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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, 06 Jan 2010 11:35:45 -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/06/t126280298815ki8s9wpfm0j0o.htm/, Retrieved Sat, 04 May 2024 07:01:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71696, Retrieved Sat, 04 May 2024 07:01:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact120

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] [eigen reeks] [2010-01-06 18:35:45] [9b42eb3f67be7a3fb50ab98e0efd6cc3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467

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=71696&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=71696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71696&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
110.65750.1807253902103040.433
210.59350.2364663471476080.574999999999999
310.4210.1163013327524670.278000000000000
410.738750.1189352064501230.247
510.5180.1051570254429060.239000000000001
611.2130.3440222860998010.749
712.845250.7787354600033741.848
815.09150.6330426525914341.461
916.030250.7850861417704431.896
1015.2610.2951440326349150.693999999999999
1116.00650.3329669653283930.768999999999998
1215.731750.1458660915588910.343
1317.227750.6188238171456141.30700000000000
1419.55850.7362452037195221.564
1518.522250.4655844892891811.099
1619.2430.5496526175685871.16700000000000
1722.2941.221985542740452.765
1821.638750.2567000519413020.545000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10.6575 & 0.180725390210304 & 0.433 \tabularnewline
2 & 10.5935 & 0.236466347147608 & 0.574999999999999 \tabularnewline
3 & 10.421 & 0.116301332752467 & 0.278000000000000 \tabularnewline
4 & 10.73875 & 0.118935206450123 & 0.247 \tabularnewline
5 & 10.518 & 0.105157025442906 & 0.239000000000001 \tabularnewline
6 & 11.213 & 0.344022286099801 & 0.749 \tabularnewline
7 & 12.84525 & 0.778735460003374 & 1.848 \tabularnewline
8 & 15.0915 & 0.633042652591434 & 1.461 \tabularnewline
9 & 16.03025 & 0.785086141770443 & 1.896 \tabularnewline
10 & 15.261 & 0.295144032634915 & 0.693999999999999 \tabularnewline
11 & 16.0065 & 0.332966965328393 & 0.768999999999998 \tabularnewline
12 & 15.73175 & 0.145866091558891 & 0.343 \tabularnewline
13 & 17.22775 & 0.618823817145614 & 1.30700000000000 \tabularnewline
14 & 19.5585 & 0.736245203719522 & 1.564 \tabularnewline
15 & 18.52225 & 0.465584489289181 & 1.099 \tabularnewline
16 & 19.243 & 0.549652617568587 & 1.16700000000000 \tabularnewline
17 & 22.294 & 1.22198554274045 & 2.765 \tabularnewline
18 & 21.63875 & 0.256700051941302 & 0.545000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71696&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]10.6575[/C][C]0.180725390210304[/C][C]0.433[/C][/ROW]
[ROW][C]2[/C][C]10.5935[/C][C]0.236466347147608[/C][C]0.574999999999999[/C][/ROW]
[ROW][C]3[/C][C]10.421[/C][C]0.116301332752467[/C][C]0.278000000000000[/C][/ROW]
[ROW][C]4[/C][C]10.73875[/C][C]0.118935206450123[/C][C]0.247[/C][/ROW]
[ROW][C]5[/C][C]10.518[/C][C]0.105157025442906[/C][C]0.239000000000001[/C][/ROW]
[ROW][C]6[/C][C]11.213[/C][C]0.344022286099801[/C][C]0.749[/C][/ROW]
[ROW][C]7[/C][C]12.84525[/C][C]0.778735460003374[/C][C]1.848[/C][/ROW]
[ROW][C]8[/C][C]15.0915[/C][C]0.633042652591434[/C][C]1.461[/C][/ROW]
[ROW][C]9[/C][C]16.03025[/C][C]0.785086141770443[/C][C]1.896[/C][/ROW]
[ROW][C]10[/C][C]15.261[/C][C]0.295144032634915[/C][C]0.693999999999999[/C][/ROW]
[ROW][C]11[/C][C]16.0065[/C][C]0.332966965328393[/C][C]0.768999999999998[/C][/ROW]
[ROW][C]12[/C][C]15.73175[/C][C]0.145866091558891[/C][C]0.343[/C][/ROW]
[ROW][C]13[/C][C]17.22775[/C][C]0.618823817145614[/C][C]1.30700000000000[/C][/ROW]
[ROW][C]14[/C][C]19.5585[/C][C]0.736245203719522[/C][C]1.564[/C][/ROW]
[ROW][C]15[/C][C]18.52225[/C][C]0.465584489289181[/C][C]1.099[/C][/ROW]
[ROW][C]16[/C][C]19.243[/C][C]0.549652617568587[/C][C]1.16700000000000[/C][/ROW]
[ROW][C]17[/C][C]22.294[/C][C]1.22198554274045[/C][C]2.765[/C][/ROW]
[ROW][C]18[/C][C]21.63875[/C][C]0.256700051941302[/C][C]0.545000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71696&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
110.65750.1807253902103040.433
210.59350.2364663471476080.574999999999999
310.4210.1163013327524670.278000000000000
410.738750.1189352064501230.247
510.5180.1051570254429060.239000000000001
611.2130.3440222860998010.749
712.845250.7787354600033741.848
815.09150.6330426525914341.461
916.030250.7850861417704431.896
1015.2610.2951440326349150.693999999999999
1116.00650.3329669653283930.768999999999998
1215.731750.1458660915588910.343
1317.227750.6188238171456141.30700000000000
1419.55850.7362452037195221.564
1518.522250.4655844892891811.099
1619.2430.5496526175685871.16700000000000
1722.2941.221985542740452.765
1821.638750.2567000519413020.545000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.276134812501914
beta0.0471207326941087
S.D.0.0151754296678826
T-STAT3.1050674495125
p-value0.00680723218461796

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.276134812501914 \tabularnewline
beta & 0.0471207326941087 \tabularnewline
S.D. & 0.0151754296678826 \tabularnewline
T-STAT & 3.1050674495125 \tabularnewline
p-value & 0.00680723218461796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71696&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.276134812501914[/C][/ROW]
[ROW][C]beta[/C][C]0.0471207326941087[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0151754296678826[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.1050674495125[/C][/ROW]
[ROW][C]p-value[/C][C]0.00680723218461796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71696&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-0.276134812501914
beta0.0471207326941087
S.D.0.0151754296678826
T-STAT3.1050674495125
p-value0.00680723218461796






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.1086549211499
beta1.87456134502828
S.D.0.529768991788352
T-STAT3.53845048329516
p-value0.00273236899680138
Lambda-0.874561345028284

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.1086549211499 \tabularnewline
beta & 1.87456134502828 \tabularnewline
S.D. & 0.529768991788352 \tabularnewline
T-STAT & 3.53845048329516 \tabularnewline
p-value & 0.00273236899680138 \tabularnewline
Lambda & -0.874561345028284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71696&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.1086549211499[/C][/ROW]
[ROW][C]beta[/C][C]1.87456134502828[/C][/ROW]
[ROW][C]S.D.[/C][C]0.529768991788352[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.53845048329516[/C][/ROW]
[ROW][C]p-value[/C][C]0.00273236899680138[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.874561345028284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71696&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71696&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-6.1086549211499
beta1.87456134502828
S.D.0.529768991788352
T-STAT3.53845048329516
p-value0.00273236899680138
Lambda-0.874561345028284


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')