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Description of Statistical Computation

Author's title

Michiel van Schaik - Standard Deviation-Mean Plot - Gemiddelde consumptiepr...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 28 May 2008 08:08:49 -0600
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/May/28/t1211983763u7iu3yuv4s8i22y.htm/, Retrieved Tue, 14 May 2024 22:46:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13442, Retrieved Tue, 14 May 2024 22:46:18 +0000
QR Codes:

Original text written by user:verbetering
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

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] [Michiel van Schai...] [2008-05-12 22:15:35] [ca7cb4900764820350c6e89b262aa59d]
-   PD    [Standard Deviation-Mean Plot] [Michiel van Schai...] [2008-05-28 14:08:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
65.05
65.84
66.6
67.55
68.07
69.06
69.06
69.11
69.29
69.38
69.28
69.75
69.9
70.21
70.48
71.55
72.18
72.64
72.77
72.74
73.13
73.44
73.34
73.34
73.81
74.26
74.72
75.11
75.26
75.89
75.91
76.43
76.56
76.76
76.76
76.56
76.82
77.09
77.51
77.76
77.86
77.89
77.94
77.99
78.17
78.91
78.87
78.88
79.08
79.41
79.51
79.73
80.38
80.56
80.46
80.45
80.58
80.68
80.52
81.49
81.66
81.95
82.3
82.4
83.14
83.17
83.11
83.21
83.33
83.88
83.8
83.73

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13442&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13442&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
168.171.56488163943944.7
272.14333333333331.293503581421993.53999999999999
375.66916666666671.021402407862782.95
477.97416666666670.6697280090160532.09000000000000
580.23750.6736619735041112.41000000000000
682.97333333333330.7323974744672872.22

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.17 & 1.5648816394394 & 4.7 \tabularnewline
2 & 72.1433333333333 & 1.29350358142199 & 3.53999999999999 \tabularnewline
3 & 75.6691666666667 & 1.02140240786278 & 2.95 \tabularnewline
4 & 77.9741666666667 & 0.669728009016053 & 2.09000000000000 \tabularnewline
5 & 80.2375 & 0.673661973504111 & 2.41000000000000 \tabularnewline
6 & 82.9733333333333 & 0.732397474467287 & 2.22 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13442&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]68.17[/C][C]1.5648816394394[/C][C]4.7[/C][/ROW]
[ROW][C]2[/C][C]72.1433333333333[/C][C]1.29350358142199[/C][C]3.53999999999999[/C][/ROW]
[ROW][C]3[/C][C]75.6691666666667[/C][C]1.02140240786278[/C][C]2.95[/C][/ROW]
[ROW][C]4[/C][C]77.9741666666667[/C][C]0.669728009016053[/C][C]2.09000000000000[/C][/ROW]
[ROW][C]5[/C][C]80.2375[/C][C]0.673661973504111[/C][C]2.41000000000000[/C][/ROW]
[ROW][C]6[/C][C]82.9733333333333[/C][C]0.732397474467287[/C][C]2.22[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13442&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
168.171.56488163943944.7
272.14333333333331.293503581421993.53999999999999
375.66916666666671.021402407862782.95
477.97416666666670.6697280090160532.09000000000000
580.23750.6736619735041112.41000000000000
682.97333333333330.7323974744672872.22






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.90825287271764
beta-0.0645145207185424
S.D.0.0118712296614831
T-STAT-5.43452721901787
p-value0.0055631572866889

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.90825287271764 \tabularnewline
beta & -0.0645145207185424 \tabularnewline
S.D. & 0.0118712296614831 \tabularnewline
T-STAT & -5.43452721901787 \tabularnewline
p-value & 0.0055631572866889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13442&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.90825287271764[/C][/ROW]
[ROW][C]beta[/C][C]-0.0645145207185424[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0118712296614831[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.43452721901787[/C][/ROW]
[ROW][C]p-value[/C][C]0.0055631572866889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13442&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)
alpha5.90825287271764
beta-0.0645145207185424
S.D.0.0118712296614831
T-STAT-5.43452721901787
p-value0.0055631572866889






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha20.2152077207701
beta-4.68205760576194
S.D.0.932102853276337
T-STAT-5.02311262035572
p-value0.00736916459365989
Lambda5.68205760576194

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 20.2152077207701 \tabularnewline
beta & -4.68205760576194 \tabularnewline
S.D. & 0.932102853276337 \tabularnewline
T-STAT & -5.02311262035572 \tabularnewline
p-value & 0.00736916459365989 \tabularnewline
Lambda & 5.68205760576194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13442&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.2152077207701[/C][/ROW]
[ROW][C]beta[/C][C]-4.68205760576194[/C][/ROW]
[ROW][C]S.D.[/C][C]0.932102853276337[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.02311262035572[/C][/ROW]
[ROW][C]p-value[/C][C]0.00736916459365989[/C][/ROW]
[ROW][C]Lambda[/C][C]5.68205760576194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13442&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)
alpha20.2152077207701
beta-4.68205760576194
S.D.0.932102853276337
T-STAT-5.02311262035572
p-value0.00736916459365989
Lambda5.68205760576194


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')