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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, 11 Aug 2008 12:18:22 -0600
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/Aug/11/t1218478727v17xq8pbybm2ivv.htm/, Retrieved Tue, 14 May 2024 23:56:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13976, Retrieved Tue, 14 May 2024 23:56:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

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] [Michaël Mertens o...] [2008-08-11 18:18:22] [8ef116c437494d1794893d3b8a73922a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.14
15.09
15.17
15.18
15.21
15.27
15.28
15.3
15.34
15.33
15.27
15.35
15.38
15.38
15.39
15.4
15.39
15.43
15.43
15.47
15.48
15.47
15.58
15.56
15.61
15.56
15.62
15.63
15.58
15.65
15.79
15.76
15.77
15.79
15.87
15.79
15.9
15.96
16.05
16.18
16.29
16.43
16.38
16.39
16.35
16.48
16.52
16.44
16.46
16.52
16.47
16.59
16.59
16.59
16.54
16.48
16.47
16.56
16.61
16.57
16.72
16.69
16.72
16.81
16.75
16.85
16.84
16.92
17.02
17.11
17.2
17.3
17.37
17.42
17.51
17.56
17.62
17.59
17.78
17.73
17.79
17.85
17.86
17.79
17.97
17.96
18.03
18.02
18.03
18.14
18.16
18.24
18.28
18.18
18.19
18.32

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13976&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13976&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115.1450.04041451884327370.0899999999999999
215.2650.03872983346207390.0899999999999999
315.32250.03593976442141310.08
415.38750.009574271077563180.0199999999999996
515.430.03265986323710910.08
615.52250.05560275772537410.109999999999999
715.6050.03109126351029590.0700000000000003
815.6950.09746794344808920.209999999999999
915.8050.04434711565216680.0999999999999996
1016.02250.1217579566188590.279999999999999
1116.37250.05909032633745310.140000000000001
1216.44750.07274384280931660.169999999999998
1316.510.05944184833375660.129999999999999
1416.550.05228129047119350.109999999999999
1516.55250.05909032633745310.140000000000001
1616.7350.05196152422706550.119999999999997
1716.840.06976149845485520.170000000000002
1817.15750.1201041214946440.280000000000001
1917.4650.08582928793055740.189999999999998
2017.680.08981462390205020.190000000000001
2117.82250.03774917217635440.0700000000000003
2217.9950.03511884584284270.0700000000000003
2318.14250.08655441448399080.209999999999997
2418.24250.06849574196011510.140000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.145 & 0.0404145188432737 & 0.0899999999999999 \tabularnewline
2 & 15.265 & 0.0387298334620739 & 0.0899999999999999 \tabularnewline
3 & 15.3225 & 0.0359397644214131 & 0.08 \tabularnewline
4 & 15.3875 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
5 & 15.43 & 0.0326598632371091 & 0.08 \tabularnewline
6 & 15.5225 & 0.0556027577253741 & 0.109999999999999 \tabularnewline
7 & 15.605 & 0.0310912635102959 & 0.0700000000000003 \tabularnewline
8 & 15.695 & 0.0974679434480892 & 0.209999999999999 \tabularnewline
9 & 15.805 & 0.0443471156521668 & 0.0999999999999996 \tabularnewline
10 & 16.0225 & 0.121757956618859 & 0.279999999999999 \tabularnewline
11 & 16.3725 & 0.0590903263374531 & 0.140000000000001 \tabularnewline
12 & 16.4475 & 0.0727438428093166 & 0.169999999999998 \tabularnewline
13 & 16.51 & 0.0594418483337566 & 0.129999999999999 \tabularnewline
14 & 16.55 & 0.0522812904711935 & 0.109999999999999 \tabularnewline
15 & 16.5525 & 0.0590903263374531 & 0.140000000000001 \tabularnewline
16 & 16.735 & 0.0519615242270655 & 0.119999999999997 \tabularnewline
17 & 16.84 & 0.0697614984548552 & 0.170000000000002 \tabularnewline
18 & 17.1575 & 0.120104121494644 & 0.280000000000001 \tabularnewline
19 & 17.465 & 0.0858292879305574 & 0.189999999999998 \tabularnewline
20 & 17.68 & 0.0898146239020502 & 0.190000000000001 \tabularnewline
21 & 17.8225 & 0.0377491721763544 & 0.0700000000000003 \tabularnewline
22 & 17.995 & 0.0351188458428427 & 0.0700000000000003 \tabularnewline
23 & 18.1425 & 0.0865544144839908 & 0.209999999999997 \tabularnewline
24 & 18.2425 & 0.0684957419601151 & 0.140000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13976&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]15.145[/C][C]0.0404145188432737[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]2[/C][C]15.265[/C][C]0.0387298334620739[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]3[/C][C]15.3225[/C][C]0.0359397644214131[/C][C]0.08[/C][/ROW]
[ROW][C]4[/C][C]15.3875[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]5[/C][C]15.43[/C][C]0.0326598632371091[/C][C]0.08[/C][/ROW]
[ROW][C]6[/C][C]15.5225[/C][C]0.0556027577253741[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]7[/C][C]15.605[/C][C]0.0310912635102959[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]8[/C][C]15.695[/C][C]0.0974679434480892[/C][C]0.209999999999999[/C][/ROW]
[ROW][C]9[/C][C]15.805[/C][C]0.0443471156521668[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]10[/C][C]16.0225[/C][C]0.121757956618859[/C][C]0.279999999999999[/C][/ROW]
[ROW][C]11[/C][C]16.3725[/C][C]0.0590903263374531[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]12[/C][C]16.4475[/C][C]0.0727438428093166[/C][C]0.169999999999998[/C][/ROW]
[ROW][C]13[/C][C]16.51[/C][C]0.0594418483337566[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]14[/C][C]16.55[/C][C]0.0522812904711935[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]15[/C][C]16.5525[/C][C]0.0590903263374531[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]16[/C][C]16.735[/C][C]0.0519615242270655[/C][C]0.119999999999997[/C][/ROW]
[ROW][C]17[/C][C]16.84[/C][C]0.0697614984548552[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]18[/C][C]17.1575[/C][C]0.120104121494644[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]19[/C][C]17.465[/C][C]0.0858292879305574[/C][C]0.189999999999998[/C][/ROW]
[ROW][C]20[/C][C]17.68[/C][C]0.0898146239020502[/C][C]0.190000000000001[/C][/ROW]
[ROW][C]21[/C][C]17.8225[/C][C]0.0377491721763544[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]22[/C][C]17.995[/C][C]0.0351188458428427[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]23[/C][C]18.1425[/C][C]0.0865544144839908[/C][C]0.209999999999997[/C][/ROW]
[ROW][C]24[/C][C]18.2425[/C][C]0.0684957419601151[/C][C]0.140000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13976&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
115.1450.04041451884327370.0899999999999999
215.2650.03872983346207390.0899999999999999
315.32250.03593976442141310.08
415.38750.009574271077563180.0199999999999996
515.430.03265986323710910.08
615.52250.05560275772537410.109999999999999
715.6050.03109126351029590.0700000000000003
815.6950.09746794344808920.209999999999999
915.8050.04434711565216680.0999999999999996
1016.02250.1217579566188590.279999999999999
1116.37250.05909032633745310.140000000000001
1216.44750.07274384280931660.169999999999998
1316.510.05944184833375660.129999999999999
1416.550.05228129047119350.109999999999999
1516.55250.05909032633745310.140000000000001
1616.7350.05196152422706550.119999999999997
1716.840.06976149845485520.170000000000002
1817.15750.1201041214946440.280000000000001
1917.4650.08582928793055740.189999999999998
2017.680.08981462390205020.190000000000001
2117.82250.03774917217635440.0700000000000003
2217.9950.03511884584284270.0700000000000003
2318.14250.08655441448399080.209999999999997
2418.24250.06849574196011510.140000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.112013942828354
beta0.0104721402044120
S.D.0.00562420644145578
T-STAT1.86197649631462
p-value0.0760183897073448

