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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 computationFri, 18 Mar 2016 11:24:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/18/t1458300340h1y3g1wxainwxq0.htm/, Retrieved Thu, 02 May 2024 05:43:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294226, Retrieved Thu, 02 May 2024 05:43:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90

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] [] [2016-03-18 11:24:47] [55e0f811d0de406b35493d0ca672d497] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.61
83.89
83.4
82.96
82.76
83.35
87.78
88.99
88.92
88.91
89.79
90.54
93.15
92.79
93.21
95.35
100.91
103.69
104.04
104.16
104.71
105.18
104.92
104.83
104.9
105.05
104.6
103.21
102.52
101.09
101.19
102.34
102.62
102.47
101.82
101.86
101.54
101.98
101.23
100.4
99.94
99.94
100
98.8
99.07
99.46
99.18
98.47
97.12
96.91
96.09
97.17
96.8
97.13
99.9
100.56
100.84
99.81
100.44
100.07
101.32
103.98
104.81
106.23
106.48
107.59
107.16
107.54
107.1
106.38
106.64
106.13

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'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294226&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294226&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
186.24166666666673.119786803127697.78
2100.5783333333335.2849939078546412.39
3102.8058333333331.370855461735373.95999999999999
4100.0008333333331.111178394427483.51000000000001
598.571.817625824080314.75
6105.9466666666671.800865111971236.27000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 86.2416666666667 & 3.11978680312769 & 7.78 \tabularnewline
2 & 100.578333333333 & 5.28499390785464 & 12.39 \tabularnewline
3 & 102.805833333333 & 1.37085546173537 & 3.95999999999999 \tabularnewline
4 & 100.000833333333 & 1.11117839442748 & 3.51000000000001 \tabularnewline
5 & 98.57 & 1.81762582408031 & 4.75 \tabularnewline
6 & 105.946666666667 & 1.80086511197123 & 6.27000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294226&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]86.2416666666667[/C][C]3.11978680312769[/C][C]7.78[/C][/ROW]
[ROW][C]2[/C][C]100.578333333333[/C][C]5.28499390785464[/C][C]12.39[/C][/ROW]
[ROW][C]3[/C][C]102.805833333333[/C][C]1.37085546173537[/C][C]3.95999999999999[/C][/ROW]
[ROW][C]4[/C][C]100.000833333333[/C][C]1.11117839442748[/C][C]3.51000000000001[/C][/ROW]
[ROW][C]5[/C][C]98.57[/C][C]1.81762582408031[/C][C]4.75[/C][/ROW]
[ROW][C]6[/C][C]105.946666666667[/C][C]1.80086511197123[/C][C]6.27000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294226&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
186.24166666666673.119786803127697.78
2100.5783333333335.2849939078546412.39
3102.8058333333331.370855461735373.95999999999999
4100.0008333333331.111178394427483.51000000000001
598.571.817625824080314.75
6105.9466666666671.800865111971236.27000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.35861163147564
beta-0.0599962370791399
S.D.0.111672985908305
T-STAT-0.537249331977232
p-value0.619588627822488

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.35861163147564 \tabularnewline
beta & -0.0599962370791399 \tabularnewline
S.D. & 0.111672985908305 \tabularnewline
T-STAT & -0.537249331977232 \tabularnewline
p-value & 0.619588627822488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294226&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.35861163147564[/C][/ROW]
[ROW][C]beta[/C][C]-0.0599962370791399[/C][/ROW]
[ROW][C]S.D.[/C][C]0.111672985908305[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.537249331977232[/C][/ROW]
[ROW][C]p-value[/C][C]0.619588627822488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294226&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)
alpha8.35861163147564
beta-0.0599962370791399
S.D.0.111672985908305
T-STAT-0.537249331977232
p-value0.619588627822488






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha13.8191261017909
beta-2.8485485064153
S.D.3.75576674435147
T-STAT-0.758446597009627
p-value0.490416096630481
Lambda3.8485485064153

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.8191261017909 \tabularnewline
beta & -2.8485485064153 \tabularnewline
S.D. & 3.75576674435147 \tabularnewline
T-STAT & -0.758446597009627 \tabularnewline
p-value & 0.490416096630481 \tabularnewline
Lambda & 3.8485485064153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294226&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.8191261017909[/C][/ROW]
[ROW][C]beta[/C][C]-2.8485485064153[/C][/ROW]
[ROW][C]S.D.[/C][C]3.75576674435147[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.758446597009627[/C][/ROW]
[ROW][C]p-value[/C][C]0.490416096630481[/C][/ROW]
[ROW][C]Lambda[/C][C]3.8485485064153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294226&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)
alpha13.8191261017909
beta-2.8485485064153
S.D.3.75576674435147
T-STAT-0.758446597009627
p-value0.490416096630481
Lambda3.8485485064153


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')