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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 computationSat, 01 Dec 2012 07:57:14 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/01/t135436665917230scaqqh1tpk.htm/, Retrieved Sun, 28 Apr 2024 21:15:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195275, Retrieved Sun, 28 Apr 2024 21:15:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Paper - exogene v...] [2010-12-01 16:02:49] [6f0e7a2d1a07390e3505a2db8288f975]
- RMP   [(Partial) Autocorrelation Function] [ACF 1] [2012-12-01 12:28:25] [aa4758794357e809405bf1fb1497cdc4]
- RMP       [Standard Deviation-Mean Plot] [SMP] [2012-12-01 12:57:14] [4289cf790da1cc09a0cb8798de13fde3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9769
9321
9939
9336
10195
9464
10010
10213
9563
9890
9305
9391
9928
8686
9843
9627
10074
9503
10119
10000
9313
9866
9172
9241
9659
8904
9755
9080
9435
8971
10063
9793
9454
9759
8820
9403
9676
8642
9402
9610
9294
9448
10319
9548
9801
9596
8923
9746
9829
9125
9782
9441
9162
9915
10444
10209
9985
9842
9429
10132
9849
9172
10313
9819
9955
10048
10082
10541
10208
10233
9439
9963
10158
9225
10474
9757
10490
10281
10444
10640
10695
10786
9832
9747
10411
9511
10402
9701
10540
10112
10915
11183
10384
10834
9886
10216

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' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195275&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195275&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' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19699.66666666667344.354820532895908
29614.33333333333439.9306419163931433
39424.66666666667402.4595594214371243
49500.41666666667426.434362067031677
59774.58333333333411.6550759011131319
69968.5374.7223214352441369
710210.75476.2713369116771561
810341.25495.9059890745421672

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9699.66666666667 & 344.354820532895 & 908 \tabularnewline
2 & 9614.33333333333 & 439.930641916393 & 1433 \tabularnewline
3 & 9424.66666666667 & 402.459559421437 & 1243 \tabularnewline
4 & 9500.41666666667 & 426.43436206703 & 1677 \tabularnewline
5 & 9774.58333333333 & 411.655075901113 & 1319 \tabularnewline
6 & 9968.5 & 374.722321435244 & 1369 \tabularnewline
7 & 10210.75 & 476.271336911677 & 1561 \tabularnewline
8 & 10341.25 & 495.905989074542 & 1672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195275&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]9699.66666666667[/C][C]344.354820532895[/C][C]908[/C][/ROW]
[ROW][C]2[/C][C]9614.33333333333[/C][C]439.930641916393[/C][C]1433[/C][/ROW]
[ROW][C]3[/C][C]9424.66666666667[/C][C]402.459559421437[/C][C]1243[/C][/ROW]
[ROW][C]4[/C][C]9500.41666666667[/C][C]426.43436206703[/C][C]1677[/C][/ROW]
[ROW][C]5[/C][C]9774.58333333333[/C][C]411.655075901113[/C][C]1319[/C][/ROW]
[ROW][C]6[/C][C]9968.5[/C][C]374.722321435244[/C][C]1369[/C][/ROW]
[ROW][C]7[/C][C]10210.75[/C][C]476.271336911677[/C][C]1561[/C][/ROW]
[ROW][C]8[/C][C]10341.25[/C][C]495.905989074542[/C][C]1672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195275&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
19699.66666666667344.354820532895908
29614.33333333333439.9306419163931433
39424.66666666667402.4595594214371243
49500.41666666667426.434362067031677
59774.58333333333411.6550759011131319
69968.5374.7223214352441369
710210.75476.2713369116771561
810341.25495.9059890745421672






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-415.801068089163
beta0.085289536214263
S.D.0.0510584314377016
T-STAT1.67043001151197
p-value0.145870823390005

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -415.801068089163 \tabularnewline
beta & 0.085289536214263 \tabularnewline
S.D. & 0.0510584314377016 \tabularnewline
T-STAT & 1.67043001151197 \tabularnewline
p-value & 0.145870823390005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195275&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-415.801068089163[/C][/ROW]
[ROW][C]beta[/C][C]0.085289536214263[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0510584314377016[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.67043001151197[/C][/ROW]
[ROW][C]p-value[/C][C]0.145870823390005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195275&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-415.801068089163
beta0.085289536214263
S.D.0.0510584314377016
T-STAT1.67043001151197
p-value0.145870823390005






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.0930682946028
beta1.86377051359285
S.D.1.24911717929091
T-STAT1.4920701952485
p-value0.186282073624853
Lambda-0.863770513592846

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.0930682946028 \tabularnewline
beta & 1.86377051359285 \tabularnewline
S.D. & 1.24911717929091 \tabularnewline
T-STAT & 1.4920701952485 \tabularnewline
p-value & 0.186282073624853 \tabularnewline
Lambda & -0.863770513592846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195275&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.0930682946028[/C][/ROW]
[ROW][C]beta[/C][C]1.86377051359285[/C][/ROW]
[ROW][C]S.D.[/C][C]1.24911717929091[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.4920701952485[/C][/ROW]
[ROW][C]p-value[/C][C]0.186282073624853[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.863770513592846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195275&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195275&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-11.0930682946028
beta1.86377051359285
S.D.1.24911717929091
T-STAT1.4920701952485
p-value0.186282073624853
Lambda-0.863770513592846


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')