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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, 07 Dec 2010 12:27:07 +0000
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/Dec/07/t12917247098857pmc7oulhrfv.htm/, Retrieved Fri, 03 May 2024 18:58:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106226, Retrieved Fri, 03 May 2024 18:58:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact95

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] [] [2010-12-07 12:27:07] [9c46b2659272a99de8fec46bf5966107] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98.6
100.1
98.8
98.3
102.8
103.6
105.2
100.1
98.2
98.4
97.4
98.4
100.3
101.1
104.1
107.3
110.1
112.6
114.3
115.3
109.9
108.2
103.2
101.8
105.6
108.2
109.8
114.6
117.2
116.5
116.1
112.1
106.8
106.9
104.5
103
105.9
107.7
107.1
112.5
114.5
114.6
113.1
112.8
111.9
112
112.4
110
112.3
109.6
111.9
110.8
110.4
110.8
114
108.4
110.5
105.1
102.3
104.3
103.4
102.4
104.5
107.3
110.1
111.8
111.8
105.7
106
106.4
107.1
111.5
109.6
109.9
109.3
111.4
112.9
115.5
118.4
116.2
113.3
113.8
114.1
117.1
115.5
115.2
114.2
115.3
118.8
118
118.1
111.8
112
114.3
115
118.5
117.6
119.1
120.6
123.6
122.7
123.8
123.1
124.5
120.7
118.7
119
122.3
118.6
118.1
118.2
120.8
119.7
119.7
117.1
114.5
116.5
116.4
114.9
115.5

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=106226&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=106226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106226&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
198.950.7937253933193761.80000000000000
2102.9252.131314148594715.10000000000001
398.10.4760952285695231
4103.23.185383284106747
5113.0752.275045787085035.2
6105.7753.887051153080798.10000000000001
7109.553.785498646149549
8115.4752.295466546623305.10000000000001
9105.31.892088792842453.90000000000001
10108.32.898275349237896.6
11113.750.9327379053088821.80000000000000
12111.5751.071991915392402.40000000000001
13111.151.212435565298222.70000000000000
14110.92.318045153428495.600
15105.553.503807452852788.2
16104.42.115025610562044.89999999999999
17109.852.880393491637326.1
18107.752.540997179586525.5
19110.050.9327379053088862.10000000000001
20115.752.266421555374615.5
21114.5751.715371679840843.8
22115.050.5802298395176391.30000000000000
23116.6753.269429104089387
24114.952.691344149924596.5
25120.2252.56173769148996
26123.5250.793200268952721.80000000000000
27120.1751.668082731761233.59999999999999
28118.9251.268529332205872.70000000000000
29117.752.489310480166485.2
30115.8250.7632168761236861.59999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 98.95 & 0.793725393319376 & 1.80000000000000 \tabularnewline
2 & 102.925 & 2.13131414859471 & 5.10000000000001 \tabularnewline
3 & 98.1 & 0.476095228569523 & 1 \tabularnewline
4 & 103.2 & 3.18538328410674 & 7 \tabularnewline
5 & 113.075 & 2.27504578708503 & 5.2 \tabularnewline
6 & 105.775 & 3.88705115308079 & 8.10000000000001 \tabularnewline
7 & 109.55 & 3.78549864614954 & 9 \tabularnewline
8 & 115.475 & 2.29546654662330 & 5.10000000000001 \tabularnewline
9 & 105.3 & 1.89208879284245 & 3.90000000000001 \tabularnewline
10 & 108.3 & 2.89827534923789 & 6.6 \tabularnewline
11 & 113.75 & 0.932737905308882 & 1.80000000000000 \tabularnewline
12 & 111.575 & 1.07199191539240 & 2.40000000000001 \tabularnewline
13 & 111.15 & 1.21243556529822 & 2.70000000000000 \tabularnewline
14 & 110.9 & 2.31804515342849 & 5.600 \tabularnewline
15 & 105.55 & 3.50380745285278 & 8.2 \tabularnewline
16 & 104.4 & 2.11502561056204 & 4.89999999999999 \tabularnewline
17 & 109.85 & 2.88039349163732 & 6.1 \tabularnewline
18 & 107.75 & 2.54099717958652 & 5.5 \tabularnewline
19 & 110.05 & 0.932737905308886 & 2.10000000000001 \tabularnewline
20 & 115.75 & 2.26642155537461 & 5.5 \tabularnewline
21 & 114.575 & 1.71537167984084 & 3.8 \tabularnewline
22 & 115.05 & 0.580229839517639 & 1.30000000000000 \tabularnewline
23 & 116.675 & 3.26942910408938 & 7 \tabularnewline
24 & 114.95 & 2.69134414992459 & 6.5 \tabularnewline
25 & 120.225 & 2.5617376914899 & 6 \tabularnewline
26 & 123.525 & 0.79320026895272 & 1.80000000000000 \tabularnewline
27 & 120.175 & 1.66808273176123 & 3.59999999999999 \tabularnewline
28 & 118.925 & 1.26852933220587 & 2.70000000000000 \tabularnewline
29 & 117.75 & 2.48931048016648 & 5.2 \tabularnewline
30 & 115.825 & 0.763216876123686 & 1.59999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106226&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]98.95[/C][C]0.793725393319376[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]2[/C][C]102.925[/C][C]2.13131414859471[/C][C]5.10000000000001[/C][/ROW]
[ROW][C]3[/C][C]98.1[/C][C]0.476095228569523[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]103.2[/C][C]3.18538328410674[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]113.075[/C][C]2.27504578708503[/C][C]5.2[/C][/ROW]
[ROW][C]6[/C][C]105.775[/C][C]3.88705115308079[/C][C]8.10000000000001[/C][/ROW]
[ROW][C]7[/C][C]109.55[/C][C]3.78549864614954[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]115.475[/C][C]2.29546654662330[/C][C]5.10000000000001[/C][/ROW]
[ROW][C]9[/C][C]105.3[/C][C]1.89208879284245[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]10[/C][C]108.3[/C][C]2.89827534923789[/C][C]6.6[/C][/ROW]
[ROW][C]11[/C][C]113.75[/C][C]0.932737905308882[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]12[/C][C]111.575[/C][C]1.07199191539240[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]13[/C][C]111.15[/C][C]1.21243556529822[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]14[/C][C]110.9[/C][C]2.31804515342849[/C][C]5.600[/C][/ROW]
[ROW][C]15[/C][C]105.55[/C][C]3.50380745285278[/C][C]8.2[/C][/ROW]
[ROW][C]16[/C][C]104.4[/C][C]2.11502561056204[/C][C]4.89999999999999[/C][/ROW]
[ROW][C]17[/C][C]109.85[/C][C]2.88039349163732[/C][C]6.1[/C][/ROW]
[ROW][C]18[/C][C]107.75[/C][C]2.54099717958652[/C][C]5.5[/C][/ROW]
[ROW][C]19[/C][C]110.05[/C][C]0.932737905308886[/C][C]2.10000000000001[/C][/ROW]
[ROW][C]20[/C][C]115.75[/C][C]2.26642155537461[/C][C]5.5[/C][/ROW]
[ROW][C]21[/C][C]114.575[/C][C]1.71537167984084[/C][C]3.8[/C][/ROW]
[ROW][C]22[/C][C]115.05[/C][C]0.580229839517639[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]23[/C][C]116.675[/C][C]3.26942910408938[/C][C]7[/C][/ROW]
[ROW][C]24[/C][C]114.95[/C][C]2.69134414992459[/C][C]6.5[/C][/ROW]
[ROW][C]25[/C][C]120.225[/C][C]2.5617376914899[/C][C]6[/C][/ROW]
[ROW][C]26[/C][C]123.525[/C][C]0.79320026895272[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]27[/C][C]120.175[/C][C]1.66808273176123[/C][C]3.59999999999999[/C][/ROW]
[ROW][C]28[/C][C]118.925[/C][C]1.26852933220587[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]29[/C][C]117.75[/C][C]2.48931048016648[/C][C]5.2[/C][/ROW]
[ROW][C]30[/C][C]115.825[/C][C]0.763216876123686[/C][C]1.59999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106226&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
198.950.7937253933193761.80000000000000
2102.9252.131314148594715.10000000000001
398.10.4760952285695231
4103.23.185383284106747
5113.0752.275045787085035.2
6105.7753.887051153080798.10000000000001
7109.553.785498646149549
8115.4752.295466546623305.10000000000001
9105.31.892088792842453.90000000000001
10108.32.898275349237896.6
11113.750.9327379053088821.80000000000000
12111.5751.071991915392402.40000000000001
13111.151.212435565298222.70000000000000
14110.92.318045153428495.600
15105.553.503807452852788.2
16104.42.115025610562044.89999999999999
17109.852.880393491637326.1
18107.752.540997179586525.5
19110.050.9327379053088862.10000000000001
20115.752.266421555374615.5
21114.5751.715371679840843.8
22115.050.5802298395176391.30000000000000
23116.6753.269429104089387
24114.952.691344149924596.5
25120.2252.56173769148996
26123.5250.793200268952721.80000000000000
27120.1751.668082731761233.59999999999999
28118.9251.268529332205872.70000000000000
29117.752.489310480166485.2
30115.8250.7632168761236861.59999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.94331179849367
beta-0.0171019792265399
S.D.0.0292093991511889
T-STAT-0.585495755596323
p-value0.562904082824184

