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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 computationTue, 18 Dec 2007 14:01:59 -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/2007/Dec/18/t11980107003uoy2p7d2lqu1l9.htm/, Retrieved Sat, 04 May 2024 18:02:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4609, Retrieved Sat, 04 May 2024 18:02:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

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] [] [2007-12-18 21:01:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99,5
101,6
103,9
106,6
108,3
102
93,8
91,6
97,7
94,8
98
103,8
97,8
91,2
89,3
87,5
90,4
94,2
102,2
101,3
96
90,8
93,2
90,9
91,1
90,2
94,3
96
99
103,3
113,1
112,8
112,1
107,4
111
110,5
110,8
112,4
111,5
116,2
122,5
121,3
113,9
110,7
120,8
106,8
109,05
109,5
108,65
110,35
118,55
120,1
124,85
129,1
124,85
120,1
112,5
106,2
107,1
108,5
106,5
108,3
125,6
124
127,2
136,9
135,8
124,3
115,4
113,6
114,4
118,4
117
116,5
115,4
113,6
117,4
116,9
116,4
111,1
110,2
118,9
131,8
130,6
138,3
148,4
148,7
144,3
152,5
162,9
167,2
166,5
166,5

Tables (Output of Computation)





Summary of compuational 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 compuational 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=4609&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4609&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 compuational 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
1100.1333333333335.1700770757984817.2
293.73333333333334.707698401812112
3103.48.8665869214914723.8
4113.78755.2450896950472635
5115.9041666666677.9656209691550338.7
6120.8666666666679.8123607884353842.7
7117.9833333333336.6875506228613638

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.133333333333 & 5.17007707579848 & 17.2 \tabularnewline
2 & 93.7333333333333 & 4.7076984018121 & 12 \tabularnewline
3 & 103.4 & 8.86658692149147 & 23.8 \tabularnewline
4 & 113.7875 & 5.24508969504726 & 35 \tabularnewline
5 & 115.904166666667 & 7.96562096915503 & 38.7 \tabularnewline
6 & 120.866666666667 & 9.81236078843538 & 42.7 \tabularnewline
7 & 117.983333333333 & 6.68755062286136 & 38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4609&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]100.133333333333[/C][C]5.17007707579848[/C][C]17.2[/C][/ROW]
[ROW][C]2[/C][C]93.7333333333333[/C][C]4.7076984018121[/C][C]12[/C][/ROW]
[ROW][C]3[/C][C]103.4[/C][C]8.86658692149147[/C][C]23.8[/C][/ROW]
[ROW][C]4[/C][C]113.7875[/C][C]5.24508969504726[/C][C]35[/C][/ROW]
[ROW][C]5[/C][C]115.904166666667[/C][C]7.96562096915503[/C][C]38.7[/C][/ROW]
[ROW][C]6[/C][C]120.866666666667[/C][C]9.81236078843538[/C][C]42.7[/C][/ROW]
[ROW][C]7[/C][C]117.983333333333[/C][C]6.68755062286136[/C][C]38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4609&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
1100.1333333333335.1700770757984817.2
293.73333333333334.707698401812112
3103.48.8665869214914723.8
4113.78755.2450896950472635
5115.9041666666677.9656209691550338.7
6120.8666666666679.8123607884353842.7
7117.9833333333336.6875506228613638






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.12501811813739
beta0.110119082844789
S.D.0.0718722784691514
T-STAT1.5321496019088
p-value0.186055389926595

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.12501811813739 \tabularnewline
beta & 0.110119082844789 \tabularnewline
S.D. & 0.0718722784691514 \tabularnewline
T-STAT & 1.5321496019088 \tabularnewline
p-value & 0.186055389926595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4609&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.12501811813739[/C][/ROW]
[ROW][C]beta[/C][C]0.110119082844789[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0718722784691514[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.5321496019088[/C][/ROW]
[ROW][C]p-value[/C][C]0.186055389926595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4609&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4609&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-5.12501811813739
beta0.110119082844789
S.D.0.0718722784691514
T-STAT1.5321496019088
p-value0.186055389926595






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.56829560671004
beta1.80488956917501
S.D.1.08462186994038
T-STAT1.66407263139016
p-value0.156981937270401
Lambda-0.804889569175006

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.56829560671004 \tabularnewline
beta & 1.80488956917501 \tabularnewline
S.D. & 1.08462186994038 \tabularnewline
T-STAT & 1.66407263139016 \tabularnewline
p-value & 0.156981937270401 \tabularnewline
Lambda & -0.804889569175006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4609&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.56829560671004[/C][/ROW]
[ROW][C]beta[/C][C]1.80488956917501[/C][/ROW]
[ROW][C]S.D.[/C][C]1.08462186994038[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.66407263139016[/C][/ROW]
[ROW][C]p-value[/C][C]0.156981937270401[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.804889569175006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4609&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4609&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-6.56829560671004
beta1.80488956917501
S.D.1.08462186994038
T-STAT1.66407263139016
p-value0.156981937270401
Lambda-0.804889569175006


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')