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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, 26 Dec 2008 07:31:28 -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/26/t12303019613wfid46gli22rz2.htm/, Retrieved Fri, 17 May 2024 23:06:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36627, Retrieved Fri, 17 May 2024 23:06:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215

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] [WS7 - SD - Machines] [2007-11-24 13:03:46] [5343e105a400b9e32bf6f011133bbaf4]
-    D    [Standard Deviation-Mean Plot] [WS7 - SD - Machines] [2008-12-26 14:31:28] [46e37ee7550ef0ff8e9e103b4ae236a6] [Current]
-           [Standard Deviation-Mean Plot] [paper - SD - Mach...] [2008-12-29 16:43:59] [c29178f7f550574a75dc881e636e0923]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93.5
94.7
112.9
99.2
105.6
113.0
83.1
81.1
96.9
104.3
97.7
102.6
89.9
96.0
112.7
107.1
106.2
121.0
101.2
83.2
105.1
113.3
99.1
100.3
93.5
98.8
106.2
98.3
102.1
117.1
101.5
80.5
105.9
109.5
97.2
114.5
93.5
100.9
121.1
116.5
109.3
118.1
108.3
105.4
116.2
111.2
105.8
122.7
99.5
107.9
124.6
115.0
110.3
132.7
99.7
96.5
118.7
112.9
130.5
137.9
115.0
116.8
140.9
120.7
134.2
147.3
112.4
107.1
128.4
137.7
135.0
151.0
137.4
132.4
161.3
139.8
146.0
154.6
142.1
120.5

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=36627&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=36627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36627&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
198.716666666666710.004347539793423.1
2102.92510.418351378915326.3
3102.0916666666679.7932684054204310.9
4110.758.6483314207791724.4
5115.51666666666713.731505468237735.8
6128.87514.359990187385938

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.7166666666667 & 10.0043475397934 & 23.1 \tabularnewline
2 & 102.925 & 10.4183513789153 & 26.3 \tabularnewline
3 & 102.091666666667 & 9.79326840542043 & 10.9 \tabularnewline
4 & 110.75 & 8.64833142077917 & 24.4 \tabularnewline
5 & 115.516666666667 & 13.7315054682377 & 35.8 \tabularnewline
6 & 128.875 & 14.3599901873859 & 38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36627&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]98.7166666666667[/C][C]10.0043475397934[/C][C]23.1[/C][/ROW]
[ROW][C]2[/C][C]102.925[/C][C]10.4183513789153[/C][C]26.3[/C][/ROW]
[ROW][C]3[/C][C]102.091666666667[/C][C]9.79326840542043[/C][C]10.9[/C][/ROW]
[ROW][C]4[/C][C]110.75[/C][C]8.64833142077917[/C][C]24.4[/C][/ROW]
[ROW][C]5[/C][C]115.516666666667[/C][C]13.7315054682377[/C][C]35.8[/C][/ROW]
[ROW][C]6[/C][C]128.875[/C][C]14.3599901873859[/C][C]38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36627&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
198.716666666666710.004347539793423.1
2102.92510.418351378915326.3
3102.0916666666679.7932684054204310.9
4110.758.6483314207791724.4
5115.51666666666713.731505468237735.8
6128.87514.359990187385938






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.670426819776
beta0.162365175972966
S.D.0.0643547564045399
T-STAT2.52297087339316
p-value0.0651502730909352

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.670426819776 \tabularnewline
beta & 0.162365175972966 \tabularnewline
S.D. & 0.0643547564045399 \tabularnewline
T-STAT & 2.52297087339316 \tabularnewline
p-value & 0.0651502730909352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36627&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.670426819776[/C][/ROW]
[ROW][C]beta[/C][C]0.162365175972966[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0643547564045399[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.52297087339316[/C][/ROW]
[ROW][C]p-value[/C][C]0.0651502730909352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36627&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36627&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-6.670426819776
beta0.162365175972966
S.D.0.0643547564045399
T-STAT2.52297087339316
p-value0.0651502730909352






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.681352499866
beta1.50732812072899
S.D.0.685574531228436
T-STAT2.19863494349491
p-value0.0927937939314514
Lambda-0.507328120728985

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.681352499866 \tabularnewline
beta & 1.50732812072899 \tabularnewline
S.D. & 0.685574531228436 \tabularnewline
T-STAT & 2.19863494349491 \tabularnewline
p-value & 0.0927937939314514 \tabularnewline
Lambda & -0.507328120728985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36627&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.681352499866[/C][/ROW]
[ROW][C]beta[/C][C]1.50732812072899[/C][/ROW]
[ROW][C]S.D.[/C][C]0.685574531228436[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.19863494349491[/C][/ROW]
[ROW][C]p-value[/C][C]0.0927937939314514[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.507328120728985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36627&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36627&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-4.681352499866
beta1.50732812072899
S.D.0.685574531228436
T-STAT2.19863494349491
p-value0.0927937939314514
Lambda-0.507328120728985


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')