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 computationMon, 17 May 2010 18:48:07 +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/May/17/t1274122132q0attcqdi3xlpkk.htm/, Retrieved Sun, 05 May 2024 12:44:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76124, Retrieved Sun, 05 May 2024 12:44:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact105

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] [] [2010-05-17 18:48:07] [2bab6b58187a1236dde7e79464907c61] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
132.8
132.5
131.4
131.4
130.7
131.5
131.2
130.1
130.5
129
128.2
128.4
127.3
127.7
127
123.9
125.4
124.6
124.5
124.8
124.1
124.2
122.8
122.3
121.1
121.7
122.2
122.2
122.7
121.7
121
119.8
120.2
116.6
116
118
117.1
116.2
113.3
114.3
113.6
113
112.9
112.7
112.5
113
111.9
110.9
109.8
108.3
109.2
109.2
108.7
109.8
110.8
110
109.6
109.5
110.8
111.6
113.1
114.3
114.1
113.8
112.6
112.7
111.5
110.7
110.4
109.7
110
111.3
109
108.2
107.2
108.7
110.3
110.3
109.5
109.5
109.4
109.6
111.3
110
109.5
110.693
109.195
108.095
108.199
106.87
105.278
108.711
111.192
109.641
109.42
109.935
111.126
110.733
110.34
111.766
111.294
111.54
112.008
111.007
114.963
112.045
110.703
108.894
107.51
111.35
112.964
115.203
115.182
115.191
112.346
110.774
113.07
111.138
109.092
107.971
107.051

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=76124&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=76124&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76124&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
1130.6416666666671.486581394483414.60000000000002
2124.8833333333331.700712863014875.40000000000001
3120.2666666666672.251194968872936.7
4113.451.72495059217786.19999999999999
5109.7750.933346861373823.3
6112.0166666666671.631415076403044.59999999999999
7109.4166666666671.069267662156364.09999999999999
8108.8940833333331.629845361227615.91399999999999
9111.368251.420538062272056.06899999999999
10111.8159166666672.694643017622977.693

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 130.641666666667 & 1.48658139448341 & 4.60000000000002 \tabularnewline
2 & 124.883333333333 & 1.70071286301487 & 5.40000000000001 \tabularnewline
3 & 120.266666666667 & 2.25119496887293 & 6.7 \tabularnewline
4 & 113.45 & 1.7249505921778 & 6.19999999999999 \tabularnewline
5 & 109.775 & 0.93334686137382 & 3.3 \tabularnewline
6 & 112.016666666667 & 1.63141507640304 & 4.59999999999999 \tabularnewline
7 & 109.416666666667 & 1.06926766215636 & 4.09999999999999 \tabularnewline
8 & 108.894083333333 & 1.62984536122761 & 5.91399999999999 \tabularnewline
9 & 111.36825 & 1.42053806227205 & 6.06899999999999 \tabularnewline
10 & 111.815916666667 & 2.69464301762297 & 7.693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76124&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]130.641666666667[/C][C]1.48658139448341[/C][C]4.60000000000002[/C][/ROW]
[ROW][C]2[/C][C]124.883333333333[/C][C]1.70071286301487[/C][C]5.40000000000001[/C][/ROW]
[ROW][C]3[/C][C]120.266666666667[/C][C]2.25119496887293[/C][C]6.7[/C][/ROW]
[ROW][C]4[/C][C]113.45[/C][C]1.7249505921778[/C][C]6.19999999999999[/C][/ROW]
[ROW][C]5[/C][C]109.775[/C][C]0.93334686137382[/C][C]3.3[/C][/ROW]
[ROW][C]6[/C][C]112.016666666667[/C][C]1.63141507640304[/C][C]4.59999999999999[/C][/ROW]
[ROW][C]7[/C][C]109.416666666667[/C][C]1.06926766215636[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]8[/C][C]108.894083333333[/C][C]1.62984536122761[/C][C]5.91399999999999[/C][/ROW]
[ROW][C]9[/C][C]111.36825[/C][C]1.42053806227205[/C][C]6.06899999999999[/C][/ROW]
[ROW][C]10[/C][C]111.815916666667[/C][C]2.69464301762297[/C][C]7.693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76124&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76124&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
1130.6416666666671.486581394483414.60000000000002
2124.8833333333331.700712863014875.40000000000001
3120.2666666666672.251194968872936.7
4113.451.72495059217786.19999999999999
5109.7750.933346861373823.3
6112.0166666666671.631415076403044.59999999999999
7109.4166666666671.069267662156364.09999999999999
8108.8940833333331.629845361227615.91399999999999
9111.368251.420538062272056.06899999999999
10111.8159166666672.694643017622977.693






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.349827784831763
beta0.0113179160782282
S.D.0.0241270145208864
T-STAT0.469097246508906
p-value0.651518538775273

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.349827784831763 \tabularnewline
beta & 0.0113179160782282 \tabularnewline
S.D. & 0.0241270145208864 \tabularnewline
T-STAT & 0.469097246508906 \tabularnewline
p-value & 0.651518538775273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76124&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.349827784831763[/C][/ROW]
[ROW][C]beta[/C][C]0.0113179160782282[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0241270145208864[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.469097246508906[/C][/ROW]
[ROW][C]p-value[/C][C]0.651518538775273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76124&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76124&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)
alpha0.349827784831763
beta0.0113179160782282
S.D.0.0241270145208864
T-STAT0.469097246508906
p-value0.651518538775273






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.27438848574768
beta1.20848052004352
S.D.1.70048566029899
T-STAT0.710667868749355
p-value0.497482139599123
Lambda-0.20848052004352

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.27438848574768 \tabularnewline
beta & 1.20848052004352 \tabularnewline
S.D. & 1.70048566029899 \tabularnewline
T-STAT & 0.710667868749355 \tabularnewline
p-value & 0.497482139599123 \tabularnewline
Lambda & -0.20848052004352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76124&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.27438848574768[/C][/ROW]
[ROW][C]beta[/C][C]1.20848052004352[/C][/ROW]
[ROW][C]S.D.[/C][C]1.70048566029899[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.710667868749355[/C][/ROW]
[ROW][C]p-value[/C][C]0.497482139599123[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.20848052004352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76124&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76124&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-5.27438848574768
beta1.20848052004352
S.D.1.70048566029899
T-STAT0.710667868749355
p-value0.497482139599123
Lambda-0.20848052004352


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')