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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 computationSun, 07 Dec 2008 14:51:17 -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/2008/Dec/07/t122868679610h2c5unr6bg45n.htm/, Retrieved Fri, 17 May 2024 04:09:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30317, Retrieved Fri, 17 May 2024 04:09:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact206

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7 : alle waarden...] [2008-12-01 22:00:51] [82d201ca7b4e7cd2c6f885d29b5b6937]
- RMPD      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-07 21:51:17] [00a0a665d7a07edd2e460056b0c0c354] [Current]
-    D        [Standard Deviation-Mean Plot] [Standard deviatio...] [2008-12-07 22:05:25] [82d201ca7b4e7cd2c6f885d29b5b6937]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
116,1
102,5
102,0
101,3
100,6
100,9
104,2
108,3
108,9
109,9
106,8
112,7
113,4
101,3
97,8
95,0
93,8
94,5
101,4
105,8
106,6
109,7
108,8
113,4
113,7
103,6
98,2
95,5
94,4
95,9
103,2
104,1
127,6
130,3
133,0
140,4
123,5
116,9
115,9
113,1
112,1
112,4
118,9
117,4
115,6
120,7
114,9
122,0
119,6
114,6
118,4
110,9
111,6
114,6
112,1
117,4
114,8
123,4
118,1
121,9
123,3

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30317&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30317&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1106.1833333333335.0882812481825415.5
2103.4583333333337.1764081080533119.6
3111.65833333333316.704297668745646
4116.953.7252211648803811.4
5116.454.0245835470608312.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.183333333333 & 5.08828124818254 & 15.5 \tabularnewline
2 & 103.458333333333 & 7.17640810805331 & 19.6 \tabularnewline
3 & 111.658333333333 & 16.7042976687456 & 46 \tabularnewline
4 & 116.95 & 3.72522116488038 & 11.4 \tabularnewline
5 & 116.45 & 4.02458354706083 & 12.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30317&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]106.183333333333[/C][C]5.08828124818254[/C][C]15.5[/C][/ROW]
[ROW][C]2[/C][C]103.458333333333[/C][C]7.17640810805331[/C][C]19.6[/C][/ROW]
[ROW][C]3[/C][C]111.658333333333[/C][C]16.7042976687456[/C][C]46[/C][/ROW]
[ROW][C]4[/C][C]116.95[/C][C]3.72522116488038[/C][C]11.4[/C][/ROW]
[ROW][C]5[/C][C]116.45[/C][C]4.02458354706083[/C][C]12.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30317&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
1106.1833333333335.0882812481825415.5
2103.4583333333337.1764081080533119.6
3111.65833333333316.704297668745646
4116.953.7252211648803811.4
5116.454.0245835470608312.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha23.5975665052310
beta-0.146509898664561
S.D.0.510248358110743
T-STAT-0.287134483307369
p-value0.79269990627261

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 23.5975665052310 \tabularnewline
beta & -0.146509898664561 \tabularnewline
S.D. & 0.510248358110743 \tabularnewline
T-STAT & -0.287134483307369 \tabularnewline
p-value & 0.79269990627261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30317&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.5975665052310[/C][/ROW]
[ROW][C]beta[/C][C]-0.146509898664561[/C][/ROW]
[ROW][C]S.D.[/C][C]0.510248358110743[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.287134483307369[/C][/ROW]
[ROW][C]p-value[/C][C]0.79269990627261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30317&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30317&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)
alpha23.5975665052310
beta-0.146509898664561
S.D.0.510248358110743
T-STAT-0.287134483307369
p-value0.79269990627261






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha18.7380116005080
beta-3.59272473523749
S.D.6.09813694818723
T-STAT-0.589151205649045
p-value0.597183412383338
Lambda4.59272473523749

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 18.7380116005080 \tabularnewline
beta & -3.59272473523749 \tabularnewline
S.D. & 6.09813694818723 \tabularnewline
T-STAT & -0.589151205649045 \tabularnewline
p-value & 0.597183412383338 \tabularnewline
Lambda & 4.59272473523749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30317&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.7380116005080[/C][/ROW]
[ROW][C]beta[/C][C]-3.59272473523749[/C][/ROW]
[ROW][C]S.D.[/C][C]6.09813694818723[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.589151205649045[/C][/ROW]
[ROW][C]p-value[/C][C]0.597183412383338[/C][/ROW]
[ROW][C]Lambda[/C][C]4.59272473523749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30317&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30317&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)
alpha18.7380116005080
beta-3.59272473523749
S.D.6.09813694818723
T-STAT-0.589151205649045
p-value0.597183412383338
Lambda4.59272473523749


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')