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.94331179849367 \tabularnewline
beta & -0.0171019792265399 \tabularnewline
S.D. & 0.0292093991511889 \tabularnewline
T-STAT & -0.585495755596323 \tabularnewline
p-value & 0.562904082824184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106226&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.94331179849367[/C][/ROW]
[ROW][C]beta[/C][C]-0.0171019792265399[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0292093991511889[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.585495755596323[/C][/ROW]
[ROW][C]p-value[/C][C]0.562904082824184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106226&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)
alpha3.94331179849367
beta-0.0171019792265399
S.D.0.0292093991511889
T-STAT-0.585495755596323
p-value0.562904082824184






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.08338889694422
beta-0.109471739713651
S.D.1.92248316790373
T-STAT-0.0569428859203061
p-value0.95499510939319
Lambda1.10947173971365

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.08338889694422 \tabularnewline
beta & -0.109471739713651 \tabularnewline
S.D. & 1.92248316790373 \tabularnewline
T-STAT & -0.0569428859203061 \tabularnewline
p-value & 0.95499510939319 \tabularnewline
Lambda & 1.10947173971365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106226&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.08338889694422[/C][/ROW]
[ROW][C]beta[/C][C]-0.109471739713651[/C][/ROW]
[ROW][C]S.D.[/C][C]1.92248316790373[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0569428859203061[/C][/ROW]
[ROW][C]p-value[/C][C]0.95499510939319[/C][/ROW]
[ROW][C]Lambda[/C][C]1.10947173971365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106226&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)
alpha1.08338889694422
beta-0.109471739713651
S.D.1.92248316790373
T-STAT-0.0569428859203061
p-value0.95499510939319
Lambda1.10947173971365


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')