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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, 20 May 2011 01:16:40 +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/2011/May/20/t130585395267rxunztvzfnco3.htm/, Retrieved Mon, 13 May 2024 06:22:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122338, Retrieved Mon, 13 May 2024 06:22:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact97

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] [] [2011-05-20 01:16:40] [7ec7c2b78d31d17737f91280a6e28d4a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90
51
47
59
54
79
59
80
46
62
55
77
72
72
71
50
66
78
59
52
71
98
70
84
90
98
98
78
59
0
58
55
62
80
91
86
61
49
61
56
73
85
82
32
39
30
51
48
57
59
32
56
54
74
62
78
72
48
59
61
80
69
58
63
27
23
34
45
51
51
73
37
35
66
54
30
66
61
37
55
64
53
63
70
72
52
53
50
60
73
66
78

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122338&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122338&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
161.7519.482898483884143
26813.441230102437326
36013.089435944047931
466.2510.843584893075422
563.7511.086778913041726
680.7513.149778198382928
7919.4516312525052220
84328.717010057919859
979.7512.658988901172229
1056.755.6789083458002712
116824.535688292770653
12429.4868329805051421
135112.727922061357927
146711.015141094572224
15609.8319208025017524
1667.59.4692484742278622
1732.259.6393291606141722
185314.877275736280936
1946.2516.740669042783236
2054.7512.658988901172229
2162.57.0474581706219917
2256.7510.242883708539622
2369.257.8898669190297518

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 61.75 & 19.4828984838841 & 43 \tabularnewline
2 & 68 & 13.4412301024373 & 26 \tabularnewline
3 & 60 & 13.0894359440479 & 31 \tabularnewline
4 & 66.25 & 10.8435848930754 & 22 \tabularnewline
5 & 63.75 & 11.0867789130417 & 26 \tabularnewline
6 & 80.75 & 13.1497781983829 & 28 \tabularnewline
7 & 91 & 9.45163125250522 & 20 \tabularnewline
8 & 43 & 28.7170100579198 & 59 \tabularnewline
9 & 79.75 & 12.6589889011722 & 29 \tabularnewline
10 & 56.75 & 5.67890834580027 & 12 \tabularnewline
11 & 68 & 24.5356882927706 & 53 \tabularnewline
12 & 42 & 9.48683298050514 & 21 \tabularnewline
13 & 51 & 12.7279220613579 & 27 \tabularnewline
14 & 67 & 11.0151410945722 & 24 \tabularnewline
15 & 60 & 9.83192080250175 & 24 \tabularnewline
16 & 67.5 & 9.46924847422786 & 22 \tabularnewline
17 & 32.25 & 9.63932916061417 & 22 \tabularnewline
18 & 53 & 14.8772757362809 & 36 \tabularnewline
19 & 46.25 & 16.7406690427832 & 36 \tabularnewline
20 & 54.75 & 12.6589889011722 & 29 \tabularnewline
21 & 62.5 & 7.04745817062199 & 17 \tabularnewline
22 & 56.75 & 10.2428837085396 & 22 \tabularnewline
23 & 69.25 & 7.88986691902975 & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122338&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]61.75[/C][C]19.4828984838841[/C][C]43[/C][/ROW]
[ROW][C]2[/C][C]68[/C][C]13.4412301024373[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]60[/C][C]13.0894359440479[/C][C]31[/C][/ROW]
[ROW][C]4[/C][C]66.25[/C][C]10.8435848930754[/C][C]22[/C][/ROW]
[ROW][C]5[/C][C]63.75[/C][C]11.0867789130417[/C][C]26[/C][/ROW]
[ROW][C]6[/C][C]80.75[/C][C]13.1497781983829[/C][C]28[/C][/ROW]
[ROW][C]7[/C][C]91[/C][C]9.45163125250522[/C][C]20[/C][/ROW]
[ROW][C]8[/C][C]43[/C][C]28.7170100579198[/C][C]59[/C][/ROW]
[ROW][C]9[/C][C]79.75[/C][C]12.6589889011722[/C][C]29[/C][/ROW]
[ROW][C]10[/C][C]56.75[/C][C]5.67890834580027[/C][C]12[/C][/ROW]
[ROW][C]11[/C][C]68[/C][C]24.5356882927706[/C][C]53[/C][/ROW]
[ROW][C]12[/C][C]42[/C][C]9.48683298050514[/C][C]21[/C][/ROW]
[ROW][C]13[/C][C]51[/C][C]12.7279220613579[/C][C]27[/C][/ROW]
[ROW][C]14[/C][C]67[/C][C]11.0151410945722[/C][C]24[/C][/ROW]
[ROW][C]15[/C][C]60[/C][C]9.83192080250175[/C][C]24[/C][/ROW]
[ROW][C]16[/C][C]67.5[/C][C]9.46924847422786[/C][C]22[/C][/ROW]
[ROW][C]17[/C][C]32.25[/C][C]9.63932916061417[/C][C]22[/C][/ROW]
[ROW][C]18[/C][C]53[/C][C]14.8772757362809[/C][C]36[/C][/ROW]
[ROW][C]19[/C][C]46.25[/C][C]16.7406690427832[/C][C]36[/C][/ROW]
[ROW][C]20[/C][C]54.75[/C][C]12.6589889011722[/C][C]29[/C][/ROW]
[ROW][C]21[/C][C]62.5[/C][C]7.04745817062199[/C][C]17[/C][/ROW]
[ROW][C]22[/C][C]56.75[/C][C]10.2428837085396[/C][C]22[/C][/ROW]
[ROW][C]23[/C][C]69.25[/C][C]7.88986691902975[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122338&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
161.7519.482898483884143
26813.441230102437326
36013.089435944047931
466.2510.843584893075422
563.7511.086778913041726
680.7513.149778198382928
7919.4516312525052220
84328.717010057919859
979.7512.658988901172229
1056.755.6789083458002712
116824.535688292770653
12429.4868329805051421
135112.727922061357927
146711.015141094572224
15609.8319208025017524
1667.59.4692484742278622
1732.259.6393291606141722
185314.877275736280936
1946.2516.740669042783236
2054.7512.658988901172229
2162.57.0474581706219917
2256.7510.242883708539622
2369.257.8898669190297518






