671.834672788925665.41
3105.7883333333331.386197108726764.24000000000001
4100.1483333333331.06217472739433.64
5284.3583333333335.288659966610112.1
6292.4083333333330.6868350779062051.89999999999998
7291.0083333333330.763316130545872.19999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.9170196159621
beta0.00114034832136204
S.D.0.00809150902597837
T-STAT0.140931477392026
p-value0.893425948575679

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.9170196159621 \tabularnewline
beta & 0.00114034832136204 \tabularnewline
S.D. & 0.00809150902597837 \tabularnewline
T-STAT & 0.140931477392026 \tabularnewline
p-value & 0.893425948575679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229977&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.9170196159621[/C][/ROW]
[ROW][C]beta[/C][C]0.00114034832136204[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00809150902597837[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.140931477392026[/C][/ROW]
[ROW][C]p-value[/C][C]0.893425948575679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229977&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229977&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)
alpha1.9170196159621
beta0.00114034832136204
S.D.0.00809150902597837
T-STAT0.140931477392026
p-value0.893425948575679






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.55530188948602
beta-0.210672087697538
S.D.0.649691724412313
T-STAT-0.324264693209851
p-value0.758863625561021
Lambda1.21067208769754

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.55530188948602 \tabularnewline
beta & -0.210672087697538 \tabularnewline
S.D. & 0.649691724412313 \tabularnewline
T-STAT & -0.324264693209851 \tabularnewline
p-value & 0.758863625561021 \tabularnewline
Lambda & 1.21067208769754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229977&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.55530188948602[/C][/ROW]
[ROW][C]beta[/C][C]-0.210672087697538[/C][/ROW]
[ROW][C]S.D.[/C][C]0.649691724412313[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.324264693209851[/C][/ROW]
[ROW][C]p-value[/C][C]0.758863625561021[/C][/ROW]
[ROW][C]Lambda[/C][C]1.21067208769754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229977&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229977&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)
alpha1.55530188948602
beta-0.210672087697538
S.D.0.649691724412313
T-STAT-0.324264693209851
p-value0.758863625561021
Lambda1.21067208769754


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')