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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 computationMon, 21 Dec 2009 07:33:34 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t1261406074iwpepzr5vaett0c.htm/, Retrieved Sun, 05 May 2024 13:36:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70202, Retrieved Sun, 05 May 2024 13:36:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

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] [Standard deviatio...] [2008-12-11 16:40:34] [12d343c4448a5f9e527bb31caeac580b]
- RM D    [Standard Deviation-Mean Plot] [Standard deviatio...] [2009-12-21 14:33:34] [4c76f32a7a0cc9034048c3cdcdaf547e] [Current]
-           [Standard Deviation-Mean Plot] [paper] [2010-12-28 16:23:32] [654616a560d52fe6eb611aa3bbf6b3c7]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70202&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70202&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1256538306.2242051039425331
223293.16666666674863.9772508688515966
323712.256639.8206865848422631
422142.255608.3585043786519045
522916.16666666677303.0689045251725139
623493.41666666675265.9772719589218386
723700.33333333336731.2083790671820425

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 25653 & 8306.22420510394 & 25331 \tabularnewline
2 & 23293.1666666667 & 4863.97725086885 & 15966 \tabularnewline
3 & 23712.25 & 6639.82068658484 & 22631 \tabularnewline
4 & 22142.25 & 5608.35850437865 & 19045 \tabularnewline
5 & 22916.1666666667 & 7303.06890452517 & 25139 \tabularnewline
6 & 23493.4166666667 & 5265.97727195892 & 18386 \tabularnewline
7 & 23700.3333333333 & 6731.20837906718 & 20425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70202&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]25653[/C][C]8306.22420510394[/C][C]25331[/C][/ROW]
[ROW][C]2[/C][C]23293.1666666667[/C][C]4863.97725086885[/C][C]15966[/C][/ROW]
[ROW][C]3[/C][C]23712.25[/C][C]6639.82068658484[/C][C]22631[/C][/ROW]
[ROW][C]4[/C][C]22142.25[/C][C]5608.35850437865[/C][C]19045[/C][/ROW]
[ROW][C]5[/C][C]22916.1666666667[/C][C]7303.06890452517[/C][C]25139[/C][/ROW]
[ROW][C]6[/C][C]23493.4166666667[/C][C]5265.97727195892[/C][C]18386[/C][/ROW]
[ROW][C]7[/C][C]23700.3333333333[/C][C]6731.20837906718[/C][C]20425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70202&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
1256538306.2242051039425331
223293.16666666674863.9772508688515966
323712.256639.8206865848422631
422142.255608.3585043786519045
522916.16666666677303.0689045251725139
623493.41666666675265.9772719589218386
723700.33333333336731.2083790671820425






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-10961.2559073271
beta0.736444102609813
S.D.0.385044712305943
T-STAT1.91261970122748
p-value0.114002550174042

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -10961.2559073271 \tabularnewline
beta & 0.736444102609813 \tabularnewline
S.D. & 0.385044712305943 \tabularnewline
T-STAT & 1.91261970122748 \tabularnewline
p-value & 0.114002550174042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70202&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10961.2559073271[/C][/ROW]
[ROW][C]beta[/C][C]0.736444102609813[/C][/ROW]
[ROW][C]S.D.[/C][C]0.385044712305943[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.91261970122748[/C][/ROW]
[ROW][C]p-value[/C][C]0.114002550174042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70202&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-10961.2559073271
beta0.736444102609813
S.D.0.385044712305943
T-STAT1.91261970122748
p-value0.114002550174042






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-16.9601228163813
beta2.55373007437422
S.D.1.51885761769694
T-STAT1.6813492223494
p-value0.153524165115246
Lambda-1.55373007437422

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -16.9601228163813 \tabularnewline
beta & 2.55373007437422 \tabularnewline
S.D. & 1.51885761769694 \tabularnewline
T-STAT & 1.6813492223494 \tabularnewline
p-value & 0.153524165115246 \tabularnewline
Lambda & -1.55373007437422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70202&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-16.9601228163813[/C][/ROW]
[ROW][C]beta[/C][C]2.55373007437422[/C][/ROW]
[ROW][C]S.D.[/C][C]1.51885761769694[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.6813492223494[/C][/ROW]
[ROW][C]p-value[/C][C]0.153524165115246[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.55373007437422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70202&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-16.9601228163813
beta2.55373007437422
S.D.1.51885761769694
T-STAT1.6813492223494
p-value0.153524165115246
Lambda-1.55373007437422


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')