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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 18 Aug 2010 22:59:20 +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/Aug/19/t1282172354ccjgszyu2a1pzjn.htm/, Retrieved Fri, 03 May 2024 09:37:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79238, Retrieved Fri, 03 May 2024 09:37:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMertens Jeroen
Estimated Impact165

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [TIJDREEKS B - STA...] [2010-08-18 22:59:20] [2c551c5731a2f7145d4349f791500f25] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
76
75
74
72
70
69
70
72
73
73
74
76
74
67
66
58
55
58
64
68
66
76
75
88
85
83
77
66
65
65
63
62
57
68
69
79
74
76
82
75
75
76
78
77
67
74
68
87
76
88
95
96
96
105
108
113
101
107
102
116
105
121
134
140
131
141
131
128
123
129
125
144
135
141
156
159
146
154
145
133
126
127
122
148

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=79238&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=79238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79238&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
174.251.707825127659934
270.251.258305739211793
3741.414213562373103
466.256.5510813356778516
561.255.8523499553598113
676.259.0323492698928222
777.758.5391256382996719
863.751.53
968.258.9953691790090922
1076.753.593976442141308
1176.51.290994448735813
12749.2014491612281720
1388.759.215023964519420
14105.57.1414284285428517
15106.56.8556546004010415
1612515.513435037626835
17132.755.6789083458002713
18130.259.521
19147.7511.586630226256524
20144.58.6602540378443921
21130.7511.701139545645426

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 74.25 & 1.70782512765993 & 4 \tabularnewline
2 & 70.25 & 1.25830573921179 & 3 \tabularnewline
3 & 74 & 1.41421356237310 & 3 \tabularnewline
4 & 66.25 & 6.55108133567785 & 16 \tabularnewline
5 & 61.25 & 5.85234995535981 & 13 \tabularnewline
6 & 76.25 & 9.03234926989282 & 22 \tabularnewline
7 & 77.75 & 8.53912563829967 & 19 \tabularnewline
8 & 63.75 & 1.5 & 3 \tabularnewline
9 & 68.25 & 8.99536917900909 & 22 \tabularnewline
10 & 76.75 & 3.59397644214130 & 8 \tabularnewline
11 & 76.5 & 1.29099444873581 & 3 \tabularnewline
12 & 74 & 9.20144916122817 & 20 \tabularnewline
13 & 88.75 & 9.2150239645194 & 20 \tabularnewline
14 & 105.5 & 7.14142842854285 & 17 \tabularnewline
15 & 106.5 & 6.85565460040104 & 15 \tabularnewline
16 & 125 & 15.5134350376268 & 35 \tabularnewline
17 & 132.75 & 5.67890834580027 & 13 \tabularnewline
18 & 130.25 & 9.5 & 21 \tabularnewline
19 & 147.75 & 11.5866302262565 & 24 \tabularnewline
20 & 144.5 & 8.66025403784439 & 21 \tabularnewline
21 & 130.75 & 11.7011395456454 & 26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79238&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]74.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]70.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]74[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]66.25[/C][C]6.55108133567785[/C][C]16[/C][/ROW]
[ROW][C]5[/C][C]61.25[/C][C]5.85234995535981[/C][C]13[/C][/ROW]
[ROW][C]6[/C][C]76.25[/C][C]9.03234926989282[/C][C]22[/C][/ROW]
[ROW][C]7[/C][C]77.75[/C][C]8.53912563829967[/C][C]19[/C][/ROW]
[ROW][C]8[/C][C]63.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]9[/C][C]68.25[/C][C]8.99536917900909[/C][C]22[/C][/ROW]
[ROW][C]10[/C][C]76.75[/C][C]3.59397644214130[/C][C]8[/C][/ROW]
[ROW][C]11[/C][C]76.5[/C][C]1.29099444873581[/C][C]3[/C][/ROW]
[ROW][C]12[/C][C]74[/C][C]9.20144916122817[/C][C]20[/C][/ROW]
[ROW][C]13[/C][C]88.75[/C][C]9.2150239645194[/C][C]20[/C][/ROW]
[ROW][C]14[/C][C]105.5[/C][C]7.14142842854285[/C][C]17[/C][/ROW]
[ROW][C]15[/C][C]106.5[/C][C]6.85565460040104[/C][C]15[/C][/ROW]
[ROW][C]16[/C][C]125[/C][C]15.5134350376268[/C][C]35[/C][/ROW]
[ROW][C]17[/C][C]132.75[/C][C]5.67890834580027[/C][C]13[/C][/ROW]
[ROW][C]18[/C][C]130.25[/C][C]9.5[/C][C]21[/C][/ROW]
[ROW][C]19[/C][C]147.75[/C][C]11.5866302262565[/C][C]24[/C][/ROW]
[ROW][C]20[/C][C]144.5[/C][C]8.66025403784439[/C][C]21[/C][/ROW]
[ROW][C]21[/C][C]130.75[/C][C]11.7011395456454[/C][C]26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79238&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
174.251.707825127659934
270.251.258305739211793
3741.414213562373103
466.256.5510813356778516
561.255.8523499553598113
676.259.0323492698928222
777.758.5391256382996719
863.751.53
968.258.9953691790090922
1076.753.593976442141308
1176.51.290994448735813
12749.2014491612281720
1388.759.215023964519420
14105.57.1414284285428517
15106.56.8556546004010415
1612515.513435037626835
17132.755.6789083458002713
18130.259.521
19147.7511.586630226256524
20144.58.6602540378443921
21130.7511.701139545645426






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.539564582660915
beta0.0792087114571817
S.D.0.0251011101843182
T-STAT3.15558598307206
p-value0.00520709122659695

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.539564582660915 \tabularnewline
beta & 0.0792087114571817 \tabularnewline
S.D. & 0.0251011101843182 \tabularnewline
T-STAT & 3.15558598307206 \tabularnewline
p-value & 0.00520709122659695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79238&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.539564582660915[/C][/ROW]
[ROW][C]beta[/C][C]0.0792087114571817[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0251011101843182[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.15558598307206[/C][/ROW]
[ROW][C]p-value[/C][C]0.00520709122659695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79238&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)
alpha-0.539564582660915
beta0.0792087114571817
S.D.0.0251011101843182
T-STAT3.15558598307206
p-value0.00520709122659695






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.01467905710545
beta1.48927621968915
S.D.0.530924073905568
T-STAT2.80506440164556
p-value0.0112983039664927
Lambda-0.489276219689145

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.01467905710545 \tabularnewline
beta & 1.48927621968915 \tabularnewline
S.D. & 0.530924073905568 \tabularnewline
T-STAT & 2.80506440164556 \tabularnewline
p-value & 0.0112983039664927 \tabularnewline
Lambda & -0.489276219689145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79238&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.01467905710545[/C][/ROW]
[ROW][C]beta[/C][C]1.48927621968915[/C][/ROW]
[ROW][C]S.D.[/C][C]0.530924073905568[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.80506440164556[/C][/ROW]
[ROW][C]p-value[/C][C]0.0112983039664927[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.489276219689145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79238&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-5.01467905710545
beta1.48927621968915
S.D.0.530924073905568
T-STAT2.80506440164556
p-value0.0112983039664927
Lambda-0.489276219689145


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')