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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, 07 Aug 2013 10:43:24 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/07/t1375886667pg1nvrt2iv1ou2q.htm/, Retrieved Tue, 30 Apr 2024 05:53:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210980, Retrieved Tue, 30 Apr 2024 05:53:29 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordskevin kofi asare
Estimated Impact169

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Inschrijvingen ni...] [2011-11-21 16:03:08] [102faec22d2a25d9aaa52ca244269a51]
- RMPD    [Standard Deviation-Mean Plot] [Tijdreeks 1 - Sta...] [2013-08-07 14:43:24] [4d26c4233714d8e4ecf99606d744931b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3207324
3178086
3148485
3087246
3693267
3661164
3207324
2905563
2934699
2934699
2967168
3025542
3207324
3148485
3239325
3388641
4238049
4238049
4056732
3874950
4024266
4205949
4238049
4328892
4601499
4419732
4419732
4692342
5448042
5509281
5357202
4993734
5266260
5266260
5295495
5448042
5568120
5629359
5629359
5811042
6508356
6689670
6718809
6264966
6508356
6417513
6235746
6628434
6718809
6566727
6598830
6809748
7597920
7990056
7990056
7808739
8080980
7808739
7656276
8233527
8323902
8110134
8654901
8868684
9504309
9926133
9867774
9835290
10078677
10049076
9686076
10230759
10412541
10230759
10986462
11349927
12196086
12529950
12439476
12257691
12409872
12591555
11985168
12468612
12773337
12650394
13438098
13710240
14861511
15072414
14800254
14952351
15043194
15134034
14556783
15101568
15403311
15101568
15980562
16252821
17433111
17614893
17673267
17977893
17977893
18097971
17553189
17825814
18007131
17673267
18642738
18824436
20034063
20247849
20549592
20822217
20851353
20883456
20338689
20883456

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210980&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210980&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13162547.25264096.324307878787704
23849059.25464409.0846664721180407
35059801.75415774.4592105691089549
46217477.5440416.0939488721150689
57488367.25628761.3114227231666800
69427976.25738530.893473122120625
711821508.25854632.9576250452360796
814341181.5937422.6503577392483640
917074357.751079127.795807352996403
1019813187.251192084.456661913210189

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3162547.25 & 264096.324307878 & 787704 \tabularnewline
2 & 3849059.25 & 464409.084666472 & 1180407 \tabularnewline
3 & 5059801.75 & 415774.459210569 & 1089549 \tabularnewline
4 & 6217477.5 & 440416.093948872 & 1150689 \tabularnewline
5 & 7488367.25 & 628761.311422723 & 1666800 \tabularnewline
6 & 9427976.25 & 738530.89347312 & 2120625 \tabularnewline
7 & 11821508.25 & 854632.957625045 & 2360796 \tabularnewline
8 & 14341181.5 & 937422.650357739 & 2483640 \tabularnewline
9 & 17074357.75 & 1079127.79580735 & 2996403 \tabularnewline
10 & 19813187.25 & 1192084.45666191 & 3210189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210980&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]3162547.25[/C][C]264096.324307878[/C][C]787704[/C][/ROW]
[ROW][C]2[/C][C]3849059.25[/C][C]464409.084666472[/C][C]1180407[/C][/ROW]
[ROW][C]3[/C][C]5059801.75[/C][C]415774.459210569[/C][C]1089549[/C][/ROW]
[ROW][C]4[/C][C]6217477.5[/C][C]440416.093948872[/C][C]1150689[/C][/ROW]
[ROW][C]5[/C][C]7488367.25[/C][C]628761.311422723[/C][C]1666800[/C][/ROW]
[ROW][C]6[/C][C]9427976.25[/C][C]738530.89347312[/C][C]2120625[/C][/ROW]
[ROW][C]7[/C][C]11821508.25[/C][C]854632.957625045[/C][C]2360796[/C][/ROW]
[ROW][C]8[/C][C]14341181.5[/C][C]937422.650357739[/C][C]2483640[/C][/ROW]
[ROW][C]9[/C][C]17074357.75[/C][C]1079127.79580735[/C][C]2996403[/C][/ROW]
[ROW][C]10[/C][C]19813187.25[/C][C]1192084.45666191[/C][C]3210189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210980&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
13162547.25264096.324307878787704
23849059.25464409.0846664721180407
35059801.75415774.4592105691089549
46217477.5440416.0939488721150689
57488367.25628761.3114227231666800
69427976.25738530.893473122120625
711821508.25854632.9576250452360796
814341181.5937422.6503577392483640
917074357.751079127.795807352996403
1019813187.251192084.456661913210189






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha180864.394404719
beta0.0529905602342328
S.D.0.00349978730639323
T-STAT15.1410801843393
p-value3.58360004233614e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 180864.394404719 \tabularnewline
beta & 0.0529905602342328 \tabularnewline
S.D. & 0.00349978730639323 \tabularnewline
T-STAT & 15.1410801843393 \tabularnewline
p-value & 3.58360004233614e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210980&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]180864.394404719[/C][/ROW]
[ROW][C]beta[/C][C]0.0529905602342328[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00349978730639323[/C][/ROW]
[ROW][C]T-STAT[/C][C]15.1410801843393[/C][/ROW]
[ROW][C]p-value[/C][C]3.58360004233614e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210980&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)
alpha180864.394404719
beta0.0529905602342328
S.D.0.00349978730639323
T-STAT15.1410801843393
p-value3.58360004233614e-07






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.46959527108573
beta0.746474750513355
S.D.0.0667776586700063
T-STAT11.1785103787809
p-value3.67346051712428e-06
Lambda0.253525249486645

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.46959527108573 \tabularnewline
beta & 0.746474750513355 \tabularnewline
S.D. & 0.0667776586700063 \tabularnewline
T-STAT & 11.1785103787809 \tabularnewline
p-value & 3.67346051712428e-06 \tabularnewline
Lambda & 0.253525249486645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210980&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.46959527108573[/C][/ROW]
[ROW][C]beta[/C][C]0.746474750513355[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0667776586700063[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.1785103787809[/C][/ROW]
[ROW][C]p-value[/C][C]3.67346051712428e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.253525249486645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210980&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)
alpha1.46959527108573
beta0.746474750513355
S.D.0.0667776586700063
T-STAT11.1785103787809
p-value3.67346051712428e-06
Lambda0.253525249486645


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')