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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, 06 Aug 2010 17:20:41 +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/2010/Aug/06/t12811152380mq0gcgsx6dus3w.htm/, Retrieved Mon, 06 May 2024 12:15:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78482, Retrieved Mon, 06 May 2024 12:15:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGosselin Claudia
Estimated Impact152

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] [Tijdsreeks A - st...] [2010-08-06 17:20:41] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
155
154
153
151
171
170
155
145
146
146
147
149
146
155
149
140
155
152
137
127
134
125
132
141
133
143
141
132
144
140
130
122
124
119
128
131
121
123
116
109
116
109
103
98
95
83
92
94
76
75
77
68
80
66
69
67
68
64
72
70
55
55
54
55
67
54
57
53
49
47
64
58
38
41
38
41
60
49
53
55
56
52
68
68
41
46
41
47
62
48
53
61
59
46
69
69
42
42
42
50
64
47
51
66
64
49
71
68
39
30
22
33
46
24
27
45
38
18
36
31

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78482&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78482&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78482&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1153.58.7230103227560826
2141.08333333333310.448647875406830
3132.258.3353027975756725
4104.91666666666712.724052622946640
5714.9726524840644916
655.66666666666675.5486826173316820
751.583333333333310.629789473099830
853.510.166790858655328
954.666666666666711.097365234663429
1032.41666666666678.8158775496088328

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 153.5 & 8.72301032275608 & 26 \tabularnewline
2 & 141.083333333333 & 10.4486478754068 & 30 \tabularnewline
3 & 132.25 & 8.33530279757567 & 25 \tabularnewline
4 & 104.916666666667 & 12.7240526229466 & 40 \tabularnewline
5 & 71 & 4.97265248406449 & 16 \tabularnewline
6 & 55.6666666666667 & 5.54868261733168 & 20 \tabularnewline
7 & 51.5833333333333 & 10.6297894730998 & 30 \tabularnewline
8 & 53.5 & 10.1667908586553 & 28 \tabularnewline
9 & 54.6666666666667 & 11.0973652346634 & 29 \tabularnewline
10 & 32.4166666666667 & 8.81587754960883 & 28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78482&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]153.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]141.083333333333[/C][C]10.4486478754068[/C][C]30[/C][/ROW]
[ROW][C]3[/C][C]132.25[/C][C]8.33530279757567[/C][C]25[/C][/ROW]
[ROW][C]4[/C][C]104.916666666667[/C][C]12.7240526229466[/C][C]40[/C][/ROW]
[ROW][C]5[/C][C]71[/C][C]4.97265248406449[/C][C]16[/C][/ROW]
[ROW][C]6[/C][C]55.6666666666667[/C][C]5.54868261733168[/C][C]20[/C][/ROW]
[ROW][C]7[/C][C]51.5833333333333[/C][C]10.6297894730998[/C][C]30[/C][/ROW]
[ROW][C]8[/C][C]53.5[/C][C]10.1667908586553[/C][C]28[/C][/ROW]
[ROW][C]9[/C][C]54.6666666666667[/C][C]11.0973652346634[/C][C]29[/C][/ROW]
[ROW][C]10[/C][C]32.4166666666667[/C][C]8.81587754960883[/C][C]28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78482&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78482&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
1153.58.7230103227560826
2141.08333333333310.448647875406830
3132.258.3353027975756725
4104.91666666666712.724052622946640
5714.9726524840644916
655.66666666666675.5486826173316820
751.583333333333310.629789473099830
853.510.166790858655328
954.666666666666711.097365234663429
1032.41666666666678.8158775496088328






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.56949369858654
beta0.00678032900978918
S.D.0.0193845721083938
T-STAT0.349779658373434
p-value0.735533790038705

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.56949369858654 \tabularnewline
beta & 0.00678032900978918 \tabularnewline
S.D. & 0.0193845721083938 \tabularnewline
T-STAT & 0.349779658373434 \tabularnewline
p-value & 0.735533790038705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78482&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.56949369858654[/C][/ROW]
[ROW][C]beta[/C][C]0.00678032900978918[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0193845721083938[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.349779658373434[/C][/ROW]
[ROW][C]p-value[/C][C]0.735533790038705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78482&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78482&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)
alpha8.56949369858654
beta0.00678032900978918
S.D.0.0193845721083938
T-STAT0.349779658373434
p-value0.735533790038705






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.88243685343495
beta0.0679452004939487
S.D.0.200874196781381
T-STAT0.338247527968442
p-value0.743882347961099
Lambda0.932054799506051

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.88243685343495 \tabularnewline
beta & 0.0679452004939487 \tabularnewline
S.D. & 0.200874196781381 \tabularnewline
T-STAT & 0.338247527968442 \tabularnewline
p-value & 0.743882347961099 \tabularnewline
Lambda & 0.932054799506051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78482&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.88243685343495[/C][/ROW]
[ROW][C]beta[/C][C]0.0679452004939487[/C][/ROW]
[ROW][C]S.D.[/C][C]0.200874196781381[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.338247527968442[/C][/ROW]
[ROW][C]p-value[/C][C]0.743882347961099[/C][/ROW]
[ROW][C]Lambda[/C][C]0.932054799506051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78482&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78482&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)
alpha1.88243685343495
beta0.0679452004939487
S.D.0.200874196781381
T-STAT0.338247527968442
p-value0.743882347961099
Lambda0.932054799506051


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')