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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, 04 Dec 2009 02:30:17 -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/2009/Dec/04/t12599192224s7ax1yk7z726m2.htm/, Retrieved Sun, 28 Apr 2024 01:16:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63209, Retrieved Sun, 28 Apr 2024 01:16:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-    D      [Standard Deviation-Mean Plot] [WS 9 SMP ] [2009-12-04 09:30:17] [a29ecf012646440cb204d2a87bf5881a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90,6
91
90,7
91,3
91,5
91,2
91,2
91,5
92
91,7
91,7
92
91,5
91,7
92,1
92
91,8
91,4
91,3
91,5
92,3
92,7
92,1
92,3
92,3
92,5
92,3
92,7
93,4
93,1
93,8
94,6
94,5
94,4
94,2
93,5
93,1
93,1
93
93,5
93,5
92,9
92,8
92,3
91,8
91,3
90,6
90
89,7
89,6
90
90,9
91,2
91,3
92,2
92,7
93
93,2
94,1
95,1
95,1
96,6
97,8
97,7
99
99,3
100,4
101,2
103,1
104,3
103,7
102
100,5
101
101,3
101,3
101,3
100,8
100,7
100,6
101,1
100,7
100,6
100,5
101,5
101,5
101,5
102,1
102,1
102,2
102,4
102,5
102,6
102,8
102,8
103,1
102,5
102,9
103,6
104
103,5
103,1
102,4
102,2
102,4
102,6
102,8
102,8
103,6
104,7
105,5
106,6
107,2
107,5
108,3
108,7
108,8
109,8
109,5
109,2
110,6
110,1
109,9
109,7
109,4
109,4
109,4
109,5
109,5
109,9
110
110,8
112,4
112,8
113,7
114,5
114,8
115,6
115,8
115,8
116,3
116,3
116,8
116,7
116,8
117
117,2
117,1
117,3
117,4
117,7
117,9
118,8
119,9
122,4
123,5
125,6
127,4
128,9
129,5
130,8
132,7
134
132,9
133,1
131,7
128,8
125,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63209&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]2 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=63209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63209&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
191.36666666666670.4559372630952511.40000000000001
291.89166666666670.4294993561924121.40000000000001
393.44166666666670.8659816640231152.30000000000000
492.3251.155323646115123.5
591.91666666666671.765751621230685.5
6100.0166666666672.932213973754109.2
7100.8666666666670.3171845844395030.799999999999997
8102.2583333333330.5451577475345721.59999999999999
9102.90.5526794237662041.80000000000000
10107.451.997043268980886.2
11109.850.4700096710803811.39999999999999
12115.1251.493698886535154.39999999999999
13118.5833333333332.228261994279746.7
14130.0416666666672.982512160558418.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 91.3666666666667 & 0.455937263095251 & 1.40000000000001 \tabularnewline
2 & 91.8916666666667 & 0.429499356192412 & 1.40000000000001 \tabularnewline
3 & 93.4416666666667 & 0.865981664023115 & 2.30000000000000 \tabularnewline
4 & 92.325 & 1.15532364611512 & 3.5 \tabularnewline
5 & 91.9166666666667 & 1.76575162123068 & 5.5 \tabularnewline
6 & 100.016666666667 & 2.93221397375410 & 9.2 \tabularnewline
7 & 100.866666666667 & 0.317184584439503 & 0.799999999999997 \tabularnewline
8 & 102.258333333333 & 0.545157747534572 & 1.59999999999999 \tabularnewline
9 & 102.9 & 0.552679423766204 & 1.80000000000000 \tabularnewline
10 & 107.45 & 1.99704326898088 & 6.2 \tabularnewline
11 & 109.85 & 0.470009671080381 & 1.39999999999999 \tabularnewline
12 & 115.125 & 1.49369888653515 & 4.39999999999999 \tabularnewline
13 & 118.583333333333 & 2.22826199427974 & 6.7 \tabularnewline
14 & 130.041666666667 & 2.98251216055841 & 8.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63209&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]91.3666666666667[/C][C]0.455937263095251[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]2[/C][C]91.8916666666667[/C][C]0.429499356192412[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]3[/C][C]93.4416666666667[/C][C]0.865981664023115[/C][C]2.30000000000000[/C][/ROW]
[ROW][C]4[/C][C]92.325[/C][C]1.15532364611512[/C][C]3.5[/C][/ROW]
[ROW][C]5[/C][C]91.9166666666667[/C][C]1.76575162123068[/C][C]5.5[/C][/ROW]
[ROW][C]6[/C][C]100.016666666667[/C][C]2.93221397375410[/C][C]9.2[/C][/ROW]
[ROW][C]7[/C][C]100.866666666667[/C][C]0.317184584439503[/C][C]0.799999999999997[/C][/ROW]
[ROW][C]8[/C][C]102.258333333333[/C][C]0.545157747534572[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]9[/C][C]102.9[/C][C]0.552679423766204[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]10[/C][C]107.45[/C][C]1.99704326898088[/C][C]6.2[/C][/ROW]
[ROW][C]11[/C][C]109.85[/C][C]0.470009671080381[/C][C]1.39999999999999[/C][/ROW]
[ROW][C]12[/C][C]115.125[/C][C]1.49369888653515[/C][C]4.39999999999999[/C][/ROW]
[ROW][C]13[/C][C]118.583333333333[/C][C]2.22826199427974[/C][C]6.7[/C][/ROW]
[ROW][C]14[/C][C]130.041666666667[/C][C]2.98251216055841[/C][C]8.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63209&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
191.36666666666670.4559372630952511.40000000000001
291.89166666666670.4294993561924121.40000000000001
393.44166666666670.8659816640231152.30000000000000
492.3251.155323646115123.5
591.91666666666671.765751621230685.5
6100.0166666666672.932213973754109.2
7100.8666666666670.3171845844395030.799999999999997
8102.2583333333330.5451577475345721.59999999999999
9102.90.5526794237662041.80000000000000
10107.451.997043268980886.2
11109.850.4700096710803811.39999999999999
12115.1251.493698886535154.39999999999999
13118.5833333333332.228261994279746.7
14130.0416666666672.982512160558418.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.19507243349179
beta0.043453605578005
S.D.0.0195440117388924
T-STAT2.22337185213273
p-value0.0461578090096398

