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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 22 Dec 2010 14:35:19 +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/22/t1293028397um5dqv0tg0xl911.htm/, Retrieved Mon, 06 May 2024 10:38:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114266, Retrieved Mon, 06 May 2024 10:38:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD          [Standard Deviation-Mean Plot] [] [2010-12-22 14:35:19] [5a59313293e5c9f616ad36f6edd018c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.769
9.321
9.939
9.336
10.195
9.464
10.010
10.213
9.563
9.890
9.305
9.391
9.928
8.686
9.843
9.627
10.074
9.503
10.119
10.000
9.313
9.866
9.172
9.241
9.659
8.904
9.755
9.080
9.435
8.971
10.063
9.793
9.454
9.759
8.820
9.403
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114266&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114266&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.699666666666670.3443548205328950.908
29.614333333333330.4399306419163931.433
39.424666666666670.4024595594214371.243
49.500416666666670.4264343620670311.677
59.774583333333330.4116550759011131.319
69.96850.3747223214352441.369
710.210750.4762713369116771.561
810.341250.4959059890745421.672

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.69966666666667 & 0.344354820532895 & 0.908 \tabularnewline
2 & 9.61433333333333 & 0.439930641916393 & 1.433 \tabularnewline
3 & 9.42466666666667 & 0.402459559421437 & 1.243 \tabularnewline
4 & 9.50041666666667 & 0.426434362067031 & 1.677 \tabularnewline
5 & 9.77458333333333 & 0.411655075901113 & 1.319 \tabularnewline
6 & 9.9685 & 0.374722321435244 & 1.369 \tabularnewline
7 & 10.21075 & 0.476271336911677 & 1.561 \tabularnewline
8 & 10.34125 & 0.495905989074542 & 1.672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114266&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]9.69966666666667[/C][C]0.344354820532895[/C][C]0.908[/C][/ROW]
[ROW][C]2[/C][C]9.61433333333333[/C][C]0.439930641916393[/C][C]1.433[/C][/ROW]
[ROW][C]3[/C][C]9.42466666666667[/C][C]0.402459559421437[/C][C]1.243[/C][/ROW]
[ROW][C]4[/C][C]9.50041666666667[/C][C]0.426434362067031[/C][C]1.677[/C][/ROW]
[ROW][C]5[/C][C]9.77458333333333[/C][C]0.411655075901113[/C][C]1.319[/C][/ROW]
[ROW][C]6[/C][C]9.9685[/C][C]0.374722321435244[/C][C]1.369[/C][/ROW]
[ROW][C]7[/C][C]10.21075[/C][C]0.476271336911677[/C][C]1.561[/C][/ROW]
[ROW][C]8[/C][C]10.34125[/C][C]0.495905989074542[/C][C]1.672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114266&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
19.699666666666670.3443548205328950.908
29.614333333333330.4399306419163931.433
39.424666666666670.4024595594214371.243
49.500416666666670.4264343620670311.677
59.774583333333330.4116550759011131.319
69.96850.3747223214352441.369
710.210750.4762713369116771.561
810.341250.4959059890745421.672






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.415801068089168
beta0.0852895362142635
S.D.0.0510584314377016
T-STAT1.67043001151198
p-value0.145870823390003

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.415801068089168 \tabularnewline
beta & 0.0852895362142635 \tabularnewline
S.D. & 0.0510584314377016 \tabularnewline
T-STAT & 1.67043001151198 \tabularnewline
p-value & 0.145870823390003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114266&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.415801068089168[/C][/ROW]
[ROW][C]beta[/C][C]0.0852895362142635[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0510584314377016[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.67043001151198[/C][/ROW]
[ROW][C]p-value[/C][C]0.145870823390003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114266&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-0.415801068089168
beta0.0852895362142635
S.D.0.0510584314377016
T-STAT1.67043001151198
p-value0.145870823390003






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.12635296950291
beta1.86377051359294
S.D.1.24911717929089
T-STAT1.49207019524861
p-value0.186282073624826
Lambda-0.86377051359294

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.12635296950291 \tabularnewline
beta & 1.86377051359294 \tabularnewline
S.D. & 1.24911717929089 \tabularnewline
T-STAT & 1.49207019524861 \tabularnewline
p-value & 0.186282073624826 \tabularnewline
Lambda & -0.86377051359294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114266&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.12635296950291[/C][/ROW]
[ROW][C]beta[/C][C]1.86377051359294[/C][/ROW]
[ROW][C]S.D.[/C][C]1.24911717929089[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.49207019524861[/C][/ROW]
[ROW][C]p-value[/C][C]0.186282073624826[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.86377051359294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114266&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114266&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-5.12635296950291
beta1.86377051359294
S.D.1.24911717929089
T-STAT1.49207019524861
p-value0.186282073624826
Lambda-0.86377051359294


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')