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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, 25 Jan 2010 12:00:42 -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/2010/Jan/25/t1264446140znvr98y02s5xn34.htm/, Retrieved Mon, 06 May 2024 03:53:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72490, Retrieved Mon, 06 May 2024 03:53:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact118

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] [standard daviatio...] [2010-01-25 19:00:42] [a00bf033610db033bc2faa6c748d42a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
76,3
71
85,9
109
83,4
101,3
81,6
84,8
88
88,4
85,2
139,5
85,3
79,4
131
91,4
88,2
113,2
81,9
89
95,7
93,2
98
140,5
93
82,1
86,3
84,8
85,7
110,8
87,4
100,4
100,4
99,4
108
161,7
109,3
99,9
110,3
97,5
102,4
122,3
104,4
122,7
127,3
128,4
125,3
187,1
131,4
125,6
142,9
116,6
129,7
155,4
138,7
167,7
155,8
157,1
159,9
244,6
154,3
143,2
147,3
155,1
152,2
166,5
161,2
180,1
169,2
164,5
166,2
267,3

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72490&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72490&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
191.218.235629460432268.5
298.919.381246793556161.1
310021.615650895505479.6
4119.74166666666724.003956428939589.6
5152.11666666666733.1209583011706128
6168.92532.6264289133267124.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 91.2 & 18.2356294604322 & 68.5 \tabularnewline
2 & 98.9 & 19.3812467935561 & 61.1 \tabularnewline
3 & 100 & 21.6156508955054 & 79.6 \tabularnewline
4 & 119.741666666667 & 24.0039564289395 & 89.6 \tabularnewline
5 & 152.116666666667 & 33.1209583011706 & 128 \tabularnewline
6 & 168.925 & 32.6264289133267 & 124.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72490&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]91.2[/C][C]18.2356294604322[/C][C]68.5[/C][/ROW]
[ROW][C]2[/C][C]98.9[/C][C]19.3812467935561[/C][C]61.1[/C][/ROW]
[ROW][C]3[/C][C]100[/C][C]21.6156508955054[/C][C]79.6[/C][/ROW]
[ROW][C]4[/C][C]119.741666666667[/C][C]24.0039564289395[/C][C]89.6[/C][/ROW]
[ROW][C]5[/C][C]152.116666666667[/C][C]33.1209583011706[/C][C]128[/C][/ROW]
[ROW][C]6[/C][C]168.925[/C][C]32.6264289133267[/C][C]124.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72490&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
191.218.235629460432268.5
298.919.381246793556161.1
310021.615650895505479.6
4119.74166666666724.003956428939589.6
5152.11666666666733.1209583011706128
6168.92532.6264289133267124.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.442069942988291
beta0.200211777258113
S.D.0.0222703329002196
T-STAT8.99006665751902
p-value0.000847420928429373

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.442069942988291 \tabularnewline
beta & 0.200211777258113 \tabularnewline
S.D. & 0.0222703329002196 \tabularnewline
T-STAT & 8.99006665751902 \tabularnewline
p-value & 0.000847420928429373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72490&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.442069942988291[/C][/ROW]
[ROW][C]beta[/C][C]0.200211777258113[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0222703329002196[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.99006665751902[/C][/ROW]
[ROW][C]p-value[/C][C]0.000847420928429373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72490&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72490&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)
alpha0.442069942988291
beta0.200211777258113
S.D.0.0222703329002196
T-STAT8.99006665751902
p-value0.000847420928429373






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.58197748645731
beta0.99806992259373
S.D.0.100635523274316
T-STAT9.91767012402921
p-value0.00058027750509102
Lambda0.00193007740626983

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.58197748645731 \tabularnewline
beta & 0.99806992259373 \tabularnewline
S.D. & 0.100635523274316 \tabularnewline
T-STAT & 9.91767012402921 \tabularnewline
p-value & 0.00058027750509102 \tabularnewline
Lambda & 0.00193007740626983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72490&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.58197748645731[/C][/ROW]
[ROW][C]beta[/C][C]0.99806992259373[/C][/ROW]
[ROW][C]S.D.[/C][C]0.100635523274316[/C][/ROW]
[ROW][C]T-STAT[/C][C]9.91767012402921[/C][/ROW]
[ROW][C]p-value[/C][C]0.00058027750509102[/C][/ROW]
[ROW][C]Lambda[/C][C]0.00193007740626983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72490&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72490&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-1.58197748645731
beta0.99806992259373
S.D.0.100635523274316
T-STAT9.91767012402921
p-value0.00058027750509102
Lambda0.00193007740626983


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')