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.112013942828354 \tabularnewline
beta & 0.0104721402044120 \tabularnewline
S.D. & 0.00562420644145578 \tabularnewline
T-STAT & 1.86197649631462 \tabularnewline
p-value & 0.0760183897073448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13976&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.112013942828354[/C][/ROW]
[ROW][C]beta[/C][C]0.0104721402044120[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00562420644145578[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.86197649631462[/C][/ROW]
[ROW][C]p-value[/C][C]0.0760183897073448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13976&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-0.112013942828354
beta0.0104721402044120
S.D.0.00562420644145578
T-STAT1.86197649631462
p-value0.0760183897073448






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-13.6888172622521
beta3.84333917301201
S.D.1.75518560374340
T-STAT2.18970527379843
p-value0.0394397513603985
Lambda-2.84333917301201

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.6888172622521 \tabularnewline
beta & 3.84333917301201 \tabularnewline
S.D. & 1.75518560374340 \tabularnewline
T-STAT & 2.18970527379843 \tabularnewline
p-value & 0.0394397513603985 \tabularnewline
Lambda & -2.84333917301201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13976&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.6888172622521[/C][/ROW]
[ROW][C]beta[/C][C]3.84333917301201[/C][/ROW]
[ROW][C]S.D.[/C][C]1.75518560374340[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.18970527379843[/C][/ROW]
[ROW][C]p-value[/C][C]0.0394397513603985[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.84333917301201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13976&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-13.6888172622521
beta3.84333917301201
S.D.1.75518560374340
T-STAT2.18970527379843
p-value0.0394397513603985
Lambda-2.84333917301201


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')