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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 computationSun, 20 Dec 2009 12:13:30 -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/20/t126133660042wrb2yuexkeavh.htm/, Retrieved Sat, 27 Apr 2024 12:18:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69990, Retrieved Sat, 27 Apr 2024 12:18:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

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...] [2008-12-11 16:40:34] [12d343c4448a5f9e527bb31caeac580b]
-  M D    [Standard Deviation-Mean Plot] [Paper SMP] [2009-12-20 19:13:30] [eba9f01697e64705b70041e6f338cb22] [Current]
-   PD      [Standard Deviation-Mean Plot] [paper] [2010-12-18 12:19:36] [d87a19cd5db53e12ea62bda70b3bb267]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,21
100,36
100,62
100,78
100,93
100,70
100,00
100,20
99,68
99,56
100,06
100,50
99,30
99,37
99,20
98,11
97,60
97,76
98,06
98,25
98,50
97,39
98,09
97,78
98,12
97,50
97,30
97,64
96,88
97,40
98,27
97,94
98,61
98,72
98,62
98,56
98,06
97,40
97,76
97,05
97,85
97,40
97,27
97,93
98,60
98,70
98,88
98,27
97,85
97,70
96,97
97,72
97,66
99,00
98,86
99,56
100,19
100,37
100,01
99,68
99,78
99,36
99,21
99,26
99,26
100,43
101,50
102,27
102,69
103,47
104,02
103,55
103,77
104,19
103,64
103,68
105,39
106,61
108,12
109,22
110,17
110,31
111,06
111,14
111,39
112,51
111,28
112,22
113,19
114,32
115,34
116,61
117,83
117,70
118,51
118,82
119,49
119,57
120,00
121,96
121,45
123,41
124,44
126,25
127,41
127,63
129,19
129,82
130,45
132,02
132,72
132,96
135,06
137,04
137,83
139,17
140,35
141,01
141,89
143,28
142,90
143,37
145,03
146,05
147,39
149,58
151,02
153,57
155,60
157,18
158,77
159,95
161,34
161,95
163,36
165,00
166,65
168,65
170,29
172,70
173,79
176,45
177,58
179,19
181,01
184,08
185,63
188,51
190,18
192,19
193,47
196,73
200,39
203,24
205,53
208,21
208,88
212,85
216,41
216,23
219,27
222,02
224,89
230,37
232,29
235,53
236,92
242,37
242,75
244,19
247,94
248,80
250,18
251,55
254,40
255,72
257,69
258,37
258,22
258,59
257,45
257,45
256,73
258,82
257,99
262,85
262,58
261,55
261,25
259,78
256,26
254,29
248,50
241,88
238,53
232,24
232,46
225,79
221,63
219,62
215,94
211,81
205,57
201,25
194,70
187,94
185,61
181,15
186,50
183,21
182,61
187,09
189,10
191,25
190,74
190,79

