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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 computationFri, 12 Dec 2008 06:19:31 -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/12/t1229088010igpou0ubnl7ysvj.htm/, Retrieved Fri, 17 May 2024 09:48:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32688, Retrieved Fri, 17 May 2024 09:48:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208

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] [WS7 Q1 G6 reeks 1] [2007-11-22 09:45:51] [22f18fc6a98517db16300404be421f9a]
- R  D    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 13:19:31] [c0a347e3519123f7eef62b705326dad9] [Current]
-    D      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 13:29:54] [29747f79f5beb5b2516e1271770ecb47]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,5
100,7
110,6
96,8
100,0
104,8
86,8
92,0
100,2
106,6
102,1
93,7
97,6
96,9
105,6
102,8
101,7
104,2
92,7
91,9
106,5
112,3
102,8
96,5
101,0
98,9
105,1
103,0
99,0
104,3
94,6
90,4
108,9
111,4
100,8
102,5
98,2
98,7
113,3
104,6
99,3
111,8
97,3
97,7
115,6
111,9
107,0
107,1
100,6
99,2
108,4
103,0
99,8
115,0
90,8
95,9
114,4
108,2
112,6
109,1
105,0
105,0
118,5
103,7
112,5
116,6
96,6
101,9
116,5
119,3
115,4
108,5
111,5
108,8
121,8
109,6
112,2
119,6
104,1
105,3
115,0
124,1
116,8
107,5
115,6
116,2
116,3
119,0
111,9
118,6
106,9
103,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32688&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32688&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.656.5563986788757523.8
2100.9583333333336.0046131255792620.4
3101.6583333333335.7294229970205521
4105.2083333333336.8367267996705418.3
5104.757.7016527151939624.2
6109.9583333333337.4896848256704922.7
7113.0256.4911303119928820

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.65 & 6.55639867887575 & 23.8 \tabularnewline
2 & 100.958333333333 & 6.00461312557926 & 20.4 \tabularnewline
3 & 101.658333333333 & 5.72942299702055 & 21 \tabularnewline
4 & 105.208333333333 & 6.83672679967054 & 18.3 \tabularnewline
5 & 104.75 & 7.70165271519396 & 24.2 \tabularnewline
6 & 109.958333333333 & 7.48968482567049 & 22.7 \tabularnewline
7 & 113.025 & 6.49113031199288 & 20 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32688&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]99.65[/C][C]6.55639867887575[/C][C]23.8[/C][/ROW]
[ROW][C]2[/C][C]100.958333333333[/C][C]6.00461312557926[/C][C]20.4[/C][/ROW]
[ROW][C]3[/C][C]101.658333333333[/C][C]5.72942299702055[/C][C]21[/C][/ROW]
[ROW][C]4[/C][C]105.208333333333[/C][C]6.83672679967054[/C][C]18.3[/C][/ROW]
[ROW][C]5[/C][C]104.75[/C][C]7.70165271519396[/C][C]24.2[/C][/ROW]
[ROW][C]6[/C][C]109.958333333333[/C][C]7.48968482567049[/C][C]22.7[/C][/ROW]
[ROW][C]7[/C][C]113.025[/C][C]6.49113031199288[/C][C]20[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32688&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
199.656.5563986788757523.8
2100.9583333333336.0046131255792620.4
3101.6583333333335.7294229970205521
4105.2083333333336.8367267996705418.3
5104.757.7016527151939624.2
6109.9583333333337.4896848256704922.7
7113.0256.4911303119928820






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.291525686994776
beta0.0608928756860845
S.D.0.0597937879577543
T-STAT1.01838130290569
p-value0.355215534302202

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.291525686994776 \tabularnewline
beta & 0.0608928756860845 \tabularnewline
S.D. & 0.0597937879577543 \tabularnewline
T-STAT & 1.01838130290569 \tabularnewline
p-value & 0.355215534302202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32688&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.291525686994776[/C][/ROW]
[ROW][C]beta[/C][C]0.0608928756860845[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0597937879577543[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.01838130290569[/C][/ROW]
[ROW][C]p-value[/C][C]0.355215534302202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32688&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32688&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)
alpha0.291525686994776
beta0.0608928756860845
S.D.0.0597937879577543
T-STAT1.01838130290569
p-value0.355215534302202






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.79404037144844
beta1.00771662386996
S.D.0.938985015816406
T-STAT1.07319776875651
p-value0.332223881332018
Lambda-0.00771662386996153

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.79404037144844 \tabularnewline
beta & 1.00771662386996 \tabularnewline
S.D. & 0.938985015816406 \tabularnewline
T-STAT & 1.07319776875651 \tabularnewline
p-value & 0.332223881332018 \tabularnewline
Lambda & -0.00771662386996153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32688&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.79404037144844[/C][/ROW]
[ROW][C]beta[/C][C]1.00771662386996[/C][/ROW]
[ROW][C]S.D.[/C][C]0.938985015816406[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.07319776875651[/C][/ROW]
[ROW][C]p-value[/C][C]0.332223881332018[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.00771662386996153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32688&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32688&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-2.79404037144844
beta1.00771662386996
S.D.0.938985015816406
T-STAT1.07319776875651
p-value0.332223881332018
Lambda-0.00771662386996153


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')