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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, 08 Dec 2008 15:32:48 -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/08/t12287757511d1uho7mf6zc498.htm/, Retrieved Thu, 16 May 2024 19:10:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31104, Retrieved Thu, 16 May 2024 19:10:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [(Partial) Autocorrelation Function] [] [2008-12-01 19:22:35] [2a0ad3a9bcadca2da0acb91636601c6c]
-   P   [(Partial) Autocorrelation Function] [] [2008-12-01 19:27:13] [2a0ad3a9bcadca2da0acb91636601c6c]
- RMPD      [Standard Deviation-Mean Plot] [SD Mean Bouwprodu...] [2008-12-08 22:32:48] [8a1195ff8db4df756ce44b463a631c76] [Current]
F             [Standard Deviation-Mean Plot] [SD Mean Bouwprodu...] [2008-12-08 22:45:41] [aa5573c1db401b164e448aef050955a1]
F RM            [Variance Reduction Matrix] [VRM Bouwproductie] [2008-12-08 22:57:37] [aa5573c1db401b164e448aef050955a1]
F RM              [(Partial) Autocorrelation Function] [PACF bouwproducti...] [2008-12-08 23:26:01] [aa5573c1db401b164e448aef050955a1]
F                   [(Partial) Autocorrelation Function] [PACF bouwproducti...] [2008-12-08 23:39:37] [aa5573c1db401b164e448aef050955a1]
F RM                [Spectral Analysis] [Spectrum analyse ...] [2008-12-08 23:49:25] [aa5573c1db401b164e448aef050955a1]
F                     [Spectral Analysis] [Spectrum analyse ...] [2008-12-08 23:53:38] [aa5573c1db401b164e448aef050955a1]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82.7
88.9
105.9
100.8
94
105
58.5
87.6
113.1
112.5
89.6
74.5
82.7
90.1
109.4
96
89.2
109.1
49.1
92.9
107.7
103.5
91.1
79.8
71.9
82.9
90.1
100.7
90.7
108.8
44.1
93.6
107.4
96.5
93.6
76.5
76.7
84
103.3
88.5
99
105.9
44.7
94
107.1
104.8
102.5
77.7
85.2
91.3
106.5
92.4
97.5
107
51.1
98.6
102.2
114.3
99.4
72.5
92.3
99.4
85.9
109.4
97.6

