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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, 29 Dec 2010 14:49:07 +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/29/t12936340131hhraw1vmqmadam.htm/, Retrieved Fri, 03 May 2024 04:52:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116884, Retrieved Fri, 03 May 2024 04:52:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

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] [Paper] [2010-12-29 14:49:07] [d5e0edb7e0239841e94676417b2a1e2e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9782
9938
10111
10259
10419
10622
11173
11542
11538
11837
12060
12423
12791
12891
13098
13418
13614
13653
13980
14087
14332
14232
14226
14186
14310
14152
14127
14163
13964
13811
14440
14724
14790
14961
15117
15452
16080
16284
16524
16782
16663
16678
17448
17745
17789
17864
18079
18483
19037
19344
19590
19862
20207
20593
21253
21507
21528
21818
22205
22621
23006
23178
23358
23519
23725
23789
24472
24773
24477
24669
24827

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116884&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116884&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
110975.3333333333898.794579962352641
213709552.252577260541541
314500.9166666667505.3620589300911641
417201.5833333333789.191468683252403
520797.08333333331188.118333434183584

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10975.3333333333 & 898.79457996235 & 2641 \tabularnewline
2 & 13709 & 552.25257726054 & 1541 \tabularnewline
3 & 14500.9166666667 & 505.362058930091 & 1641 \tabularnewline
4 & 17201.5833333333 & 789.19146868325 & 2403 \tabularnewline
5 & 20797.0833333333 & 1188.11833343418 & 3584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116884&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]10975.3333333333[/C][C]898.79457996235[/C][C]2641[/C][/ROW]
[ROW][C]2[/C][C]13709[/C][C]552.25257726054[/C][C]1541[/C][/ROW]
[ROW][C]3[/C][C]14500.9166666667[/C][C]505.362058930091[/C][C]1641[/C][/ROW]
[ROW][C]4[/C][C]17201.5833333333[/C][C]789.19146868325[/C][C]2403[/C][/ROW]
[ROW][C]5[/C][C]20797.0833333333[/C][C]1188.11833343418[/C][C]3584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116884&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
110975.3333333333898.794579962352641
213709552.252577260541541
314500.9166666667505.3620589300911641
417201.5833333333789.191468683252403
520797.08333333331188.118333434183584






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha141.552047773224
beta0.0417957382667714
S.D.0.035535157591668
T-STAT1.1761799046185
p-value0.324359785642123

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 141.552047773224 \tabularnewline
beta & 0.0417957382667714 \tabularnewline
S.D. & 0.035535157591668 \tabularnewline
T-STAT & 1.1761799046185 \tabularnewline
p-value & 0.324359785642123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116884&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]141.552047773224[/C][/ROW]
[ROW][C]beta[/C][C]0.0417957382667714[/C][/ROW]
[ROW][C]S.D.[/C][C]0.035535157591668[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.1761799046185[/C][/ROW]
[ROW][C]p-value[/C][C]0.324359785642123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116884&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)
alpha141.552047773224
beta0.0417957382667714
S.D.0.035535157591668
T-STAT1.1761799046185
p-value0.324359785642123






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.74653978190248
beta0.610286926804588
S.D.0.76719066709604
T-STAT0.795482730668033
p-value0.484459047245149
Lambda0.389713073195412

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.74653978190248 \tabularnewline
beta & 0.610286926804588 \tabularnewline
S.D. & 0.76719066709604 \tabularnewline
T-STAT & 0.795482730668033 \tabularnewline
p-value & 0.484459047245149 \tabularnewline
Lambda & 0.389713073195412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116884&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.74653978190248[/C][/ROW]
[ROW][C]beta[/C][C]0.610286926804588[/C][/ROW]
[ROW][C]S.D.[/C][C]0.76719066709604[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.795482730668033[/C][/ROW]
[ROW][C]p-value[/C][C]0.484459047245149[/C][/ROW]
[ROW][C]Lambda[/C][C]0.389713073195412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116884&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116884&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)
alpha0.74653978190248
beta0.610286926804588
S.D.0.76719066709604
T-STAT0.795482730668033
p-value0.484459047245149
Lambda0.389713073195412


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 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')