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha16.8883142367622
beta-0.0675595054474844
S.D.0.0867168686871296
T-STAT-0.779081469041923
p-value0.444623088036804

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 16.8883142367622 \tabularnewline
beta & -0.0675595054474844 \tabularnewline
S.D. & 0.0867168686871296 \tabularnewline
T-STAT & -0.779081469041923 \tabularnewline
p-value & 0.444623088036804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122338&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16.8883142367622[/C][/ROW]
[ROW][C]beta[/C][C]-0.0675595054474844[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0867168686871296[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.779081469041923[/C][/ROW]
[ROW][C]p-value[/C][C]0.444623088036804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122338&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122338&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)
alpha16.8883142367622
beta-0.0675595054474844
S.D.0.0867168686871296
T-STAT-0.779081469041923
p-value0.444623088036804






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.24851775734887
beta-0.188787158374898
S.D.0.346609277924387
T-STAT-0.544668508314085
p-value0.591719164224765
Lambda1.1887871583749

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.24851775734887 \tabularnewline
beta & -0.188787158374898 \tabularnewline
S.D. & 0.346609277924387 \tabularnewline
T-STAT & -0.544668508314085 \tabularnewline
p-value & 0.591719164224765 \tabularnewline
Lambda & 1.1887871583749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122338&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.24851775734887[/C][/ROW]
[ROW][C]beta[/C][C]-0.188787158374898[/C][/ROW]
[ROW][C]S.D.[/C][C]0.346609277924387[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.544668508314085[/C][/ROW]
[ROW][C]p-value[/C][C]0.591719164224765[/C][/ROW]
[ROW][C]Lambda[/C][C]1.1887871583749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122338&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122338&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)
alpha3.24851775734887
beta-0.188787158374898
S.D.0.346609277924387
T-STAT-0.544668508314085
p-value0.591719164224765
Lambda1.1887871583749


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 4 ;
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')