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Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 02 Dec 2013 17:22:48 -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/2013/Dec/02/t13860229862viucg2nylyw99p.htm/, Retrieved Fri, 29 Mar 2024 13:32:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230157, Retrieved Fri, 29 Mar 2024 13:32:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2013-12-02 22:22:48] [8ac251e42bd40906c127555d6859e07b] [Current]
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Dataseries X:
28.53
28.48
28.68
28.89
29.2
29.21
29.15
29.22
29.34
29.13
28.84
28.76
28.75
28.89
28.82
29.12
29.21
29.3
29.32
29.52
29.64
29.54
29.54
29.34
29.34
29.54
29.94
30.17
30.23
30.34
30.34
30.36
30.3
30.28
29.89
29.58
29.68
29.73
30.07
30.32
30.55
30.62
30.67
30.79
30.8
30.5
30.07
29.41
29.42
29.99
30.14
30.41
30.78
30.88
30.92
30.93
31.62
31.48
31.3
31.11
31.16
31.22
31.66
32.11
32.27
32.36
32.42
32.52
32.41
31.87
31.04
30.58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230157&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230157&T=0

As an alternative you can also use a 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' @ jenkins.wessa.net







Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128.95250.293787956928740.859999999999999
229.24916666666670.3002562037307270.890000000000001
330.02583333333330.362101400497741.02
430.26750.4697025170737911.39
530.74833333333330.6491369561801182.2
631.80166666666670.6565728282436611.94

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28.9525 & 0.29378795692874 & 0.859999999999999 \tabularnewline
2 & 29.2491666666667 & 0.300256203730727 & 0.890000000000001 \tabularnewline
3 & 30.0258333333333 & 0.36210140049774 & 1.02 \tabularnewline
4 & 30.2675 & 0.469702517073791 & 1.39 \tabularnewline
5 & 30.7483333333333 & 0.649136956180118 & 2.2 \tabularnewline
6 & 31.8016666666667 & 0.656572828243661 & 1.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230157&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]28.9525[/C][C]0.29378795692874[/C][C]0.859999999999999[/C][/ROW]
[ROW][C]2[/C][C]29.2491666666667[/C][C]0.300256203730727[/C][C]0.890000000000001[/C][/ROW]
[ROW][C]3[/C][C]30.0258333333333[/C][C]0.36210140049774[/C][C]1.02[/C][/ROW]
[ROW][C]4[/C][C]30.2675[/C][C]0.469702517073791[/C][C]1.39[/C][/ROW]
[ROW][C]5[/C][C]30.7483333333333[/C][C]0.649136956180118[/C][C]2.2[/C][/ROW]
[ROW][C]6[/C][C]31.8016666666667[/C][C]0.656572828243661[/C][C]1.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230157&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128.95250.293787956928740.859999999999999
229.24916666666670.3002562037307270.890000000000001
330.02583333333330.362101400497741.02
430.26750.4697025170737911.39
530.74833333333330.6491369561801182.2
631.80166666666670.6565728282436611.94







Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.02118484340474
beta0.148353541512239
S.D.0.029929528885914
T-STAT4.95676166764053
p-value0.00772389870523781

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.02118484340474 \tabularnewline
beta & 0.148353541512239 \tabularnewline
S.D. & 0.029929528885914 \tabularnewline
T-STAT & 4.95676166764053 \tabularnewline
p-value & 0.00772389870523781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230157&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.02118484340474[/C][/ROW]
[ROW][C]beta[/C][C]0.148353541512239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.029929528885914[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.95676166764053[/C][/ROW]
[ROW][C]p-value[/C][C]0.00772389870523781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230157&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230157&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.02118484340474
beta0.148353541512239
S.D.0.029929528885914
T-STAT4.95676166764053
p-value0.00772389870523781







Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-34.7898548291258
beta9.96559738089639
S.D.1.8723805375158
T-STAT5.32242094019965
p-value0.0059957768730528
Lambda-8.96559738089639

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -34.7898548291258 \tabularnewline
beta & 9.96559738089639 \tabularnewline
S.D. & 1.8723805375158 \tabularnewline
T-STAT & 5.32242094019965 \tabularnewline
p-value & 0.0059957768730528 \tabularnewline
Lambda & -8.96559738089639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230157&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-34.7898548291258[/C][/ROW]
[ROW][C]beta[/C][C]9.96559738089639[/C][/ROW]
[ROW][C]S.D.[/C][C]1.8723805375158[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.32242094019965[/C][/ROW]
[ROW][C]p-value[/C][C]0.0059957768730528[/C][/ROW]
[ROW][C]Lambda[/C][C]-8.96559738089639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230157&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230157&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-34.7898548291258
beta9.96559738089639
S.D.1.8723805375158
T-STAT5.32242094019965
p-value0.0059957768730528
Lambda-8.96559738089639



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')