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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, 30 Nov 2011 05:29:19 -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/2011/Nov/30/t1322649009i1zkcluf6r90uz7.htm/, Retrieved Fri, 19 Apr 2024 16:06:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148854, Retrieved Fri, 19 Apr 2024 16:06:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact86

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] [] [2011-11-30 10:29:19] [7d095200a4be23015976b6928166d958] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.29
8.27
8.27
8.43
8.46
8.48
8.46
8.46
8.43
8.4
8.38
8.3
8.39
8.53
8.52
8.54
8.62
8.52
8.49
8.44
8.31
8.26
8.21
8.03
7.89
7.83
7.85
7.84
7.88
8.01
8.08
8.11
8.11
8.07
8.06
7.95
7.95
8.07
8.17
8.21
8.2
8.19
8.18
8.16
8.17
8.17
8.19
8.01
8.04
8.13
8.14
8.17
8.25
8.27
8.27
8.26
8.24
8.21
8.25
8.06
8.16
8.32
8.43
8.39
8.41
8.45
8.43
8.52
8.52
8.51
8.56
8.36
8.4
8.44
8.5
8.31
8.38
8.45
8.42
8.46
8.45
8.32
8.4
8.18

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'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148854&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148854&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.3150.07724420150837660.16
28.4650.009999999999999790.0199999999999996
38.37750.05560275772537390.129999999999999
48.4950.07047458170621930.149999999999999
58.51750.07588368291888120.18
68.20250.1220314167199040.280000000000001
77.85250.02629955639676570.0599999999999996
88.020.1023067283548190.23
98.04750.06849574196011490.159999999999999
108.10.1160459679035280.260000000000001
118.18250.0170782512765990.0399999999999991
128.1350.08386497083606080.18
138.120.05597618541248940.130000000000001
148.26250.009574271077563180.0199999999999996
158.190.08831760866327830.19
168.3250.1190238071423810.27
178.45250.04787135538781670.109999999999999
188.48750.08770214744615280.200000000000001
198.41250.07973915809270430.19
208.42750.03593976442141280.0800000000000001
218.33750.1178629147215810.27

