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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 computationWed, 28 Nov 2007 08:52:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/28/t1196265746f3i5ib3j9ykhi0j.htm/, Retrieved Thu, 02 May 2024 06:27:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7125, Retrieved Thu, 02 May 2024 06:27:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173

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] [Standard deviatio...] [2007-11-28 15:52:16] [757ef2b8266f339cc1cb96dcaefa4cf0] [Current]
-    D    [Standard Deviation-Mean Plot] [Tijdreeks 1: indu...] [2007-12-12 19:34:29] [74be16979710d4c4e7c6647856088456]
-    D      [Standard Deviation-Mean Plot] [Tijdreeks 2: omze...] [2007-12-12 19:57:56] [74be16979710d4c4e7c6647856088456]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
138,1
138,6
160,8
151,5
142,7
157,4
138,9
141,0
150,9
149,9
153,0
144,3
128,1
123,3
155,9
144,1
134,1
153,1
131,0
129,8
139,9
135,6
126,8
134,4
113,5
107,5
133,8
119,0
125,9
130,1
114,2
111,6
131,2
124,1
127,1
123,4
100,7
100,3
121,6
110,5
110,3
122,7
102,6
101,8
113,6
107,2
116,8
112,5
89,0
95,2
110,6
102,6
106,4
112,7
103,2
104,2
111,3
115,7
111,6
112,2
92,2
97,1
108,1
107,2
107,2
110,3
97,6
100,6
102,8
105,3
109,5
105,7
93,7
91,7
111,6
109,2
101,2
114,3
100,9
106,0
109,0
110,4
110,7
105,7
89,6
83,1
103,5
104,8
93,5
106,7
93,7
84,7
99,2
91,9
94,9
94,1
80,8
72,6
94,0
80,0
85,4
91,5
76,1
76,1
89,5
85,3
91,0
93,0
73,4
76,6
95,0
84,5
88,7
93,1
83,4
82,2
95,6
83,7
94,3
93,0
71,8
75,3
91,8
80,7
84,8
83,1
78,4
78,7
84,7
80,5
91,8
83,5
66,6
68,6
83,6
79,7
79,9
81,2
74,3
73,0
78,8
81,6
85,0
91,1
68,2
59,8
83,1
76,7
73,2
83,9
73,0
70,9

Tables (Output of Computation)





