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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 computationThu, 16 Dec 2010 21:31:52 +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/16/t12925350146vpko3qu0ortl09.htm/, Retrieved Fri, 03 May 2024 08:14:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111293, Retrieved Fri, 03 May 2024 08:14:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

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] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [Standard Deviation-Mean Plot] [] [2010-12-16 21:31:52] [40b262140b988d7b8204c4955f8b7651] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-0.9
1.2
1.4
1.5
1.3
1.4
-0.4
1.9
1.6
1.4
1.3
1.6
1.7
1.5
1.4
1.7
1.9
2.0
2.3
2.0
2.2
2.5
2.8
2.7
2.7
3.0
3.0
2.3
2.4
2.3
2.1
2.2
1.9
1.5
1.4
1.4
1.2
1.1
1.1
1.8
1.5
1.5
1.4
1.4
1.5
1.7
1.7
1.7
1.5
1.7
1.4
1.3
1.3
1.2
1.2
1.3
1.2
1.2
1.1
0.9
1.2
1.0
1.3
0.8
1.2
1.3
1.0
1.3
1.3
1.5
1.6
1.6
1.1
1.7
1.4
1.8
1.6
1.7
1.8
1.7
1.7
1.4
1.2
1.4
1.3
1.4
1.7
1.5
1.5
1.4
1.4
1.5
1.2
1.3
1.3
1.6
1.5
1.4
1.6
1.2
1.4
1.8
1.8
1.9
2.1
2.4
2.4
2.4
1.9
2.4
2.2
2.7
2.4
2.3
2.0
2.0
2.2
1.8
1.7
1.6
1.4
1.2
1.1
1.0
1.3
1.1
0.7
1.1
1.1
1.2
1.4

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111293&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111293&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' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.108333333333330.8479476113034062.8
22.058333333333330.4541892543729751.4
32.183333333333330.5605732996160491.6
41.466666666666670.2386832565759420.7
51.2750.2005673770264560.8
61.258333333333330.2429303429280740.8
71.541666666666670.2353269807709860.7
81.4250.1422226167923820.5
91.8250.4245318276964321.2
102.10.3247376563543951.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.10833333333333 & 0.847947611303406 & 2.8 \tabularnewline
2 & 2.05833333333333 & 0.454189254372975 & 1.4 \tabularnewline
3 & 2.18333333333333 & 0.560573299616049 & 1.6 \tabularnewline
4 & 1.46666666666667 & 0.238683256575942 & 0.7 \tabularnewline
5 & 1.275 & 0.200567377026456 & 0.8 \tabularnewline
6 & 1.25833333333333 & 0.242930342928074 & 0.8 \tabularnewline
7 & 1.54166666666667 & 0.235326980770986 & 0.7 \tabularnewline
8 & 1.425 & 0.142222616792382 & 0.5 \tabularnewline
9 & 1.825 & 0.424531827696432 & 1.2 \tabularnewline
10 & 2.1 & 0.324737656354395 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111293&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]1.10833333333333[/C][C]0.847947611303406[/C][C]2.8[/C][/ROW]
[ROW][C]2[/C][C]2.05833333333333[/C][C]0.454189254372975[/C][C]1.4[/C][/ROW]
[ROW][C]3[/C][C]2.18333333333333[/C][C]0.560573299616049[/C][C]1.6[/C][/ROW]
[ROW][C]4[/C][C]1.46666666666667[/C][C]0.238683256575942[/C][C]0.7[/C][/ROW]
[ROW][C]5[/C][C]1.275[/C][C]0.200567377026456[/C][C]0.8[/C][/ROW]
[ROW][C]6[/C][C]1.25833333333333[/C][C]0.242930342928074[/C][C]0.8[/C][/ROW]
[ROW][C]7[/C][C]1.54166666666667[/C][C]0.235326980770986[/C][C]0.7[/C][/ROW]
[ROW][C]8[/C][C]1.425[/C][C]0.142222616792382[/C][C]0.5[/C][/ROW]
[ROW][C]9[/C][C]1.825[/C][C]0.424531827696432[/C][C]1.2[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]0.324737656354395[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111293&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
11.108333333333330.8479476113034062.8
22.058333333333330.4541892543729751.4
32.183333333333330.5605732996160491.6
41.466666666666670.2386832565759420.7
51.2750.2005673770264560.8
61.258333333333330.2429303429280740.8
71.541666666666670.2353269807709860.7
81.4250.1422226167923820.5
91.8250.4245318276964321.2
102.10.3247376563543951.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.285078489884304
beta0.0505444017194906
S.D.0.192963191678032
T-STAT0.261938047769371
p-value0.799987384330492

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.285078489884304 \tabularnewline
beta & 0.0505444017194906 \tabularnewline
S.D. & 0.192963191678032 \tabularnewline
T-STAT & 0.261938047769371 \tabularnewline
p-value & 0.799987384330492 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111293&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.285078489884304[/C][/ROW]
[ROW][C]beta[/C][C]0.0505444017194906[/C][/ROW]
[ROW][C]S.D.[/C][C]0.192963191678032[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.261938047769371[/C][/ROW]
[ROW][C]p-value[/C][C]0.799987384330492[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111293&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111293&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)
alpha0.285078489884304
beta0.0505444017194906
S.D.0.192963191678032
T-STAT0.261938047769371
p-value0.799987384330492






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.35819924288501
beta0.482627125183645
S.D.0.77441945043849
T-STAT0.62321152304526
p-value0.550495232330131
Lambda0.517372874816355

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.35819924288501 \tabularnewline
beta & 0.482627125183645 \tabularnewline
S.D. & 0.77441945043849 \tabularnewline
T-STAT & 0.62321152304526 \tabularnewline
p-value & 0.550495232330131 \tabularnewline
Lambda & 0.517372874816355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111293&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.35819924288501[/C][/ROW]
[ROW][C]beta[/C][C]0.482627125183645[/C][/ROW]
[ROW][C]S.D.[/C][C]0.77441945043849[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.62321152304526[/C][/ROW]
[ROW][C]p-value[/C][C]0.550495232330131[/C][/ROW]
[ROW][C]Lambda[/C][C]0.517372874816355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111293&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111293&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-1.35819924288501
beta0.482627125183645
S.D.0.77441945043849
T-STAT0.62321152304526
p-value0.550495232330131
Lambda0.517372874816355


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')