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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 computationMon, 12 May 2008 16:13:06 -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/13/t1210630431wp4b3cay1j5o80d.htm/, Retrieved Wed, 15 May 2024 16:47:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12465, Retrieved Wed, 15 May 2024 16:47:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact228

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 22:13:06] [f1389fff7fe55b9c206fc4c1b90cd78e] [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 time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12465&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]1 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=12465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12465&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
166.261.067739044273772.5
268.8250.5038849074937691.04000000000001
369.4250.2212841310773690.469999999999999
470.5350.7169611797952041.64999999999999
572.58250.2740285873164770.589999999999989
673.31250.1304798835070010.310000000000002
774.4750.5632347053700891.30000000000000
875.87250.4787744771810631.17000000000000
976.660.1154700538379270.200000000000003
1077.2950.4203569911396790.940000000000012
1177.920.05715476066493860.129999999999995
1278.70750.3587362076326640.739999999999995
1379.43250.2703547052793200.650000000000006
1480.46250.07410578025138830.180000000000007
1580.81750.4531647971029210.969999999999999
1682.07750.3386615813266510.740000000000009
1783.15750.04272001872658540.0999999999999943
1883.6850.2444722206441180.549999999999997

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.26 & 1.06773904427377 & 2.5 \tabularnewline
2 & 68.825 & 0.503884907493769 & 1.04000000000001 \tabularnewline
3 & 69.425 & 0.221284131077369 & 0.469999999999999 \tabularnewline
4 & 70.535 & 0.716961179795204 & 1.64999999999999 \tabularnewline
5 & 72.5825 & 0.274028587316477 & 0.589999999999989 \tabularnewline
6 & 73.3125 & 0.130479883507001 & 0.310000000000002 \tabularnewline
7 & 74.475 & 0.563234705370089 & 1.30000000000000 \tabularnewline
8 & 75.8725 & 0.478774477181063 & 1.17000000000000 \tabularnewline
9 & 76.66 & 0.115470053837927 & 0.200000000000003 \tabularnewline
10 & 77.295 & 0.420356991139679 & 0.940000000000012 \tabularnewline
11 & 77.92 & 0.0571547606649386 & 0.129999999999995 \tabularnewline
12 & 78.7075 & 0.358736207632664 & 0.739999999999995 \tabularnewline
13 & 79.4325 & 0.270354705279320 & 0.650000000000006 \tabularnewline
14 & 80.4625 & 0.0741057802513883 & 0.180000000000007 \tabularnewline
15 & 80.8175 & 0.453164797102921 & 0.969999999999999 \tabularnewline
16 & 82.0775 & 0.338661581326651 & 0.740000000000009 \tabularnewline
17 & 83.1575 & 0.0427200187265854 & 0.0999999999999943 \tabularnewline
18 & 83.685 & 0.244472220644118 & 0.549999999999997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12465&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]66.26[/C][C]1.06773904427377[/C][C]2.5[/C][/ROW]
[ROW][C]2[/C][C]68.825[/C][C]0.503884907493769[/C][C]1.04000000000001[/C][/ROW]
[ROW][C]3[/C][C]69.425[/C][C]0.221284131077369[/C][C]0.469999999999999[/C][/ROW]
[ROW][C]4[/C][C]70.535[/C][C]0.716961179795204[/C][C]1.64999999999999[/C][/ROW]
[ROW][C]5[/C][C]72.5825[/C][C]0.274028587316477[/C][C]0.589999999999989[/C][/ROW]
[ROW][C]6[/C][C]73.3125[/C][C]0.130479883507001[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]7[/C][C]74.475[/C][C]0.563234705370089[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]8[/C][C]75.8725[/C][C]0.478774477181063[/C][C]1.17000000000000[/C][/ROW]
[ROW][C]9[/C][C]76.66[/C][C]0.115470053837927[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]10[/C][C]77.295[/C][C]0.420356991139679[/C][C]0.940000000000012[/C][/ROW]
[ROW][C]11[/C][C]77.92[/C][C]0.0571547606649386[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]12[/C][C]78.7075[/C][C]0.358736207632664[/C][C]0.739999999999995[/C][/ROW]
[ROW][C]13[/C][C]79.4325[/C][C]0.270354705279320[/C][C]0.650000000000006[/C][/ROW]
[ROW][C]14[/C][C]80.4625[/C][C]0.0741057802513883[/C][C]0.180000000000007[/C][/ROW]
[ROW][C]15[/C][C]80.8175[/C][C]0.453164797102921[/C][C]0.969999999999999[/C][/ROW]
[ROW][C]16[/C][C]82.0775[/C][C]0.338661581326651[/C][C]0.740000000000009[/C][/ROW]
[ROW][C]17[/C][C]83.1575[/C][C]0.0427200187265854[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]18[/C][C]83.685[/C][C]0.244472220644118[/C][C]0.549999999999997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12465&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
166.261.067739044273772.5
268.8250.5038849074937691.04000000000001
369.4250.2212841310773690.469999999999999
470.5350.7169611797952041.64999999999999
572.58250.2740285873164770.589999999999989
673.31250.1304798835070010.310000000000002
774.4750.5632347053700891.30000000000000
875.87250.4787744771810631.17000000000000
976.660.1154700538379270.200000000000003
1077.2950.4203569911396790.940000000000012
1177.920.05715476066493860.129999999999995
1278.70750.3587362076326640.739999999999995
1379.43250.2703547052793200.650000000000006
1480.46250.07410578025138830.180000000000007
1580.81750.4531647971029210.969999999999999
1682.07750.3386615813266510.740000000000009
1783.15750.04272001872658540.0999999999999943
1883.6850.2444722206441180.549999999999997






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.60132512777320
beta-0.0295240207489937
S.D.0.0101723626125703
T-STAT-2.90237596450896
p-value0.0103896413775685

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.60132512777320 \tabularnewline
beta & -0.0295240207489937 \tabularnewline
S.D. & 0.0101723626125703 \tabularnewline
T-STAT & -2.90237596450896 \tabularnewline
p-value & 0.0103896413775685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12465&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.60132512777320[/C][/ROW]
[ROW][C]beta[/C][C]-0.0295240207489937[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0101723626125703[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.90237596450896[/C][/ROW]
[ROW][C]p-value[/C][C]0.0103896413775685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12465&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)
alpha2.60132512777320
beta-0.0295240207489937
S.D.0.0101723626125703
T-STAT-2.90237596450896
p-value0.0103896413775685






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha26.7654833077433
beta-6.4923659769773
S.D.2.78865606378659
T-STAT-2.32813435162801
p-value0.0333456163930565
Lambda7.4923659769773

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 26.7654833077433 \tabularnewline
beta & -6.4923659769773 \tabularnewline
S.D. & 2.78865606378659 \tabularnewline
T-STAT & -2.32813435162801 \tabularnewline
p-value & 0.0333456163930565 \tabularnewline
Lambda & 7.4923659769773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12465&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26.7654833077433[/C][/ROW]
[ROW][C]beta[/C][C]-6.4923659769773[/C][/ROW]
[ROW][C]S.D.[/C][C]2.78865606378659[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.32813435162801[/C][/ROW]
[ROW][C]p-value[/C][C]0.0333456163930565[/C][/ROW]
[ROW][C]Lambda[/C][C]7.4923659769773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12465&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)
alpha26.7654833077433
beta-6.4923659769773
S.D.2.78865606378659
T-STAT-2.32813435162801
p-value0.0333456163930565
Lambda7.4923659769773


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')