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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 computationSat, 29 Nov 2008 17:14:02 -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/Nov/30/t1228004122cvztu568tqvxmok.htm/, Retrieved Thu, 26 Jun 2025 10:52:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26392, Retrieved Thu, 26 Jun 2025 10:52:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact352

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  [Standard Deviation-Mean Plot] [Q5 Standard DMP] [2008-11-29 16:26:32] [aa5573c1db401b164e448aef050955a1]
-   PD      [Standard Deviation-Mean Plot] [Q8 SDMN bouwprod] [2008-11-30 00:14:02] [8a1195ff8db4df756ce44b463a631c76] [Current]
- RM          [Variance Reduction Matrix] [Q8 RVM bouwprod] [2008-11-30 00:21:08] [aa5573c1db401b164e448aef050955a1]
-    D          [Variance Reduction Matrix] [Q8 VRM tot prod] [2008-11-30 00:41:13] [aa5573c1db401b164e448aef050955a1]
-    D        [Standard Deviation-Mean Plot] [Q8 SDMP tot prod] [2008-11-30 00:28:07] [aa5573c1db401b164e448aef050955a1]
-             [Standard Deviation-Mean Plot] [Q8 SDMN bouwprod] [2008-11-30 00:31:28] [aa5573c1db401b164e448aef050955a1]
-   P           [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 12:06:26] [aa5573c1db401b164e448aef050955a1]
-   P           [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 12:06:26] [aa5573c1db401b164e448aef050955a1]
-   P           [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 12:06:26] [aa5573c1db401b164e448aef050955a1]
- RMP             [Box-Cox Normality Plot] [Box Cox Normality...] [2008-12-12 12:35:24] [aa5573c1db401b164e448aef050955a1]
- RM              [Variance Reduction Matrix] [VRM Bouwproductie] [2008-12-12 13:22:47] [aa5573c1db401b164e448aef050955a1]
- RMP               [(Partial) Autocorrelation Function] [ACF bouwproductie...] [2008-12-12 13:31:29] [aa5573c1db401b164e448aef050955a1]
-   P                 [(Partial) Autocorrelation Function] [ACF bouwproductie...] [2008-12-12 13:45:52] [aa5573c1db401b164e448aef050955a1]
-   P                   [(Partial) Autocorrelation Function] [ACF bouwproductie...] [2008-12-12 13:59:06] [aa5573c1db401b164e448aef050955a1]
- RM              [Spectral Analysis] [Spectral Analysis...] [2008-12-12 14:26:07] [aa5573c1db401b164e448aef050955a1]
- RM              [Spectral Analysis] [Spectral Analysis...] [2008-12-12 14:42:38] [aa5573c1db401b164e448aef050955a1]
-    D            [Standard Deviation-Mean Plot] [SDMP Totale Produ...] [2008-12-12 15:57:50] [aa5573c1db401b164e448aef050955a1]
- RM                [Variance Reduction Matrix] [VRM Totale Productie] [2008-12-12 16:00:44] [aa5573c1db401b164e448aef050955a1]
- RMPD              [Cross Correlation Function] [CCF Bouwproductie...] [2008-12-12 16:06:05] [aa5573c1db401b164e448aef050955a1]
-   P                 [Cross Correlation Function] [CCF Bouwproductie...] [2008-12-12 16:12:34] [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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26392&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26392&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'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=26392&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=26392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26392&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=26392&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=26392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26392&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=26392&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=26392&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26392&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 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 1 ;
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')