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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, 24 Dec 2008 06:33:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/24/t1230125637jxqwg31sysb2li1.htm/, Retrieved Sun, 19 May 2024 11:38:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36561, Retrieved Sun, 19 May 2024 11:38:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMPD  [Standard Deviation-Mean Plot] [Identification an...] [2008-12-09 21:54:11] [1a689e9ccc515e1757f0522229a687e9]
-    D      [Standard Deviation-Mean Plot] [Paper SMP] [2008-12-24 13:33:03] [74a138e5b32af267311b5ad4cd13bf7e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.7
109.5
105.3
102.8
100.6
97.6
110.3
107.2
107.2
108.1
97.1
92.2
112.2
111.6
115.7
111.3
104.2
103.2
112.7
106.4
102.6
110.6
95.2
89
112.5
116.8
107.2
113.6
101.8
102.6
122.7
110.3
110.5
121.6
100.3
100.7
123.4
127.1
124.1
131.2
111.6
114.2
130.1
125.9
119
133.8
107.5
113.5
134.4
126.8
135.6
139.9
129.8
131
153.1
134.1
144.1
155.9
123.3
128.1
144.3
153
149.9
150.9
141
138.9
157.4
142.9
151.7
161
138.5
135.9
151.5
164
159.1
157
142.1
144.8
152.1
154.6
148.7
157.7
146.4
136.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36561&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36561&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.6333333333335.6488668748428618.1
2106.2257.8962735745183226.7
3110.057.8162418311894922.4
4121.7833333333338.5121125818483326.3
5136.34166666666710.206723125944832.6
6147.1166666666678.0163280341759425.1
7151.2083333333337.8840988801203627.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.633333333333 & 5.64886687484286 & 18.1 \tabularnewline
2 & 106.225 & 7.89627357451832 & 26.7 \tabularnewline
3 & 110.05 & 7.81624183118949 & 22.4 \tabularnewline
4 & 121.783333333333 & 8.51211258184833 & 26.3 \tabularnewline
5 & 136.341666666667 & 10.2067231259448 & 32.6 \tabularnewline
6 & 147.116666666667 & 8.01632803417594 & 25.1 \tabularnewline
7 & 151.208333333333 & 7.88409888012036 & 27.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36561&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]103.633333333333[/C][C]5.64886687484286[/C][C]18.1[/C][/ROW]
[ROW][C]2[/C][C]106.225[/C][C]7.89627357451832[/C][C]26.7[/C][/ROW]
[ROW][C]3[/C][C]110.05[/C][C]7.81624183118949[/C][C]22.4[/C][/ROW]
[ROW][C]4[/C][C]121.783333333333[/C][C]8.51211258184833[/C][C]26.3[/C][/ROW]
[ROW][C]5[/C][C]136.341666666667[/C][C]10.2067231259448[/C][C]32.6[/C][/ROW]
[ROW][C]6[/C][C]147.116666666667[/C][C]8.01632803417594[/C][C]25.1[/C][/ROW]
[ROW][C]7[/C][C]151.208333333333[/C][C]7.88409888012036[/C][C]27.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36561&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
1103.6333333333335.6488668748428618.1
2106.2257.8962735745183226.7
3110.057.8162418311894922.4
4121.7833333333338.5121125818483326.3
5136.34166666666710.206723125944832.6
6147.1166666666678.0163280341759425.1
7151.2083333333337.8840988801203627.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.9629945712705
beta0.0322238995506936
S.D.0.0265620464220915
T-STAT1.21315575760357
p-value0.279250866570473

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.9629945712705 \tabularnewline
beta & 0.0322238995506936 \tabularnewline
S.D. & 0.0265620464220915 \tabularnewline
T-STAT & 1.21315575760357 \tabularnewline
p-value & 0.279250866570473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36561&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.9629945712705[/C][/ROW]
[ROW][C]beta[/C][C]0.0322238995506936[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0265620464220915[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21315575760357[/C][/ROW]
[ROW][C]p-value[/C][C]0.279250866570473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36561&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36561&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)
alpha3.9629945712705
beta0.0322238995506936
S.D.0.0265620464220915
T-STAT1.21315575760357
p-value0.279250866570473






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.747748114601565
beta0.583944238295709
S.D.0.424304232477322
T-STAT1.3762394847827
p-value0.227188542356679
Lambda0.416055761704291

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.747748114601565 \tabularnewline
beta & 0.583944238295709 \tabularnewline
S.D. & 0.424304232477322 \tabularnewline
T-STAT & 1.3762394847827 \tabularnewline
p-value & 0.227188542356679 \tabularnewline
Lambda & 0.416055761704291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36561&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.747748114601565[/C][/ROW]
[ROW][C]beta[/C][C]0.583944238295709[/C][/ROW]
[ROW][C]S.D.[/C][C]0.424304232477322[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.3762394847827[/C][/ROW]
[ROW][C]p-value[/C][C]0.227188542356679[/C][/ROW]
[ROW][C]Lambda[/C][C]0.416055761704291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36561&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36561&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-0.747748114601565
beta0.583944238295709
S.D.0.424304232477322
T-STAT1.3762394847827
p-value0.227188542356679
Lambda0.416055761704291


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')