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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, 17 Dec 2008 12:55:28 -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/17/t12295437668wbjcsxo3396apf.htm/, Retrieved Sun, 19 May 2024 07:16:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34532, Retrieved Sun, 19 May 2024 07:16:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Dooren Leen
Estimated Impact145

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] [paper] [2008-12-17 19:55:28] [d175f84d503eb4f2a43145d5e67795b5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98.6
98.0
106.8
96.6
100.1
107.7
91.5
97.8
107.4
117.5
105.6
97.4
99.5
98.0
104.3
100.6
101.1
103.9
96.9
95.5
108.4
117.0
103.8
100.8
110.6
104.0
112.6
107.3
98.9
109.8
104.9
102.2
123.9
124.9
112.7
121.9
100.6
104.3
120.4
107.5
102.9
125.6
107.5
108.8
128.4
121.1
119.5
128.7
108.7
105.5
119.8
111.3
110.6
120.1
97.5
107.7
127.3
117.2
119.8
116.2
111.0
112.4
130.6
109.1
118.8
123.9
101.6
112.8
128.0
129.6
125.8
119.5
115.7
113.6
129.7
112.0
116.8
127.0
112.1
114.2
121.1
131.6
125.0
120.4
117.7
117.5
120.6
127.5
112.3
124.5
115.2
104.7
130.5

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=34532&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=34532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34532&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
1102.0833333333337.0530242814803626
2102.4833333333335.7998171340033521.5
3111.1416666666678.575807232964726
4114.60833333333310.372994512266728.1
5113.4758.1144231856838529.8
6118.5916666666679.260027325046429
7119.9333333333336.9655428990702419.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.083333333333 & 7.05302428148036 & 26 \tabularnewline
2 & 102.483333333333 & 5.79981713400335 & 21.5 \tabularnewline
3 & 111.141666666667 & 8.5758072329647 & 26 \tabularnewline
4 & 114.608333333333 & 10.3729945122667 & 28.1 \tabularnewline
5 & 113.475 & 8.11442318568385 & 29.8 \tabularnewline
6 & 118.591666666667 & 9.2600273250464 & 29 \tabularnewline
7 & 119.933333333333 & 6.96554289907024 & 19.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34532&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]102.083333333333[/C][C]7.05302428148036[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]102.483333333333[/C][C]5.79981713400335[/C][C]21.5[/C][/ROW]
[ROW][C]3[/C][C]111.141666666667[/C][C]8.5758072329647[/C][C]26[/C][/ROW]
[ROW][C]4[/C][C]114.608333333333[/C][C]10.3729945122667[/C][C]28.1[/C][/ROW]
[ROW][C]5[/C][C]113.475[/C][C]8.11442318568385[/C][C]29.8[/C][/ROW]
[ROW][C]6[/C][C]118.591666666667[/C][C]9.2600273250464[/C][C]29[/C][/ROW]
[ROW][C]7[/C][C]119.933333333333[/C][C]6.96554289907024[/C][C]19.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34532&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
1102.0833333333337.0530242814803626
2102.4833333333335.7998171340033521.5
3111.1416666666678.575807232964726
4114.60833333333310.372994512266728.1
5113.4758.1144231856838529.8
6118.5916666666679.260027325046429
7119.9333333333336.9655428990702419.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.30787013499757
beta0.119256985682054
S.D.0.0811758885499665
T-STAT1.46911832826624
p-value0.201743201955855

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.30787013499757 \tabularnewline
beta & 0.119256985682054 \tabularnewline
S.D. & 0.0811758885499665 \tabularnewline
T-STAT & 1.46911832826624 \tabularnewline
p-value & 0.201743201955855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34532&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.30787013499757[/C][/ROW]
[ROW][C]beta[/C][C]0.119256985682054[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0811758885499665[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.46911832826624[/C][/ROW]
[ROW][C]p-value[/C][C]0.201743201955855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34532&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34532&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-5.30787013499757
beta0.119256985682054
S.D.0.0811758885499665
T-STAT1.46911832826624
p-value0.201743201955855






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.27477128287612
beta1.76907829520238
S.D.1.102790874927
T-STAT1.60418292844461
p-value0.169578936035568
Lambda-0.769078295202383

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.27477128287612 \tabularnewline
beta & 1.76907829520238 \tabularnewline
S.D. & 1.102790874927 \tabularnewline
T-STAT & 1.60418292844461 \tabularnewline
p-value & 0.169578936035568 \tabularnewline
Lambda & -0.769078295202383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34532&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.27477128287612[/C][/ROW]
[ROW][C]beta[/C][C]1.76907829520238[/C][/ROW]
[ROW][C]S.D.[/C][C]1.102790874927[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.60418292844461[/C][/ROW]
[ROW][C]p-value[/C][C]0.169578936035568[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.769078295202383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34532&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34532&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-6.27477128287612
beta1.76907829520238
S.D.1.102790874927
T-STAT1.60418292844461
p-value0.169578936035568
Lambda-0.769078295202383


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')