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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 computationSat, 04 May 2013 09:09:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/04/t1367673034c0w7gwtu6vub8l2.htm/, Retrieved Mon, 29 Apr 2024 09:43:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208716, Retrieved Mon, 29 Apr 2024 09:43:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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] [Opgave 8: Standar...] [2013-05-04 13:09:45] [7bf0202b24d13a3918d58b8a1b5b6350] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
39,28
39,36
39,55
39,64
39,8
39,79
39,79
39,86
39,91
40
40,01
40,01
40,01
39,96
40
39,76
39,68
39,7
39,7
39,73
39,64
39,56
39,67
39,66
39,66
40,05
39,99
40,06
40,08
40,1
40,1
40,12
40,07
40,24
40,58
40,72
40,72
40,89
40,9
41,04
41,27
41,29
41,29
41,33
41,34
41,37
41,33
41,37
41,37
41,42
41,61
41,58
41,75
41,75
41,75
41,85
41,84
41,97
42,01
42,04
42,04
42,06
41,93
41,93
41,99
42,03
42,03
42,12
42,22
42,21
42,23
42,22

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208716&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208716&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
139.750.2460968028309920.729999999999997
239.75583333333330.1498155431512260.449999999999996
340.14750.2728344486380641.06
441.17833333333330.2273896668849770.649999999999999
541.7450.2173601954025960.670000000000002
642.08416666666670.1128521424723780.299999999999997

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 39.75 & 0.246096802830992 & 0.729999999999997 \tabularnewline
2 & 39.7558333333333 & 0.149815543151226 & 0.449999999999996 \tabularnewline
3 & 40.1475 & 0.272834448638064 & 1.06 \tabularnewline
4 & 41.1783333333333 & 0.227389666884977 & 0.649999999999999 \tabularnewline
5 & 41.745 & 0.217360195402596 & 0.670000000000002 \tabularnewline
6 & 42.0841666666667 & 0.112852142472378 & 0.299999999999997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208716&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]39.75[/C][C]0.246096802830992[/C][C]0.729999999999997[/C][/ROW]
[ROW][C]2[/C][C]39.7558333333333[/C][C]0.149815543151226[/C][C]0.449999999999996[/C][/ROW]
[ROW][C]3[/C][C]40.1475[/C][C]0.272834448638064[/C][C]1.06[/C][/ROW]
[ROW][C]4[/C][C]41.1783333333333[/C][C]0.227389666884977[/C][C]0.649999999999999[/C][/ROW]
[ROW][C]5[/C][C]41.745[/C][C]0.217360195402596[/C][C]0.670000000000002[/C][/ROW]
[ROW][C]6[/C][C]42.0841666666667[/C][C]0.112852142472378[/C][C]0.299999999999997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208716&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
139.750.2460968028309920.729999999999997
239.75583333333330.1498155431512260.449999999999996
340.14750.2728344486380641.06
441.17833333333330.2273896668849770.649999999999999
541.7450.2173601954025960.670000000000002
642.08416666666670.1128521424723780.299999999999997






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.18953703501914
beta-0.024159459159045
S.D.0.0269375732437183
T-STAT-0.896868435046534
p-value0.420488876683468

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.18953703501914 \tabularnewline
beta & -0.024159459159045 \tabularnewline
S.D. & 0.0269375732437183 \tabularnewline
T-STAT & -0.896868435046534 \tabularnewline
p-value & 0.420488876683468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208716&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.18953703501914[/C][/ROW]
[ROW][C]beta[/C][C]-0.024159459159045[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0269375732437183[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.896868435046534[/C][/ROW]
[ROW][C]p-value[/C][C]0.420488876683468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208716&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208716&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)
alpha1.18953703501914
beta-0.024159459159045
S.D.0.0269375732437183
T-STAT-0.896868435046534
p-value0.420488876683468






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha18.9955685848363
beta-5.56304884010381
S.D.6.09760532106024
T-STAT-0.912333374692168
p-value0.413205628708308
Lambda6.56304884010381

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 18.9955685848363 \tabularnewline
beta & -5.56304884010381 \tabularnewline
S.D. & 6.09760532106024 \tabularnewline
T-STAT & -0.912333374692168 \tabularnewline
p-value & 0.413205628708308 \tabularnewline
Lambda & 6.56304884010381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208716&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.9955685848363[/C][/ROW]
[ROW][C]beta[/C][C]-5.56304884010381[/C][/ROW]
[ROW][C]S.D.[/C][C]6.09760532106024[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.912333374692168[/C][/ROW]
[ROW][C]p-value[/C][C]0.413205628708308[/C][/ROW]
[ROW][C]Lambda[/C][C]6.56304884010381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208716&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208716&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)
alpha18.9955685848363
beta-5.56304884010381
S.D.6.09760532106024
T-STAT-0.912333374692168
p-value0.413205628708308
Lambda6.56304884010381


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')