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.315 & 0.0772442015083766 & 0.16 \tabularnewline
2 & 8.465 & 0.00999999999999979 & 0.0199999999999996 \tabularnewline
3 & 8.3775 & 0.0556027577253739 & 0.129999999999999 \tabularnewline
4 & 8.495 & 0.0704745817062193 & 0.149999999999999 \tabularnewline
5 & 8.5175 & 0.0758836829188812 & 0.18 \tabularnewline
6 & 8.2025 & 0.122031416719904 & 0.280000000000001 \tabularnewline
7 & 7.8525 & 0.0262995563967657 & 0.0599999999999996 \tabularnewline
8 & 8.02 & 0.102306728354819 & 0.23 \tabularnewline
9 & 8.0475 & 0.0684957419601149 & 0.159999999999999 \tabularnewline
10 & 8.1 & 0.116045967903528 & 0.260000000000001 \tabularnewline
11 & 8.1825 & 0.017078251276599 & 0.0399999999999991 \tabularnewline
12 & 8.135 & 0.0838649708360608 & 0.18 \tabularnewline
13 & 8.12 & 0.0559761854124894 & 0.130000000000001 \tabularnewline
14 & 8.2625 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
15 & 8.19 & 0.0883176086632783 & 0.19 \tabularnewline
16 & 8.325 & 0.119023807142381 & 0.27 \tabularnewline
17 & 8.4525 & 0.0478713553878167 & 0.109999999999999 \tabularnewline
18 & 8.4875 & 0.0877021474461528 & 0.200000000000001 \tabularnewline
19 & 8.4125 & 0.0797391580927043 & 0.19 \tabularnewline
20 & 8.4275 & 0.0359397644214128 & 0.0800000000000001 \tabularnewline
21 & 8.3375 & 0.117862914721581 & 0.27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148854&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]8.315[/C][C]0.0772442015083766[/C][C]0.16[/C][/ROW]
[ROW][C]2[/C][C]8.465[/C][C]0.00999999999999979[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]3[/C][C]8.3775[/C][C]0.0556027577253739[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]4[/C][C]8.495[/C][C]0.0704745817062193[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]5[/C][C]8.5175[/C][C]0.0758836829188812[/C][C]0.18[/C][/ROW]
[ROW][C]6[/C][C]8.2025[/C][C]0.122031416719904[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]7[/C][C]7.8525[/C][C]0.0262995563967657[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]8[/C][C]8.02[/C][C]0.102306728354819[/C][C]0.23[/C][/ROW]
[ROW][C]9[/C][C]8.0475[/C][C]0.0684957419601149[/C][C]0.159999999999999[/C][/ROW]
[ROW][C]10[/C][C]8.1[/C][C]0.116045967903528[/C][C]0.260000000000001[/C][/ROW]
[ROW][C]11[/C][C]8.1825[/C][C]0.017078251276599[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]12[/C][C]8.135[/C][C]0.0838649708360608[/C][C]0.18[/C][/ROW]
[ROW][C]13[/C][C]8.12[/C][C]0.0559761854124894[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]14[/C][C]8.2625[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]15[/C][C]8.19[/C][C]0.0883176086632783[/C][C]0.19[/C][/ROW]
[ROW][C]16[/C][C]8.325[/C][C]0.119023807142381[/C][C]0.27[/C][/ROW]
[ROW][C]17[/C][C]8.4525[/C][C]0.0478713553878167[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]18[/C][C]8.4875[/C][C]0.0877021474461528[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]19[/C][C]8.4125[/C][C]0.0797391580927043[/C][C]0.19[/C][/ROW]
[ROW][C]20[/C][C]8.4275[/C][C]0.0359397644214128[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]21[/C][C]8.3375[/C][C]0.117862914721581[/C][C]0.27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148854&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
18.3150.07724420150837660.16
28.4650.009999999999999790.0199999999999996
38.37750.05560275772537390.129999999999999
48.4950.07047458170621930.149999999999999
58.51750.07588368291888120.18
68.20250.1220314167199040.280000000000001
77.85250.02629955639676570.0599999999999996
88.020.1023067283548190.23
98.04750.06849574196011490.159999999999999
108.10.1160459679035280.260000000000001
118.18250.0170782512765990.0399999999999991
128.1350.08386497083606080.18
138.120.05597618541248940.130000000000001
148.26250.009574271077563180.0199999999999996
158.190.08831760866327830.19
168.3250.1190238071423810.27
178.45250.04787135538781670.109999999999999
188.48750.08770214744615280.200000000000001
198.41250.07973915809270430.19
208.42750.03593976442141280.0800000000000001
218.33750.1178629147215810.27






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.150920633407298
beta-0.0097970829292343
S.D.0.0447510936480303
T-STAT-0.218923877174687
p-value0.829043856777197

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.150920633407298 \tabularnewline
beta & -0.0097970829292343 \tabularnewline
S.D. & 0.0447510936480303 \tabularnewline
T-STAT & -0.218923877174687 \tabularnewline
p-value & 0.829043856777197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148854&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.150920633407298[/C][/ROW]
[ROW][C]beta[/C][C]-0.0097970829292343[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0447510936480303[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.218923877174687[/C][/ROW]
[ROW][C]p-value[/C][C]0.829043856777197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148854&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148854&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)
alpha0.150920633407298
beta-0.0097970829292343
S.D.0.0447510936480303
T-STAT-0.218923877174687
p-value0.829043856777197






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.815865942191441
beta-0.971689834045725
S.D.7.94123177483068
T-STAT-0.122360089920237
p-value0.903898802822294
Lambda1.97168983404572

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.815865942191441 \tabularnewline
beta & -0.971689834045725 \tabularnewline
S.D. & 7.94123177483068 \tabularnewline
T-STAT & -0.122360089920237 \tabularnewline
p-value & 0.903898802822294 \tabularnewline
Lambda & 1.97168983404572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148854&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.815865942191441[/C][/ROW]
[ROW][C]beta[/C][C]-0.971689834045725[/C][/ROW]
[ROW][C]S.D.[/C][C]7.94123177483068[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.122360089920237[/C][/ROW]
[ROW][C]p-value[/C][C]0.903898802822294[/C][/ROW]
[ROW][C]Lambda[/C][C]1.97168983404572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148854&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148854&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-0.815865942191441
beta-0.971689834045725
S.D.7.94123177483068
T-STAT-0.122360089920237
p-value0.903898802822294
Lambda1.97168983404572


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')