FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 19 Aug 2010 22:19:11 +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/20/t1282256347lpupwxwuc79zz5k.htm/, Retrieved Wed, 08 May 2024 21:09:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79404, Retrieved Wed, 08 May 2024 21:09:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMertens Jeroen
Estimated Impact157

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...] [2010-08-19 22:19:11] [2c551c5731a2f7145d4349f791500f25] [Current]
Feedback Forum

Post a new message

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79404&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79404&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
172.83333333333332.329000305762637
267.91666666666679.2584932343063833
369.91666666666678.9285887445719528
475.755.361902647381820
5100.2511.054616477044640
6129.33333333333310.50829398257639
714112.395013660192737

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 72.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 67.9166666666667 & 9.25849323430638 & 33 \tabularnewline
3 & 69.9166666666667 & 8.92858874457195 & 28 \tabularnewline
4 & 75.75 & 5.3619026473818 & 20 \tabularnewline
5 & 100.25 & 11.0546164770446 & 40 \tabularnewline
6 & 129.333333333333 & 10.508293982576 & 39 \tabularnewline
7 & 141 & 12.3950136601927 & 37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79404&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]72.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]67.9166666666667[/C][C]9.25849323430638[/C][C]33[/C][/ROW]
[ROW][C]3[/C][C]69.9166666666667[/C][C]8.92858874457195[/C][C]28[/C][/ROW]
[ROW][C]4[/C][C]75.75[/C][C]5.3619026473818[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]100.25[/C][C]11.0546164770446[/C][C]40[/C][/ROW]
[ROW][C]6[/C][C]129.333333333333[/C][C]10.508293982576[/C][C]39[/C][/ROW]
[ROW][C]7[/C][C]141[/C][C]12.3950136601927[/C][C]37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79404&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
172.83333333333332.329000305762637
267.91666666666679.2584932343063833
369.91666666666678.9285887445719528
475.755.361902647381820
5100.2511.054616477044640
6129.33333333333310.50829398257639
714112.395013660192737






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.29704099815344
beta0.0772551325186635
S.D.0.0386444786216713
T-STAT1.999124720377
p-value0.102053489788052

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.29704099815344 \tabularnewline
beta & 0.0772551325186635 \tabularnewline
S.D. & 0.0386444786216713 \tabularnewline
T-STAT & 1.999124720377 \tabularnewline
p-value & 0.102053489788052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79404&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.29704099815344[/C][/ROW]
[ROW][C]beta[/C][C]0.0772551325186635[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0386444786216713[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.999124720377[/C][/ROW]
[ROW][C]p-value[/C][C]0.102053489788052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79404&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)
alpha1.29704099815344
beta0.0772551325186635
S.D.0.0386444786216713
T-STAT1.999124720377
p-value0.102053489788052






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.70587863363631
beta1.05247608625132
S.D.0.717560150366153
T-STAT1.46674266361401
p-value0.202358751475069
Lambda-0.0524760862513176

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.70587863363631 \tabularnewline
beta & 1.05247608625132 \tabularnewline
S.D. & 0.717560150366153 \tabularnewline
T-STAT & 1.46674266361401 \tabularnewline
p-value & 0.202358751475069 \tabularnewline
Lambda & -0.0524760862513176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79404&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.70587863363631[/C][/ROW]
[ROW][C]beta[/C][C]1.05247608625132[/C][/ROW]
[ROW][C]S.D.[/C][C]0.717560150366153[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.46674266361401[/C][/ROW]
[ROW][C]p-value[/C][C]0.202358751475069[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0524760862513176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79404&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79404&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-2.70587863363631
beta1.05247608625132
S.D.0.717560150366153
T-STAT1.46674266361401
p-value0.202358751475069
Lambda-0.0524760862513176


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')