Summary of compuational 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 compuational 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=7125&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7125&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 compuational 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
1147.2583333333337.7155637669858194.2
2136.34166666666710.206723125944887.3
3121.7833333333338.5121125818483350.2
4110.057.8162418311894943
5106.2257.8962735745183235.8
6103.6333333333335.6488668748428629.1
7105.3666666666677.1417254514747640
894.9757.4714152243430733.7
984.60833333333337.3653313612223915.2
1086.95833333333337.4686567288457815.1
1182.09166666666675.933641888470026.8
1278.61666666666676.972391442270187.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 147.258333333333 & 7.71556376698581 & 94.2 \tabularnewline
2 & 136.341666666667 & 10.2067231259448 & 87.3 \tabularnewline
3 & 121.783333333333 & 8.51211258184833 & 50.2 \tabularnewline
4 & 110.05 & 7.81624183118949 & 43 \tabularnewline
5 & 106.225 & 7.89627357451832 & 35.8 \tabularnewline
6 & 103.633333333333 & 5.64886687484286 & 29.1 \tabularnewline
7 & 105.366666666667 & 7.14172545147476 & 40 \tabularnewline
8 & 94.975 & 7.47141522434307 & 33.7 \tabularnewline
9 & 84.6083333333333 & 7.36533136122239 & 15.2 \tabularnewline
10 & 86.9583333333333 & 7.46865672884578 & 15.1 \tabularnewline
11 & 82.0916666666667 & 5.93364188847002 & 6.8 \tabularnewline
12 & 78.6166666666667 & 6.97239144227018 & 7.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7125&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]147.258333333333[/C][C]7.71556376698581[/C][C]94.2[/C][/ROW]
[ROW][C]2[/C][C]136.341666666667[/C][C]10.2067231259448[/C][C]87.3[/C][/ROW]
[ROW][C]3[/C][C]121.783333333333[/C][C]8.51211258184833[/C][C]50.2[/C][/ROW]
[ROW][C]4[/C][C]110.05[/C][C]7.81624183118949[/C][C]43[/C][/ROW]
[ROW][C]5[/C][C]106.225[/C][C]7.89627357451832[/C][C]35.8[/C][/ROW]
[ROW][C]6[/C][C]103.633333333333[/C][C]5.64886687484286[/C][C]29.1[/C][/ROW]
[ROW][C]7[/C][C]105.366666666667[/C][C]7.14172545147476[/C][C]40[/C][/ROW]
[ROW][C]8[/C][C]94.975[/C][C]7.47141522434307[/C][C]33.7[/C][/ROW]
[ROW][C]9[/C][C]84.6083333333333[/C][C]7.36533136122239[/C][C]15.2[/C][/ROW]
[ROW][C]10[/C][C]86.9583333333333[/C][C]7.46865672884578[/C][C]15.1[/C][/ROW]
[ROW][C]11[/C][C]82.0916666666667[/C][C]5.93364188847002[/C][C]6.8[/C][/ROW]
[ROW][C]12[/C][C]78.6166666666667[/C][C]6.97239144227018[/C][C]7.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7125&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
1147.2583333333337.7155637669858194.2
2136.34166666666710.206723125944887.3
3121.7833333333338.5121125818483350.2
4110.057.8162418311894943
5106.2257.8962735745183235.8
6103.6333333333335.6488668748428629.1
7105.3666666666677.1417254514747640
894.9757.4714152243430733.7
984.60833333333337.3653313612223915.2
1086.95833333333337.4686567288457815.1
1182.09166666666675.933641888470026.8
1278.61666666666676.972391442270187.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.06985698438167
beta0.0328407555182552
S.D.0.0135322811810223
T-STAT2.4268454873899
p-value0.0356419572947348

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.06985698438167 \tabularnewline
beta & 0.0328407555182552 \tabularnewline
S.D. & 0.0135322811810223 \tabularnewline
T-STAT & 2.4268454873899 \tabularnewline
p-value & 0.0356419572947348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7125&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.06985698438167[/C][/ROW]
[ROW][C]beta[/C][C]0.0328407555182552[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0135322811810223[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.4268454873899[/C][/ROW]
[ROW][C]p-value[/C][C]0.0356419572947348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7125&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7125&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)
alpha4.06985698438167
beta0.0328407555182552
S.D.0.0135322811810223
T-STAT2.4268454873899
p-value0.0356419572947348






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.0699862107395961
beta0.447968560117043
S.D.0.197064755317030
T-STAT2.27320486302266
p-value0.0463176348444212
Lambda0.552031439882957

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.0699862107395961 \tabularnewline
beta & 0.447968560117043 \tabularnewline
S.D. & 0.197064755317030 \tabularnewline
T-STAT & 2.27320486302266 \tabularnewline
p-value & 0.0463176348444212 \tabularnewline
Lambda & 0.552031439882957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7125&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0699862107395961[/C][/ROW]
[ROW][C]beta[/C][C]0.447968560117043[/C][/ROW]
[ROW][C]S.D.[/C][C]0.197064755317030[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.27320486302266[/C][/ROW]
[ROW][C]p-value[/C][C]0.0463176348444212[/C][/ROW]
[ROW][C]Lambda[/C][C]0.552031439882957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7125&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7125&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-0.0699862107395961
beta0.447968560117043
S.D.0.197064755317030
T-STAT2.27320486302266
p-value0.0463176348444212
Lambda0.552031439882957


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')