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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 computationTue, 06 Dec 2011 10:56:54 -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/2011/Dec/06/t1323187057mw4vfvh8vna0x77.htm/, Retrieved Sun, 28 Apr 2024 21:26:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151711, Retrieved Sun, 28 Apr 2024 21:26:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [WS 9 - Spectrum A...] [2011-12-06 15:50:47] [ae1339cb5a7cf28362d01e7220b4a16c]
- RMP     [Standard Deviation-Mean Plot] [WS 9 - Std. Dev. ...] [2011-12-06 15:56:54] [e598b5cd83fcb010b35e92a01f5e81e9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6827
6178
7084
8162
8462
9644
10466
10748
9963
8194
6848
7027
7269
6775
7819
8371
9069
10248
11030
10882
10333
9109
7685
7602
8350
7829
8829
9948
10638
11253
11424
11391
10665
9396
7775
7933
8186
7444
8484
9864
10252
12282
11637
11577
12417
9637
8094
9280
8334
7899
9994
10078
10801
12950
12222
12246
13281
10366
8730
9614
8639
8772
10894
10455
11179
10588
10794
12770
13812
10857
9290
10925
9491
8919
11607
8852
12537
14759
13667
13731
15110
12185
10645
12161
10840
10436
13589
13402
13103
14933
14147
14057
16234
12389
11595
12772

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'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151711&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151711&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18300.251572.282366786924570
28849.333333333331482.089147934174255
39619.251447.251446708553649
49929.51722.668674944884973
510542.91666666671800.138603670355382
610747.91666666671486.871423085365173
7119722155.04815385986258
813124.751667.865054765855798

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8300.25 & 1572.28236678692 & 4570 \tabularnewline
2 & 8849.33333333333 & 1482.08914793417 & 4255 \tabularnewline
3 & 9619.25 & 1447.25144670855 & 3649 \tabularnewline
4 & 9929.5 & 1722.66867494488 & 4973 \tabularnewline
5 & 10542.9166666667 & 1800.13860367035 & 5382 \tabularnewline
6 & 10747.9166666667 & 1486.87142308536 & 5173 \tabularnewline
7 & 11972 & 2155.0481538598 & 6258 \tabularnewline
8 & 13124.75 & 1667.86505476585 & 5798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151711&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]8300.25[/C][C]1572.28236678692[/C][C]4570[/C][/ROW]
[ROW][C]2[/C][C]8849.33333333333[/C][C]1482.08914793417[/C][C]4255[/C][/ROW]
[ROW][C]3[/C][C]9619.25[/C][C]1447.25144670855[/C][C]3649[/C][/ROW]
[ROW][C]4[/C][C]9929.5[/C][C]1722.66867494488[/C][C]4973[/C][/ROW]
[ROW][C]5[/C][C]10542.9166666667[/C][C]1800.13860367035[/C][C]5382[/C][/ROW]
[ROW][C]6[/C][C]10747.9166666667[/C][C]1486.87142308536[/C][C]5173[/C][/ROW]
[ROW][C]7[/C][C]11972[/C][C]2155.0481538598[/C][C]6258[/C][/ROW]
[ROW][C]8[/C][C]13124.75[/C][C]1667.86505476585[/C][C]5798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151711&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
18300.251572.282366786924570
28849.333333333331482.089147934174255
39619.251447.251446708553649
49929.51722.668674944884973
510542.91666666671800.138603670355382
610747.91666666671486.871423085365173
7119722155.04815385986258
813124.751667.865054765855798






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha869.685689733696
beta0.0767486188961386
S.D.0.0512641352258577
T-STAT1.49712110733951
p-value0.185004984174216

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 869.685689733696 \tabularnewline
beta & 0.0767486188961386 \tabularnewline
S.D. & 0.0512641352258577 \tabularnewline
T-STAT & 1.49712110733951 \tabularnewline
p-value & 0.185004984174216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151711&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]869.685689733696[/C][/ROW]
[ROW][C]beta[/C][C]0.0767486188961386[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0512641352258577[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.49712110733951[/C][/ROW]
[ROW][C]p-value[/C][C]0.185004984174216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151711&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151711&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)
alpha869.685689733696
beta0.0767486188961386
S.D.0.0512641352258577
T-STAT1.49712110733951
p-value0.185004984174216






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.09162433689093
beta0.467524242808624
S.D.0.303159228425315
T-STAT1.54217387752655
p-value0.173970749429324
Lambda0.532475757191376

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.09162433689093 \tabularnewline
beta & 0.467524242808624 \tabularnewline
S.D. & 0.303159228425315 \tabularnewline
T-STAT & 1.54217387752655 \tabularnewline
p-value & 0.173970749429324 \tabularnewline
Lambda & 0.532475757191376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151711&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.09162433689093[/C][/ROW]
[ROW][C]beta[/C][C]0.467524242808624[/C][/ROW]
[ROW][C]S.D.[/C][C]0.303159228425315[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.54217387752655[/C][/ROW]
[ROW][C]p-value[/C][C]0.173970749429324[/C][/ROW]
[ROW][C]Lambda[/C][C]0.532475757191376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151711&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151711&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)
alpha3.09162433689093
beta0.467524242808624
S.D.0.303159228425315
T-STAT1.54217387752655
p-value0.173970749429324
Lambda0.532475757191376


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')