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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, 19 Nov 2014 15:05:58 +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/2014/Nov/19/t1416409570wbp4lvpzat3v57h.htm/, Retrieved Sun, 19 May 2024 15:41:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=256508, Retrieved Sun, 19 May 2024 15:41:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

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] [] [2014-11-19 15:05:58] [0c3693ead1e3fa463b40b3108c1b2028] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11236
10954
9580
10337
8961
10372
12782
15119
19940
13957
10849
9429
11816
11329
11334
9898
8961
10783
13149
16244
20067
13601
10573
8623
10962
11911
11677
9679
9116
11394
13240
18983
21545
14360
11839
9726
12347
12624
11918
10028
10228
11026
13878
22165
23533
13445
12164
9606
12177
13142
11210
9485
10082
10680
13579
21709
22205
14687
11222
8196
12794
12627
11080
10425
10865
10771
14771
20993
23882
14825
11648
10091

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' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256508&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256508&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256508&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111959.66666666673123.4325620536410979
212198.16666666673247.4229176472511444
312869.33333333333794.3265382394112429
413580.16666666674535.1274179420513927
513197.83333333334468.9219939353114009
6137314397.0666668504413791

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11959.6666666667 & 3123.43256205364 & 10979 \tabularnewline
2 & 12198.1666666667 & 3247.42291764725 & 11444 \tabularnewline
3 & 12869.3333333333 & 3794.32653823941 & 12429 \tabularnewline
4 & 13580.1666666667 & 4535.12741794205 & 13927 \tabularnewline
5 & 13197.8333333333 & 4468.92199393531 & 14009 \tabularnewline
6 & 13731 & 4397.06666685044 & 13791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256508&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]11959.6666666667[/C][C]3123.43256205364[/C][C]10979[/C][/ROW]
[ROW][C]2[/C][C]12198.1666666667[/C][C]3247.42291764725[/C][C]11444[/C][/ROW]
[ROW][C]3[/C][C]12869.3333333333[/C][C]3794.32653823941[/C][C]12429[/C][/ROW]
[ROW][C]4[/C][C]13580.1666666667[/C][C]4535.12741794205[/C][C]13927[/C][/ROW]
[ROW][C]5[/C][C]13197.8333333333[/C][C]4468.92199393531[/C][C]14009[/C][/ROW]
[ROW][C]6[/C][C]13731[/C][C]4397.06666685044[/C][C]13791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256508&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256508&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
111959.66666666673123.4325620536410979
212198.16666666673247.4229176472511444
312869.33333333333794.3265382394112429
413580.16666666674535.1274179420513927
513197.83333333334468.9219939353114009
6137314397.0666668504413791






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6948.60840036067
beta0.841645277350124
S.D.0.122140110690923
T-STAT6.89081803339707
p-value0.00232502030635402

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6948.60840036067 \tabularnewline
beta & 0.841645277350124 \tabularnewline
S.D. & 0.122140110690923 \tabularnewline
T-STAT & 6.89081803339707 \tabularnewline
p-value & 0.00232502030635402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256508&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6948.60840036067[/C][/ROW]
[ROW][C]beta[/C][C]0.841645277350124[/C][/ROW]
[ROW][C]S.D.[/C][C]0.122140110690923[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.89081803339707[/C][/ROW]
[ROW][C]p-value[/C][C]0.00232502030635402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256508&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256508&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-6948.60840036067
beta0.841645277350124
S.D.0.122140110690923
T-STAT6.89081803339707
p-value0.00232502030635402






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-18.7718677209109
beta2.85632627547015
S.D.0.381780985547168
T-STAT7.48158337790572
p-value0.00170664843764693
Lambda-1.85632627547015

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -18.7718677209109 \tabularnewline
beta & 2.85632627547015 \tabularnewline
S.D. & 0.381780985547168 \tabularnewline
T-STAT & 7.48158337790572 \tabularnewline
p-value & 0.00170664843764693 \tabularnewline
Lambda & -1.85632627547015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256508&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-18.7718677209109[/C][/ROW]
[ROW][C]beta[/C][C]2.85632627547015[/C][/ROW]
[ROW][C]S.D.[/C][C]0.381780985547168[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.48158337790572[/C][/ROW]
[ROW][C]p-value[/C][C]0.00170664843764693[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.85632627547015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256508&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256508&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-18.7718677209109
beta2.85632627547015
S.D.0.381780985547168
T-STAT7.48158337790572
p-value0.00170664843764693
Lambda-1.85632627547015


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')