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=69990&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=69990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69990&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
1100.30.4296933367372181.37000000000000
298.28416666666670.6750280577782521.98000000000000
397.96333333333330.6140229982860931.84000000000000
497.93083333333330.5942062441661641.83
598.79751.174889743376343.40000000000001
6101.2333333333331.896208337869564.81
7107.2753.064291405558857.5
8114.9766666666672.851635362809257.53999999999999
9124.2183333333333.7812307600311910.33
10136.9816666666674.2869248001830212.8300000000000
11150.86756.0696055360819217.0500000000000
12169.7458333333336.2261230579979217.85
13194.09758.8106672175370427.2
14224.83583333333310.601222449521733.49
15252.3666666666675.639565317442215.8400000000000
16258.9166666666672.704055315912608.56000000000003
17224.60166666666714.662825495625047.25
18187.55754.0149382990843713.5500000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.3 & 0.429693336737218 & 1.37000000000000 \tabularnewline
2 & 98.2841666666667 & 0.675028057778252 & 1.98000000000000 \tabularnewline
3 & 97.9633333333333 & 0.614022998286093 & 1.84000000000000 \tabularnewline
4 & 97.9308333333333 & 0.594206244166164 & 1.83 \tabularnewline
5 & 98.7975 & 1.17488974337634 & 3.40000000000001 \tabularnewline
6 & 101.233333333333 & 1.89620833786956 & 4.81 \tabularnewline
7 & 107.275 & 3.06429140555885 & 7.5 \tabularnewline
8 & 114.976666666667 & 2.85163536280925 & 7.53999999999999 \tabularnewline
9 & 124.218333333333 & 3.78123076003119 & 10.33 \tabularnewline
10 & 136.981666666667 & 4.28692480018302 & 12.8300000000000 \tabularnewline
11 & 150.8675 & 6.06960553608192 & 17.0500000000000 \tabularnewline
12 & 169.745833333333 & 6.22612305799792 & 17.85 \tabularnewline
13 & 194.0975 & 8.81066721753704 & 27.2 \tabularnewline
14 & 224.835833333333 & 10.6012224495217 & 33.49 \tabularnewline
15 & 252.366666666667 & 5.6395653174422 & 15.8400000000000 \tabularnewline
16 & 258.916666666667 & 2.70405531591260 & 8.56000000000003 \tabularnewline
17 & 224.601666666667 & 14.6628254956250 & 47.25 \tabularnewline
18 & 187.5575 & 4.01493829908437 & 13.5500000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69990&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]100.3[/C][C]0.429693336737218[/C][C]1.37000000000000[/C][/ROW]
[ROW][C]2[/C][C]98.2841666666667[/C][C]0.675028057778252[/C][C]1.98000000000000[/C][/ROW]
[ROW][C]3[/C][C]97.9633333333333[/C][C]0.614022998286093[/C][C]1.84000000000000[/C][/ROW]
[ROW][C]4[/C][C]97.9308333333333[/C][C]0.594206244166164[/C][C]1.83[/C][/ROW]
[ROW][C]5[/C][C]98.7975[/C][C]1.17488974337634[/C][C]3.40000000000001[/C][/ROW]
[ROW][C]6[/C][C]101.233333333333[/C][C]1.89620833786956[/C][C]4.81[/C][/ROW]
[ROW][C]7[/C][C]107.275[/C][C]3.06429140555885[/C][C]7.5[/C][/ROW]
[ROW][C]8[/C][C]114.976666666667[/C][C]2.85163536280925[/C][C]7.53999999999999[/C][/ROW]
[ROW][C]9[/C][C]124.218333333333[/C][C]3.78123076003119[/C][C]10.33[/C][/ROW]
[ROW][C]10[/C][C]136.981666666667[/C][C]4.28692480018302[/C][C]12.8300000000000[/C][/ROW]
[ROW][C]11[/C][C]150.8675[/C][C]6.06960553608192[/C][C]17.0500000000000[/C][/ROW]
[ROW][C]12[/C][C]169.745833333333[/C][C]6.22612305799792[/C][C]17.85[/C][/ROW]
[ROW][C]13[/C][C]194.0975[/C][C]8.81066721753704[/C][C]27.2[/C][/ROW]
[ROW][C]14[/C][C]224.835833333333[/C][C]10.6012224495217[/C][C]33.49[/C][/ROW]
[ROW][C]15[/C][C]252.366666666667[/C][C]5.6395653174422[/C][C]15.8400000000000[/C][/ROW]
[ROW][C]16[/C][C]258.916666666667[/C][C]2.70405531591260[/C][C]8.56000000000003[/C][/ROW]
[ROW][C]17[/C][C]224.601666666667[/C][C]14.6628254956250[/C][C]47.25[/C][/ROW]
[ROW][C]18[/C][C]187.5575[/C][C]4.01493829908437[/C][C]13.5500000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69990&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
1100.30.4296933367372181.37000000000000
298.28416666666670.6750280577782521.98000000000000
397.96333333333330.6140229982860931.84000000000000
497.93083333333330.5942062441661641.83
598.79751.174889743376343.40000000000001
6101.2333333333331.896208337869564.81
7107.2753.064291405558857.5
8114.9766666666672.851635362809257.53999999999999
9124.2183333333333.7812307600311910.33
10136.9816666666674.2869248001830212.8300000000000
11150.86756.0696055360819217.0500000000000
12169.7458333333336.2261230579979217.85
13194.09758.8106672175370427.2
14224.83583333333310.601222449521733.49
15252.3666666666675.639565317442215.8400000000000
16258.9166666666672.704055315912608.56000000000003
17224.60166666666714.662825495625047.25
18187.55754.0149382990843713.5500000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.63622676629143
beta0.0458050002842972
S.D.0.0121985481042060
T-STAT3.75495508916375
p-value0.00172957482965163

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.63622676629143 \tabularnewline
beta & 0.0458050002842972 \tabularnewline
S.D. & 0.0121985481042060 \tabularnewline
T-STAT & 3.75495508916375 \tabularnewline
p-value & 0.00172957482965163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69990&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.63622676629143[/C][/ROW]
[ROW][C]beta[/C][C]0.0458050002842972[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0121985481042060[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.75495508916375[/C][/ROW]
[ROW][C]p-value[/C][C]0.00172957482965163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69990&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-2.63622676629143
beta0.0458050002842972
S.D.0.0121985481042060
T-STAT3.75495508916375
p-value0.00172957482965163






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.2023057905218
beta2.26317496566319
S.D.0.460823468513047
T-STAT4.91115388060823
p-value0.000156620149715978
Lambda-1.26317496566319

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.2023057905218 \tabularnewline
beta & 2.26317496566319 \tabularnewline
S.D. & 0.460823468513047 \tabularnewline
T-STAT & 4.91115388060823 \tabularnewline
p-value & 0.000156620149715978 \tabularnewline
Lambda & -1.26317496566319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69990&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.2023057905218[/C][/ROW]
[ROW][C]beta[/C][C]2.26317496566319[/C][/ROW]
[ROW][C]S.D.[/C][C]0.460823468513047[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.91115388060823[/C][/ROW]
[ROW][C]p-value[/C][C]0.000156620149715978[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.26317496566319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69990&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69990&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-10.2023057905218
beta2.26317496566319
S.D.0.460823468513047
T-STAT4.91115388060823
p-value0.000156620149715978
Lambda-1.26317496566319


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')