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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 computationWed, 13 Dec 2017 08:43:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/13/t1513151015v88ho4xrllamwzn.htm/, Retrieved Wed, 15 May 2024 10:09:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309208, Retrieved Wed, 15 May 2024 10:09:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86

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] [] [2017-12-13 07:43:30] [8829069b4432872c842806a35f4fa8df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
122.2
136.1
145.5
116.7
137.1
125.5
112.4
106.3
145.7
151.5
144.6
116.4
137.7
138.8
149.5
125
133.4
134.4
124.8
110.6
142.4
149.6
134.6
103.3
136.5
137.1
140.7
131.4
126.2
125.3
126.6
107.7
144.5
154.2
131.4
105.7
136.2
133.3
130
129.3
113.1
117.7
116.3
97.3
140.6
141.2
120.8
106.2
121.5
122.6
137.2
118.9
107.2
127.4
111.8
100
138.3
128
121.2
105.9
112.5
123.1
129
115.5
105.7
122.3
106.4
101.1
131.6
119.5
127
106.9
115.9
122.7
137.2
108.5
115.2
129.4
112.3
104.3
140
139.9
134.9
105.1
127
135.5
143.9
115.8
117.5
129.3
117.9
108.1
131.7
143.7
126.2
96.9
125.8
129.6
124.9
136.8
107.5
114.3
110.3
85.5
116.8
115.1
95.2
83.4
95.4
96.3
100.5
90.9
80.6
94.8
93.9
75.9
101.6
103.3
91.8
83.5
92
101.2
109.1
99.8
90.8
110.6
97.8
81.9
114.4
108.8
103.1
90.4
94.4
100.5
115.1
93.9
102.5
97.1
91.2
82.3
107.1
99.2
94.8
81.1
92.5
97.7
98.5
81.2
86.2
92
86.3
74.8
90
101.1
87.8
66.3
88.6
90
92
85.1
85.9
88.5
92.3
68
93.6
97.7
85.1
69.9
96.1
97
95.9
91.3
83.5
91.4
96.8
71
106.9
102.7
84.9
75.8
93.6
100.7
100.5
95.9
85.7
104.1
93.5
81.5
102.1
98.2
88.4
77.8
90.1
101
98.6
91.5
86.4
98.9
85.2
77.3
93
86.8
91.3
74.9
93.9
95
103.1
81.4
93.1
97.2
86.4
75.5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309208&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309208&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1131.00416666666714.428579102861748.2
2127.05416666666714.091532430217956.9
3118.35833333333311.035197311790338.3
4123.287513.573481578943347
5102.237516.516258458811560.9
698.29583333333339.6281507171358734
787.12916666666679.3458420965022534.8
892.30416666666679.4653821975093835.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 131.004166666667 & 14.4285791028617 & 48.2 \tabularnewline
2 & 127.054166666667 & 14.0915324302179 & 56.9 \tabularnewline
3 & 118.358333333333 & 11.0351973117903 & 38.3 \tabularnewline
4 & 123.2875 & 13.5734815789433 & 47 \tabularnewline
5 & 102.2375 & 16.5162584588115 & 60.9 \tabularnewline
6 & 98.2958333333333 & 9.62815071713587 & 34 \tabularnewline
7 & 87.1291666666667 & 9.34584209650225 & 34.8 \tabularnewline
8 & 92.3041666666667 & 9.46538219750938 & 35.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309208&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]131.004166666667[/C][C]14.4285791028617[/C][C]48.2[/C][/ROW]
[ROW][C]2[/C][C]127.054166666667[/C][C]14.0915324302179[/C][C]56.9[/C][/ROW]
[ROW][C]3[/C][C]118.358333333333[/C][C]11.0351973117903[/C][C]38.3[/C][/ROW]
[ROW][C]4[/C][C]123.2875[/C][C]13.5734815789433[/C][C]47[/C][/ROW]
[ROW][C]5[/C][C]102.2375[/C][C]16.5162584588115[/C][C]60.9[/C][/ROW]
[ROW][C]6[/C][C]98.2958333333333[/C][C]9.62815071713587[/C][C]34[/C][/ROW]
[ROW][C]7[/C][C]87.1291666666667[/C][C]9.34584209650225[/C][C]34.8[/C][/ROW]
[ROW][C]8[/C][C]92.3041666666667[/C][C]9.46538219750938[/C][C]35.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309208&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
1131.00416666666714.428579102861748.2
2127.05416666666714.091532430217956.9
3118.35833333333311.035197311790338.3
4123.287513.573481578943347
5102.237516.516258458811560.9
698.29583333333339.6281507171358734
787.12916666666679.3458420965022534.8
892.30416666666679.4653821975093835.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.44621754349024
beta0.0983489281075974
S.D.0.052417576627343
T-STAT1.8762585841539
p-value0.109722675130377

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.44621754349024 \tabularnewline
beta & 0.0983489281075974 \tabularnewline
S.D. & 0.052417576627343 \tabularnewline
T-STAT & 1.8762585841539 \tabularnewline
p-value & 0.109722675130377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309208&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.44621754349024[/C][/ROW]
[ROW][C]beta[/C][C]0.0983489281075974[/C][/ROW]
[ROW][C]S.D.[/C][C]0.052417576627343[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.8762585841539[/C][/ROW]
[ROW][C]p-value[/C][C]0.109722675130377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309208&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)
alpha1.44621754349024
beta0.0983489281075974
S.D.0.052417576627343
T-STAT1.8762585841539
p-value0.109722675130377






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.00574415890826
beta0.957503703573738
S.D.0.433560569246367
T-STAT2.20846583267042
p-value0.0692895189653163
Lambda0.0424962964262622

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.00574415890826 \tabularnewline
beta & 0.957503703573738 \tabularnewline
S.D. & 0.433560569246367 \tabularnewline
T-STAT & 2.20846583267042 \tabularnewline
p-value & 0.0692895189653163 \tabularnewline
Lambda & 0.0424962964262622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309208&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.00574415890826[/C][/ROW]
[ROW][C]beta[/C][C]0.957503703573738[/C][/ROW]
[ROW][C]S.D.[/C][C]0.433560569246367[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.20846583267042[/C][/ROW]
[ROW][C]p-value[/C][C]0.0692895189653163[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0424962964262622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309208&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309208&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-2.00574415890826
beta0.957503703573738
S.D.0.433560569246367
T-STAT2.20846583267042
p-value0.0692895189653163
Lambda0.0424962964262622


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ;
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')