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.19507243349179 \tabularnewline
beta & 0.043453605578005 \tabularnewline
S.D. & 0.0195440117388924 \tabularnewline
T-STAT & 2.22337185213273 \tabularnewline
p-value & 0.0461578090096398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63209&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.19507243349179[/C][/ROW]
[ROW][C]beta[/C][C]0.043453605578005[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0195440117388924[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.22337185213273[/C][/ROW]
[ROW][C]p-value[/C][C]0.0461578090096398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63209&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63209&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)
alpha-3.19507243349179
beta0.043453605578005
S.D.0.0195440117388924
T-STAT2.22337185213273
p-value0.0461578090096398






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.3143673162180
beta3.30377301335953
S.D.1.82743871198211
T-STAT1.80787076015049
p-value0.0957397588102637
Lambda-2.30377301335953

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.3143673162180 \tabularnewline
beta & 3.30377301335953 \tabularnewline
S.D. & 1.82743871198211 \tabularnewline
T-STAT & 1.80787076015049 \tabularnewline
p-value & 0.0957397588102637 \tabularnewline
Lambda & -2.30377301335953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63209&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.3143673162180[/C][/ROW]
[ROW][C]beta[/C][C]3.30377301335953[/C][/ROW]
[ROW][C]S.D.[/C][C]1.82743871198211[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.80787076015049[/C][/ROW]
[ROW][C]p-value[/C][C]0.0957397588102637[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.30377301335953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63209&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63209&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-15.3143673162180
beta3.30377301335953
S.D.1.82743871198211
T-STAT1.80787076015049
p-value0.0957397588102637
Lambda-2.30377301335953


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')