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=31104&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=31104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31104&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
194.57510.649374003511523.2
286.27519.862087000111546.5
397.42518.794923960119338.6
494.5511.296754696224326.7
585.07525.492793099227160
695.52512.631805096659827.9
786.412.119955995519728.8
884.327.950790090204464.7
993.512.796093153771630.9
1088.12511.224489594928926.6
1185.927.896594774273161.2
1298.02513.679516316985329.4
1393.859.0083294788767621.3
1488.5525.324625696477155.9
1597.117.628575287489041.8
1696.7510.075878787149723.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 94.575 & 10.6493740035115 & 23.2 \tabularnewline
2 & 86.275 & 19.8620870001115 & 46.5 \tabularnewline
3 & 97.425 & 18.7949239601193 & 38.6 \tabularnewline
4 & 94.55 & 11.2967546962243 & 26.7 \tabularnewline
5 & 85.075 & 25.4927930992271 & 60 \tabularnewline
6 & 95.525 & 12.6318050966598 & 27.9 \tabularnewline
7 & 86.4 & 12.1199559955197 & 28.8 \tabularnewline
8 & 84.3 & 27.9507900902044 & 64.7 \tabularnewline
9 & 93.5 & 12.7960931537716 & 30.9 \tabularnewline
10 & 88.125 & 11.2244895949289 & 26.6 \tabularnewline
11 & 85.9 & 27.8965947742731 & 61.2 \tabularnewline
12 & 98.025 & 13.6795163169853 & 29.4 \tabularnewline
13 & 93.85 & 9.00832947887676 & 21.3 \tabularnewline
14 & 88.55 & 25.3246256964771 & 55.9 \tabularnewline
15 & 97.1 & 17.6285752874890 & 41.8 \tabularnewline
16 & 96.75 & 10.0758787871497 & 23.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31104&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]94.575[/C][C]10.6493740035115[/C][C]23.2[/C][/ROW]
[ROW][C]2[/C][C]86.275[/C][C]19.8620870001115[/C][C]46.5[/C][/ROW]
[ROW][C]3[/C][C]97.425[/C][C]18.7949239601193[/C][C]38.6[/C][/ROW]
[ROW][C]4[/C][C]94.55[/C][C]11.2967546962243[/C][C]26.7[/C][/ROW]
[ROW][C]5[/C][C]85.075[/C][C]25.4927930992271[/C][C]60[/C][/ROW]
[ROW][C]6[/C][C]95.525[/C][C]12.6318050966598[/C][C]27.9[/C][/ROW]
[ROW][C]7[/C][C]86.4[/C][C]12.1199559955197[/C][C]28.8[/C][/ROW]
[ROW][C]8[/C][C]84.3[/C][C]27.9507900902044[/C][C]64.7[/C][/ROW]
[ROW][C]9[/C][C]93.5[/C][C]12.7960931537716[/C][C]30.9[/C][/ROW]
[ROW][C]10[/C][C]88.125[/C][C]11.2244895949289[/C][C]26.6[/C][/ROW]
[ROW][C]11[/C][C]85.9[/C][C]27.8965947742731[/C][C]61.2[/C][/ROW]
[ROW][C]12[/C][C]98.025[/C][C]13.6795163169853[/C][C]29.4[/C][/ROW]
[ROW][C]13[/C][C]93.85[/C][C]9.00832947887676[/C][C]21.3[/C][/ROW]
[ROW][C]14[/C][C]88.55[/C][C]25.3246256964771[/C][C]55.9[/C][/ROW]
[ROW][C]15[/C][C]97.1[/C][C]17.6285752874890[/C][C]41.8[/C][/ROW]
[ROW][C]16[/C][C]96.75[/C][C]10.0758787871497[/C][C]23.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31104&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
194.57510.649374003511523.2
286.27519.862087000111546.5
397.42518.794923960119338.6
494.5511.296754696224326.7
585.07525.492793099227160
695.52512.631805096659827.9
786.412.119955995519728.8
884.327.950790090204464.7
993.512.796093153771630.9
1088.12511.224489594928926.6
1185.927.896594774273161.2
1298.02513.679516316985329.4
1393.859.0083294788767621.3
1488.5525.324625696477155.9
1597.117.628575287489041.8
1696.7510.075878787149723.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha92.720664992951
beta-0.830259428589926
S.D.0.280939426952267
T-STAT-2.95529693926154
p-value0.0104358937671527

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 92.720664992951 \tabularnewline
beta & -0.830259428589926 \tabularnewline
S.D. & 0.280939426952267 \tabularnewline
T-STAT & -2.95529693926154 \tabularnewline
p-value & 0.0104358937671527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31104&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]92.720664992951[/C][/ROW]
[ROW][C]beta[/C][C]-0.830259428589926[/C][/ROW]
[ROW][C]S.D.[/C][C]0.280939426952267[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.95529693926154[/C][/ROW]
[ROW][C]p-value[/C][C]0.0104358937671527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31104&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)
alpha92.720664992951
beta-0.830259428589926
S.D.0.280939426952267
T-STAT-2.95529693926154
p-value0.0104358937671527






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha21.3692350195497
beta-4.12504082180652
S.D.1.53080471103068
T-STAT-2.69468782796544
p-value0.0174370776919627
Lambda5.12504082180652

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 21.3692350195497 \tabularnewline
beta & -4.12504082180652 \tabularnewline
S.D. & 1.53080471103068 \tabularnewline
T-STAT & -2.69468782796544 \tabularnewline
p-value & 0.0174370776919627 \tabularnewline
Lambda & 5.12504082180652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31104&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.3692350195497[/C][/ROW]
[ROW][C]beta[/C][C]-4.12504082180652[/C][/ROW]
[ROW][C]S.D.[/C][C]1.53080471103068[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.69468782796544[/C][/ROW]
[ROW][C]p-value[/C][C]0.0174370776919627[/C][/ROW]
[ROW][C]Lambda[/C][C]5.12504082180652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31104&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)
alpha21.3692350195497
beta-4.12504082180652
S.D.1.53080471103068
T-STAT-2.69468782796544
p-value0.0174370776919627
Lambda5.12504082180652


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.0 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; par5 = 0.0 ; par6 = 1 ; par7 = 0 ;
Parameters (R input):
par1 = 4 ;
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')